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Discrete optics in femtosecond-laser-written photonic structures
Open accessAbstract
Over the last few years arrays of evanescently coupled waveguides have been brought into focus as a particular representation of functionalized optical materials, in which the dispersion and diffraction of propagating light can be specifically tuned. Moreover, it turns out that the light evolution in these systems shares fundamental similarities to the quantum evolution of particle wavefunctions, so that waveguide arrays can act as a model system for emulating quantum mechanics. Recently, a novel technique was developed with which waveguides can be directly 'written' into various optical bulk materials using femtosecond laser pulses, which allows for the realization of a variety of innovative concepts which are not feasible using other fabrication methods. The aim of this tutorial is to give an introduction to this topic.
Overview
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Written from the paper’s full text.
TL;DR
This tutorial/review explains how femtosecond-laser-written waveguide arrays in fused silica act as discrete optical systems that can emulate quantum lattice dynamics. It surveys fabrication, linear discrete effects such as Bloch oscillations and dynamic localization, and nonlinear discrete solitons.
Key findings
- Femtosecond direct writing produces permanent, homogeneous, arbitrarily shaped 1D and 2D coupled waveguide arrays; writing velocity tunes the refractive-index change and evanescent coupling, enabling artificial defects and interfaces. Representative fabrication parameters include 100 kHz, 800 nm, 20×/0.45 NA, about 150 fs, and 0.3 μJ, with losses around 0.4 dB cm⁻¹.
- Linear discrete optics demonstrations include Bloch oscillations in curved arrays with R = 1.9 m, a 75 mm period, and about a 30-waveguide shift at d = 11 μm; Bloch-Zener dynamics in binary arrays with detuning σ = 0.22c and 0.41c giving tunneling rates of about 65% and 25%; and dynamic localization at 633 nm with d = 14 μm, z₀ = 25 mm, and A₀ = 47.5 μm, collapsing after 25 mm. Polychromatic dynamic localization is reported across 450–700 nm.
- Segmentation with a π phase shift in every second waveguide restores arbitrary 1D and 2D input patterns; a 1D example used L = 50 mm, d = 16 μm, λ = 633 nm, segmentation period 26 μm, and s = 2.6 mm, while a 2D example used d = 20 μm.
- Nonlinear discrete solitons form at high peak powers: a 1D soliton in a 74.5 mm, nine-waveguide, 48 μm-spaced sample localized at P_peak = 1000 kW, with an intermediate state at 500 kW; a 2D 7×7, 105 mm, 40 μm-spaced lattice formed a soliton at 2000 kW; surface/corner solitons required 4800 kW, and an interface soliton formed at 3.2 MW. The effective nonlinear refractive index can drop to 0.25 of the bulk value at lower writing velocities.
Methods
- This is a tutorial/review that synthesizes prior theory and experiments rather than presenting one new primary dataset.
- Fabrication and characterization are described for fused-silica samples written with a Ti:sapphire femtosecond laser, typically at 100 kHz, 800 nm, 20×/0.45 NA, about 150 fs, and 0.3 μJ; fluorescence microscopy with Suprasil 311 and a 633 nm HeNe laser, plus near-field inverse-Helmholtz reconstruction, are used to observe propagation and index profiles.
- The main analysis uses coupled-mode equations with nearest-neighbor coupling, Floquet-Bloch band structure, and numerical integration compared with fluorescence images.
Limitations
- The paper states that the coupled-mode approach is a paraxial approximation valid only in the first propagation band, and that dynamic localization is exact only for nearest-neighbor coupling; higher-order coupling of about 3% and array imperfections prevent perfect refocusing.
- The paper states that self-imaging by modifying coupling constants requires precision not currently viable, and that the examples are restricted to fused silica, with extension to other materials such as LiNbO₃ left as future work.
- Evident from the text: nonlinear experiments require high peak powers and are constrained by sample damage thresholds and propagation losses around 0.4 dB cm⁻¹, and 2D solitons need higher power than 1D solitons.
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Claims the paper makes
69 No basis given · 47 No full text of the sources · 40 Own interpretation · 38 Own result · 8 Own method · 3 Supported · 3 Supported so far · 3 Not checked yet · 2 Partly supported · 1 Sources not found · accuracy not yet measured
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In the paper
“Hence, G(β x d) moves for α > 0 with a constant velocity towards +β x d during the propagation, where the velocity is given by α/ - λ [35].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
- Partly supportedcites [35] Longhi S, 2006, Europhys. Lett. sourceExperimental — accuracy not yet measured
The passage on spectral coefficients (section labeled Abstract; page unavailable) gives c₁,₂(z, κ) = f₁,₂(Fz/h)g(κ − Fz/h), supporting a constant shift toward positive κ during propagation. The paper uses F and κ, however, and does not establish that the cited sentence’s G(βₓd) moves at the stated velocity α/λ. (LLM, conf=0.86)
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- Partly supported
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In the paper
“One can formally show [25,33,47] that after every full period z → z + z 0 , an effective coupling constant”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
What the sources say
- Not checked — no full text of the sourcecites [25] source
- Not checked — no full text of the sourcecites [33] source
- Supportedcites [47] source
On p. 2, the paper describes self-imaging at multiples of the modulation period and gives the curved-array response in terms of ΔJ₀(Γ), where Δ is the original coupling constant. It also writes the effective coupling magnitude as Δeff = Δ|J₀(Γ)|. The citing formula expresses the same Bessel-function dependence using different notation, with a signed rather than magnitude convention. (LLM, conf=0.87)
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In the paper
“This allows analysis of the influence of boundary and interfacing effects, making fs-laser-written waveguide arrays today the only systems where complex two-dimensional interfaces can be realized [93].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
What the sources say
- Partly supportedcites [93] sourceExperimental — accuracy not yet measured
The paper (p. 3) describes a femtosecond-laser-written array containing five types of wedge-like interface in one structure, supporting the claim that this method can realize complex two-dimensional interfaces. It does not say these arrays are the only systems capable of doing so. (LLM, conf=0.87)
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In the paper
“This is due to the repulsive character of the array surface [90], which the nonlinearity has to overcome in addition.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
What the sources say
- Supportedcites [90] source
The paper explains on p. 3 that truncating the array introduces an effective repulsive potential absent from an infinite array. It states that a surface-localized state becomes possible only when power exceeds a threshold and discreteness overcomes the surface’s repulsive force; p. 1 contrasts this threshold with solitons in infinite lattices. (LLM, conf=0.92)
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In the paper
“arrays of evanescently coupled waveguides have been brought into focus as a particular representation of functionalized optical materials, in which the dispersion and diffraction of propagating light can be specifically tuned.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Abstract
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In the paper
“the reduced band structure with the allowed propagation bands, separated by photonic bandgaps, is shown.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
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In the paper
“In 2004, waveguide arrays fabricated by the femtosecond (fs) direct-writing method were demonstrated for the very first time [6,7].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Introduction
What the sources say
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In the paper
“The centre of the beams experiences a shift of about 30 waveguides, according to the coupling strength at the lattice site spacing of d = 11 μm.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
- Not checked — no full text of the sourcecites [40] source
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In the paper
“In this case light can no longer distinguish between left and right, since also the complex-conjugated wave packet ϕ * m is a solution of equation (17).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“the beam experienced until now a transverse shift (which is proportional to the coupling coefficient c).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“The guiding properties of the individual waveguides are strongly dependent on the writing parameters.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“At this point, the transverse group velocity reaches its maximum due to the maximal absolute value of the first derivative ∂β z /∂β x of the band structure”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“Due to the symmetry of the band structure the propagation from z = π/α to z = 2π/α is similar to the first half period but with opposite sign of the transverse group velocity”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“Propagating further to z = π/α, G(β x d) reaches b x d = π which is the edge of the Brillouin zone, where the transverse group velocity vanishes”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“At the beginning of the Bloch cycle one obtains a vanishing transverse group velocity, which arises from the vanishing derivative of the band structure at β x d = 0.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“Keeping these parameters fixed, by only changing the writing velocity v a specific tuning of the refractive index modulation is achieved.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“Following the propagation from z = 0 to z = π/(2α) corresponds to a motion in reciprocal space of G(β x d) from β x d = 0 to β x d = π/2”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“the refractive index modulation decreases for increasing writing velocities due to the smaller overlap between successive pulses, as shown in figure 7(b).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“The occurring Bragg reflection on the periodic structure changes the transverse momentum, which corresponds to a transfer of G(β x d) to the other side of the Brillouin zone β x d = -π”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“A radius of curvature of R = 1.9 m yields to an oscillation period of 75 mm.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
- Not checked — no full text of the sourcecites [40] source
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In the paper
“for writing velocities of about 500 μm < v writing < 1500 μm the waveguide losses, measured by a cut-back method, are approximately constant (see figure 7(a)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“The experimental realization of DL in fs-laser-written waveguide arrays is presented in figure 15.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
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In the paper
“This is even more pronounced after two periods, where imperfections and coupling effects have accumulated.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
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In the paper
“Further propagation results in refocusing of the light field at the edges of the Brillouin zone.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“The corresponding dispersion relation of the first band can be calculated as”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“Propagating further results in a motion of G(β x d) from β x d = -π/2 to the opposite band edge at β x d = +π/2 in both minibands”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“Increasing the gap between the bands further to σ = 0.41 c by reducing the writing velocity to 88 mm min -1 in every second waveguide decreases the tunnelling rate to ∼25%.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“Here, we present a generalized DL, in which the stringent resonant condition ( 23) is softened in order to achieve an approximated DL over an extremely broad spectral region.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
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In the paper
“in figure 12(d) the detuning is set to σ = c/2.As predicted, the band splits into two minibands separated by a gap with a size ∼σ .”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“in figure 18(f) the spectrally resolved output pattern for the straight lattice is shown, exhibiting strong diffraction for all spectral components.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
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In the paper
“the array is detuned with σ = 0.22 c, corresponding to a tunnelling rate of 65%”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“The experiments demonstrate that with such a device DL is achieved over the entire visible spectral region from 450 nm to 700 nm.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
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In the paper
“Since the investigated systems feature slight higher-order coupling to sites beyond direct neighbours with a relative strength of 3% and also contain small imperfections inside the array, no perfect refocusing of the excitation is obtained.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
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In the paper
“When exciting the lattice with a broad Gaussian beam with a flat phase, the resulting initial narrow spectral distribution G(β x d) is centred around β x d = 0”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“Therefore, a sample was fabricated which exhibits a bending consisting of two segments where the first segment meets condition (23) for η 1 = 2.405 (first-order DL) and the second one for η 2 = 5.520 (second-order DL).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
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In the paper
“Due to the acceleration theorem, G(β x d) moves towards the band edge β x d = π/2 during the propagation.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“Since the lower miniband is now occupied, the Bragg reflected part of the wave packet in the upper band (from β x d = π/2 to β x d = -π/2) interferes with the fraction that tunnels from the lower band (β x d = π/2) to the upper band (β x d = -π/2)”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“The observed diffraction patterns in the unsegmented array for two different excitation sites are shown in figures 23(a) and (b).In both cases, light spreads across a significant part of the array.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
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In the paper
“increasing the input peak power affects the sensitive phase relation between the adjacent guides due to the induced nonlinear change of the refractive index in the guides, resulting in delocalization of the output pattern, although the nonlinearity is focusing.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“In the unsegmented array, light at a wavelength of λ = 633 nm experiences strong diffraction and spreads across the array, as shown in the fluorescence images (figures 22(a) and (b)) for central and edge waveguide excitations.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
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In the paper
“the power required for soliton formation in a 2D lattice is usually considerably higher compared to the 1D case (for the same fabrication parameters).”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
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In the paper
“At P peak = 1400 kW (see figure 29(b)) the linear coupling is reduced”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
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In the paper
“at P peak = 500 kW input peak power the pattern already shows some light which is trapped in the excited guide.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“the intrinsic waveguide losses (approximately 0.4 dB cm -1 in our experiments)”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“preliminary numerical simulations have revealed that this imaging method is also applicable to large bandwidth signals and accordingly for short pulses as well.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
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In the paper
“there is always some linear background in the non-excited guides and localization will never be perfect due to the excitation with pulsed light.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“This effect is independent of the presence of array boundaries, as can be observed for central as well as edge excitation”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
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In the paper
“Under the influence of segmentation, the light has returned to the respective excited waveguides when it reaches the end facet, as shown in figures 23(e) and (f).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
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In the paper
“in the lower peak power range almost all of the guided energy is coupled to the adjacent waveguides due to linear coupling”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“For P peak = 70 kW launched into a single waveguide light dynamically localizes in the excited channel at the output facet.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“since during the writing process the molecular structure of the bulk material is modified, also the nonlinear refractive index is a function of the writing velocity, as summarized in figure 24(b).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Reduced nonlinear refractive index
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In the paper
“When the peak power is increased to P peak = 1030 kW, the light spreads significantly since the phase relation between adjacent guides is changed so that DL is no longer observed.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“The suppression of the linear diffraction due to DL is overcome by the nonlinearity, so the beam spreads.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“The threshold for soliton formation in this lattice is well below the threshold in the curved lattice.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“at a peak power of P peak = 1000 kW the output intensity pattern is almost completely localized [73].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“The required power for soliton formation at the surface is considerably higher than in the bulk of the array.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
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In the paper
“For increasing power the light starts to penetrate into the hexagonal region (figures 32(b) and (c), for P peak = 1400 kW and P peak = 2000 kW, respectively)”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
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In the paper
“Importantly, the generalized dispersion relations (compare equation ( 7)) for the square lattice (figure 31(b)) and the hexagonal lattice (figure 31(c)) are different.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
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In the paper
“The high accuracy of the writing process results in waveguide arrays which exhibit sharply defined boundaries.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
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In the paper
“When a waveguide in the first (interface) row of the square array is excited, for low peak power P peak = 40 kW the light is almost confined to the square region since it is reflected at the interface (figure 32(a)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
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In the paper
“lattices of evanescently coupled waveguides are not just a simple model system for a comparative investigation of discreteness, but constitute a unique discrete physical system on their own as well [2].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Introduction
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In the paper
“In a continuous medium, a light beam experiences normal diffraction and always spreads during propagation (figure 2(a)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
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In the paper
“in most relevant cases the coupled mode approach is fully adequate, describing all of the observed propagation effects.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
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In the paper
“When ultrashort laser pulses are tightly focused into the bulk material, nonlinear absorption takes place leading to optical breakdown and the formation of a micro plasma, which induces a permanent change in the material's molecular structure.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“revealed strong limitations of the available techniques with respect to the fabrication of waveguide arrays with specifically tailored shapes and functionalities in one and two dimensions.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Introduction
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In the paper
“This technique offers a versatile method for the fabrication of waveguide arrays with distinct properties and features.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Introduction
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In the paper
“weakly guiding and evanescently coupled photonic waveguide structures provide an excellent model system for the analysis of the characteristics of discrete systems [1]”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
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In the paper
“Hence, the experimental demonstration of discrete phenomena in waveguide arrays reveals the fundamental properties of discreteness in general.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Introduction
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In the paper
“The equivalence is evident when the correspondence between the characteristic values is borne in mind: time t and distance z, Planck's constant h = h/2π and reduced wavelength λ = λ/2π , mass m and refractive index of the bulk n 0 , and potential V and refractive index change n = n 0n(x, y, z).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
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In the paper
“all structural changes are permanent and stable after fabrication.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“In a straight array the plane wave does not change during propagation (figure 9(a)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“During the writing process non-bridging oxygen hole centres (NBOHCs) are generated due to breaking of the molecular bonds.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“there is a much more sophisticated way to impose transverse gradients on the waveguide array, employing a curvature of the individual waveguides [32].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“Due to the similarity of the Schrödinger equation ( 1) and the paraxial Helmholtz equation (2), waveguide arrays provide an exceptional model system since the wave dynamics are the same in both systems.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“Therefore, employing a curvature allows for the optical simulation of a constant transverse electrical field (z).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“As G(β x d) moves through the band structure without changing its shape, the spatial transverse profile of the beam remains in its shape as well.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“the light intensity distribution can be directly monitored inside the samples using a fluorescence microscopy technique [24,25].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“In the optical setting, the transverse force q (z) is equivalent to a detuning of the local refractive index of the waveguides.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“the arc length which is passed by the plane wave is now a function of the position of the individual guides.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“The challenge was to overcome the limit of a short electron coherence lifetime, which is lower than the oscillation time scale [1] of 40 ps for an atomic lattice period of 10 Å and an electric field strength of 10 6 V m -1 [31].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“Such a guide can be written along arbitrary paths since the only limiting factor in the placement of the focus is the focal length of the writing objective [17].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“If the waveguides are slightly curved, the plane wave will still propagate straight, being almost not affected by the bending (figure 9(b)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“The transverse group velocity given by the derivative of the band determines the path of the beam propagation, which follows the band structure.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“This relatively low focusing ensures that the created refractive index change is almost independent of the writing depth inside the material, so even large waveguide structures are still homogeneous in the vertical dimension.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“Bloch oscillations come along with tunnelling to higher order bands [41], which is known as the Zener tunnelling [42].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“The optical analogue in a waveguide array would then require a parabolic curvature x 0 ∼ z 2 of the array such that ẍ0 = const.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
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In the paper
“The basic idea relies on the fact that equation ( 23) has infinite solutions as sketched in figure 18(a) [56].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
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In the paper
“A combination of both resonances would therefore yield a strongly reduced effective coupling, which effectively vanishes over a broad spectral region”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
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In the paper
“truncated array structures lead to considerable distortions of the self-imaging effect.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
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In the paper
“the observation is difficult in most quantum systems as the required field strengths are too high.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The main drawback of these mechanisms is the rather small bandwidth of operation.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As the size of the tunnelling regions is given by the width of G(β x d), a sufficiently broad beam experiences rapid tunnelling.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the optical analogue, the transverse ac field can be mimicked by a periodic bending of the waveguides”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“in the vicinity of the resonances at η j the sign of the effective coupling alternates.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
plaincorrelational- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“DL is only exact for coupling restricted to the immediate neighbours.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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None of the sources cited for this claim have been checked yet.
In the paper
“for a periodic ac field, the entire band collapses, preventing the wave packet from spreading over the lattice.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“DL is based on fundamentally different mechanisms.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“One can show [55] that this equation is fulfilled by a set of M propagation invariant orthonormal supermodes”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
What the sources say
- Not checked — no full text of the sourcecites [55] source
plain- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“at z 0 the effective coupling vanishes for the resonance condition”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This is in strong contrast to Bloch oscillations, which are obtained for every transverse constant field.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Hence, 2D discrete solitons exhibit unusual features, with no counterpart in the continuous regime [5].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
What the sources say
- Not checked — no full text of the sourcecites [5] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The concept of phase shift-induced image reconstruction can be extended to the 2D square lattice, since it can be described by the superposition of horizontal and vertical 1D lattices as long as the impact of coupling between waveguides along the diagonal is negligible.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
plainconditional- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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- Rests on an assumption: A two-dimensional square waveguide lattice can be described as a superposition of horizontal and vertical one-dimensional lattices.
- The authors state this as an assumption: Coupling between waveguides along the diagonal in the two-dimensional square lattice is negligible.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“solitons form only for much higher peak power compared to their counterparts in straight lattices due to the altered phase relation between adjacent guides which is caused by the bending.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The additional phase shift induced by the nonlinear term γ |ϕ m | 2 ϕ m in equation ( 27) moves the propagation constant of the excited guide into the semi-infinite gap above the first band as shown in figure 25(a).Hence, this guide cannot 'communicate' with the rest of the array, so it forms an isolated state and the light remains 'trapped'.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
plaindirect- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“the progress in their experimental observation was severely limited because of unrealistically high power levels required for a surface wave excitation at the interfaces of natural materials.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“one can show that the shallow refractive index variations of a waveguide array support the stability of 2D solitons [3].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
What the sources say
- Not checked — no full text of the sourcecites [3] source
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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In the paper
“In some materials, under particular conditions, γ may be negative, so the propagation constant can be decreased until it reaches the finite gap between the first and the second band, resulting in the formation of discrete gap solitons [72].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
What the sources say
- Not checked — no full text of the sourcecites [72] source
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus, the effective nonlinearity can be specifically tuned in order to tailor the nonlinear propagation properties.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Reduced nonlinear refractive index
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The formation of discrete surface solitons is subject to somewhat different physical factors than for discrete solitons without any boundary interaction.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaincorrelational- Asserted: passes — The authors put it forward as true.
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What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Obviously, the segmented region is sufficiently small compared to the coupling length l c = π/2c ≈ 15 mm to satisfy the condition of an abrupt phase shift with reasonable accuracy, as is confirmed by the agreement with the respective simulations”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
boosteddirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The resolution of the image is only restricted by the number of waveguides in the array.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“assuming a sample of length L and introducing the phase shift at position L/2, the diffraction occurring in the region z < L/2 is reversed in the region z > L/2, so the initial intensity distribution |ϕ(0)| 2 is imaged on the output facet”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the critical power for soliton formation can be roughly estimated by |ϕ m | 2 crit = 2c/γ .”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“A comparison of the experimental data with simulation is shown in figure 27, which still exhibits an excellent agreement in the dependence of the amplitudes in the individual waveguides.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
None of the sources cited for this claim have been checked yet.
In the paper
“the relatively shallow refractive index modulation in waveguide arrays facilitates the formation of nonlinear optical surface waves significantly and they can be observed already at moderate power levels at the edge of semi-infinite arrays in the 1D [85,86] as well as in the twodimensional case [87][88][89].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The required periodicity is also approximately satisfied in a finite lattice, when the influence of the boundary on the propagation of the mode can be neglected.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plainconditional- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: In a finite waveguide lattice, the influence of the boundary on the propagation of the mode can be neglected.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“introducing a phase shift of π in every second waveguide results in a pairwise conversion of the individual supermodes”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“and proves that the fs laser writing technique is ideally suited for studying surface phenomena.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Although all examples in this tutorial have been restricted to fused silica, the fs writing technique allows us to process a variety of materials [94][95][96][97], which exhibit other kinds of nonlinearity, in particular a χ (2) nonlinearity, as can be found e.g. in LiNbO 3 [98][99][100].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
What the sources say
- Not matchedcites [94][95][96][97]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [98][99][100]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The additional possibility of writing the waveguides along arbitrary paths with high precision allows the implementation of external potentials by curving the guides.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This ensures the absence of scattering or noticeable statistical distortions of the output pattern caused by small waveguide displacements or inhomogeneities”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Probably not a substantial claim. 20
- It may state two separate claims as one. 74
- The quote only partly states this claim. 5
Every source the paper cites for this claim was checked and supports it.
In the paper
“Notably, polychromatic DL, together with recently proposed polychromatic Bloch oscillations [58], opens up new avenues for applications in various physical contexts.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
What the sources say
- Supportedcites [58] source
The citation identifies the recently proposed polychromatic Bloch oscillations, not the citing authors’ broader claim about applications. The Introduction (p. 1) says the paper shows how to achieve them approximately, and the Conclusion (p. 3) describes its proposal for broadband self-imaging based on them. (LLM, conf=0.94)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
- Supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“The benefit is that the Bloch oscillations are not damped which significantly simplifies the observation of Bloch-Zener dynamics [35].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
What the sources say
- Supportedcites [35] Longhi S, 2006, Europhys. Lett. source
The paper contrasts irreversible damping from tunneling into higher bands with coherent dynamics when tunneling couples only two bands. It describes the binary waveguide array as an ideal system for direct observation of that two-band Zener-Bloch dynamics (both passages labeled Abstract in our copy; no page given). (LLM, conf=0.88)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Supported
The sources with a verdict support this claim; the rest weren’t checked yet, have no full text we could read, or their verdicts aren’t rated yet.
In the paper
“photonic structures provide the possibility of simulating such external potentials in curved waveguide arrays as well as of resolving the evolution dynamics [33,47,48].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
What the sources say
- Not checked — no full text of the sourcecites [33] source
- Supportedcites [47] source
On p. 1, the paper explains that waveguide bending acts as the optical equivalent of an applied field and maps the quantum system’s temporal evolution onto the light’s propagation coordinate. Figures 2–4 (p. 2) show simulated beam evolution alongside measured output patterns from curved arrays, supporting the claimed possibility of resolving the dynamics; the paper does not present those evolution views as direct measurements. (LLM, conf=0.87)
- Not checked — no full text of the sourcecites [48] source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The sources with a verdict support this claim; the rest weren’t checked yet, have no full text we could read, or their verdicts aren’t rated yet.
In the paper
“Nonlinear surface waves are also possible at an interface between two dissimilar discrete media in 1D geometries [87,91] as well as in 2D settings, e.g. at the interface between a square lattice and a hexagonal lattice [92]”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
What the sources say
- Not checked — no full text of the sourcecites [87] source
- Not checked — no full text of the sourcecites [91] source
- Supportedcites [92] source
The paper’s opening summary (p. 1) reports the experimental observation of two-dimensional solitons at the interface between square and hexagonal waveguide arrays. Its conclusion (p. 4) confirms that surface lattice solitons formed at that interface. The separate 1D claim is attributed to other citations. (LLM, conf=0.95)
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“two-dimensional (2D) lattices were experimentally realized in 2003, using optical induction in photorefractive crystals [3,4].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Introduction
What the sources say
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Hence, the field in every guide is perturbed by its neighbours, which causes an energy flow, also known as evanescent coupling, from one waveguide to adjacent guides (figure 2(c)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“at z = 2π/α the beam reaches its initial position so the initial field distribution is restored and the periodic process is complete.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Hence, the beam experiences a symmetric breathing and periodic refocusing.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“The optimal processing parameters with respect to the described setup are a pulse duration of about 150 fs and a pulse energy of 0.3 μJ [23].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
What the sources say
- Not checked — no full text of the sourcecites [23] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“In a more general context, this experiment was repeated in 2009 [40].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
- Not checked — no full text of the sourcecites [40] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“Optical Bloch oscillations were first observed in waveguide lattices in 1999 by two groups [36,37], by implementing a real transverse refractive index gradient in the lattice.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“it took almost 65 years to experimentally observe such Bloch oscillations [30] by replacing the atomic lattice with a semiconductor superlattice.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
What the sources say
- Not checked — no full text of the sourcecites [30] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“reaches a width of about 11 waveguides at a spacing of 14 μm, before it relocalizes after every 37.5 mm of propagation (figure 11(b)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
- Not checked — no full text of the sourcecites [40] source
plainSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“The first experimental observation of Bloch oscillations in curved lattices was reported in 2004 [38]”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
- Not checked — no full text of the sourcecites [38] source
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In the paper
“Bloch oscillations in fs-laser-written waveguide arrays were demonstrated for the first time in 2006 [39].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As the lattice period now is twice the one of the homogeneous array, the first band splits into two minibands separated by a minigap, which is determined by the different depths of the wells.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“In both images it is clearly shown that DL occurs for the design wavelengths solely, whereas for other wavelengths in the vicinity of the design wavelengths the localization is incomplete.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
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In the paper
“the excited upper band is fully occupied at the beginning and at the end of the sample, whereas the lower band has its maximum occupation at the sample's centre.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“Again, tunnelling and Bragg reflection occur; however, at this point the dynamics is much more complex due to the coherent combination of tunnelling and Bragg reflection.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“After a propagation distance of 12.5 mm the light field spreads across about nine waveguides before it starts to relocalize in order to collapse after 25 mm.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
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In the paper
“For a waveguide spacing of d = 26 μm and a design wavelength of λ = 550 nm, following the analysis in [56] yields for the first section A 1 = 56 μm and z 1 = 63 mm, and for the second section A 2 = 86 μm and z 2 = 42 mm.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
What the sources say
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In the paper
“In this case the gap between the bands vanishes, the Zener tunnelling rate is 100%”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“for the design wavelength λ = 550 nm at the first two resonances one finds c eff (λ 1ε) < 0 and c eff (λ 2ε) > 0”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
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In the paper
“For a sample length of 50 mm, a waveguide spacing of 14 μm and a chosen period of z 0 = 25 mm, a bending amplitude of A 0 = 47.5 μm”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plaindirect- Asserted: fails — The authors may not put it forward as true.
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Probably not a substantial claim. The authors may not put it forward as true. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. The quote only partly states this claim.
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In the paper
“the beam spatially breaks up into two parts at the edge of the Brillouin zone, and then follows different paths due to the opposite curvature of the upper and the lower miniband.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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In the paper
“the initially excited band remains mostly occupied for the first Bloch period and only a small fraction of the light tunnels into the second miniband (figure 14(c)), effectively doubling the oscillation frequency compared to figure 14(a).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“There, the presence of the minigap causes the wave to split into two parts.One part tunnels through the minigap (Zenerlike tunnelling) to β x d = -π/2 in the lower band, while the other part is Bragg reflected into the initial, upper miniband to β x d = -π/2”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The geometric parameters of d = 11 μm and a radius of curvature R = 1.90 m yield an oscillations period of 75 mm, corresponding to the sample length.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
plaindirect- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For increasing writing velocities during the fabrication process the refractive index change becomes smaller (see figure 7(b)) causing a weaker guiding and, hence, a weaker confinement which results in an increase of r.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Reduced nonlinear refractive index
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“while for high writing speeds the nonlinearity is almost not affected and reaches the value for the unprocessed bulk material (n 2(bulk) = 2.7 × 10 -20 m 2 W -1 at λ = 800 nm [68]), with decreasing velocity also the effective nonlinear refractive index drops to only n 2(eff) = 0.25n 2(bulk) [23,69].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Reduced nonlinear refractive index
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“the required power for soliton formation is much higher than in the straight lattice, where localization takes place already at P peak = 1200 kW”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The linear coupling is only marginally influenced by the anisotropy (ellipticity) of the waveguides, since the waveguide separations are large, so the coupling is only weakly anisotropic.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
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In the paper
“Eventually, at P peak = 3450 kW the nonlinear focusing overcomes the spreading and a discrete soliton forms.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Only at sufficiently high power the beam localizes and forms a soliton.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
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In the paper
“at P peak = 2000 kW (figure 29(c)), almost all of the guided energy remains in the excited waveguide: a 2D discrete soliton has been generated [79].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
What the sources say
- Not checked — no full text of the sourcecites [79] source
plaindirect- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, this behaviour is significantly altered by the segmentation.As soon as the light encounters the phase shift, diffraction reverses and the initial light distribution is restored.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
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In the paper
“However, even for large input peak powers one can clearly observe nearinterface localization (figures 32(d) (P peak = 2300 kW) and (e) (P peak = 2700 kW)), so that finally at P peak = 3200 kW an interface lattice soliton forms (figure 32(f)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
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In the paper
“Note the reduced power threshold compared to the surface soliton case, which, however, is still higher than for 2D solitons in the array bulk.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
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In the paper
“Additionally, the hexagonal region exhibits a higher packing density of the waveguides, leading to a higher mean refractive index.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
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In the paper
“Additionally, the refractive index of the individual guides in the hexagonal lattice is slightly higher, achieved by a slightly lower writing speed in this region (1800 μm s -1 ), compared to the square region (2000 μm s -1 ).”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It turns out that the fs laser writing technique is an excellent approach to fulfilling these requirements.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“the coupled mode approach used to derive the basic equations of propagation is a paraxial approximation and, furthermore, only valid in the first propagation band.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: In the coupled mode description, the transverse shape of the modes in individual guides remains constant, so only the amplitudes evolve.
- The authors state this as an assumption: Only coupling to the nearest lattice sites is considered because interaction between waveguides drops exponentially with increasing spacing.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“This phenomenon is commonly explained by the fact that bulk fused silica consists of molecular ring structures which are composed of several SiO 2 molecules each, which are partially broken by the fs laser radiation”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
What the sources say
hedgeddirect- Asserted: passes — The authors put it forward as true.
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The quote only partly states this claim.
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In the paper
“the light evolution in these systems shares fundamental similarities to the quantum evolution of particle wavefunctions, so that waveguide arrays can act as a model system for emulating quantum mechanics.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Abstract
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A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“In the particular case of fused silica as the processed material, the density is locally increased [14], yielding an increase of the refractive index [15].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“a novel technique was developed with which waveguides can be directly 'written' into various optical bulk materials using femtosecond laser pulses, which allows for the realization of a variety of innovative concepts which are not feasible using other fabrication methods.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Abstract
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In the paper
“By moving the sample transversely with respect to the beam a continuous modification is obtained and a waveguide is created [16].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
What the sources say
- Not checked — no full text of the sourcecites [16] source
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“This changes strongly when the index of refraction is periodically modulated [8,9] (figure 2(b)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
What the sources say
boosteddirect- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“there is a fundamental difference between the longitudinal propagation direction z and the transverse directions x, y in which the energy transport occurs only by evanescent fields.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Discrete systems and arrays of evanescently coupled waveguides
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“in optics the evolution takes place in space instead of time, so the temporal evolution is mapped onto a spatial dimension (the propagation direction) and can therefore be directly observed at an arbitrary resolution.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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In the paper
“Since the colour centres are formed exclusively inside the waveguides, this technique yields a high signal-to-noise ratio.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
plaindirect- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The term ω ẍ0 m represents the transverse electrical field and can be tuned by an appropriate curvature of the waveguide array.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
plaindirect- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The respective Fourier transform G(β x d) is a narrow distribution and initially located around β x d = 0.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the plane waves seem to have travelled different distances, resulting in different effective group velocities and, hence, a different effective index of the individual guides.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Assuming the bending to be much smaller than the waveguide spacing d, in the 1D case the paraxial Helmholtz equation ( 2) converts into”
- Also stated in: § Quantum-optical analogies · plain
“The term ẍ0 x , where the dots stand for the derivative with respect to z , acts now as the transverse force.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
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The quote only partly states this claim.
- The authors state this as an assumption: The bending of the waveguides is much smaller than the waveguide spacing.
- Also stated in: § Quantum-optical analogies · plain
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Importantly, the dependence of the fluorescence intensity on the intensity of the propagating light is approximately linear, so that not only qualitative but also quantitative measurements can be performed.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
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In the paper
“the famous acceleration theorem [29] states that a constant gradient in real space yields a constant motion in Fourier space.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch oscillations
What the sources say
- Not checked — no full text of the sourcecites [29] source
boosteddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“The NBOHCs have a broad absorption band around 2.0 eV [26] and exhibit an absorption maximum at 620 nm [27].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
What the sources say
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“when launching red light from a HeNe laser at λ = 633 nm (corresponding to 1.95 eV) into the waveguides, these colour centres are excited and the resulting fluorescence (at λ = 650 nm) can be directly observed.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Femtoecond-laser-written waveguide arrays: fabrication and characterization
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“It was shown by Felix Bloch in 1928 [29] that a linear transverse potential yields a periodic oscillation of the wavefunction.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Quantum-optical analogies
What the sources say
- Not checked — no full text of the sourcecites [29] source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“But this process strongly dampens the Bloch oscillations and, more importantly, the larger width of higher propagation bands impeded the investigation of the interplay between Bloch oscillations and Zener tunnelling.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
What the sources say
boosteddirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the Zener tunnelling is much more complex at the second and later tunnelling points since light occupies both minibands and coherent interference determines the band occupancy after the crossings.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“for a fixed waveguide spacing d and a wavelength λ, DL is obtained only for the particular ratios A 0 /z 0 and the wave packet collapses at z 0 .”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“in the homogeneous array the Brillouin zone is -π β x d π (instead of -π/2 β x d π/2 in the binary array)”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“Recently, it was suggested that introducing specific phase shifts to the propagating modes by a segmentation of the waveguide arrays can yield image reconstruction for arbitrary 1D and 2D intensity distributions even in finite configurations involving boundary reflections [60].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
What the sources say
- Not checked — no full text of the sourcecites [60] source
hedgeddirect- Asserted: passes — The authors put it forward as true.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
In the paper
“This can be overcome by a particular modification of the coupling constants [59]; however, the extreme precision required does not seem viable with current fabrication techniques.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
What the sources say
- Not checked — no full text of the sourcecites [59] source
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“complex semiconductor superlattices with larger lattice periods have been used [30,44,45], although definitive evidence was still lacking [46].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“in most cases the impact of next-nearest neighbour coupling can be safely neglected since the deviations from pure nearestneighbour coupling is only marginal; however, when this first order is suppressed as for DL, any higher-order coupling becomes visible.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“it was predicted in 1986 that a transverse electric field, which is periodic in time (ac field), yields periodic collapse of the evolving wavefunction, which is well known as dynamic localization (DL) [43].”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
What the sources say
- Not checked — no full text of the sourcecites [43] source
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
In the paper
“for a constant transverse field the eigenvalues of the system are equally distributed [29,34] yielding a periodic recovery of the initial field distribution”
§ Discrete optics in femtosecond-laserwritten photonic structures > Dynamic localization
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In optics the corresponding potential is achieved by waveguides with alternating high and low refractive indices (figure 12(b)), which are expressed in terms of a detuning σ to the average propagation constant of the system.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The binary lattice has a unit cell, which contains two dissimilar sites.The corresponding potential consists of alternating deep and shallow wells”
§ Discrete optics in femtosecond-laserwritten photonic structures > Optical Bloch-Zener dynamics
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In the case of DL, the destruction of self-imaging for broadband beams stems from the resonant nature of equation ( 23), whereas for BO the self-imaging period turns out to be proportional to the wavelength λ.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Polychromatic dynamic localization
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
In the paper
“This phenomenon is known as nonlinear diffusion [74].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
What the sources say
- Not checked — no full text of the sourcecites [74] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Whereas the high power is sufficient for localization in the central part of the pulse, the pulse wings still experience linear diffraction due to their significantly lower power.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A genuine way of impressing such a phase shift on the propagating modes is the alternating segmentation of the waveguides”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one. The quote only partly states this claim.
In the paper
“The first experimental observation of a discrete 2D soliton was accomplished in lattices optically induced in a photorefractive crystal [77].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
What the sources say
- Not checked — no full text of the sourcecites [77] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“for the numerical modelling a reduced nonlinear coefficient γ using n 2(eff) = 0.25n 2(bulk) was used, which is consistent with figure 24(b) since the array was fabricated with a writing velocity of 500 μm s -1 .”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“in fused silica γ is positive; therefore, the nonlinear contribution is also positive.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“in contrast the alternative approach based on the fs direct writing technique has some inherent advantages, including e.g. the insertion of artificial defects, the creation of anisotropic coupling, and the realization of boundaries and interfaces between different array topologies.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“It was demonstrated by Kelley [76] that 2D solitons in homogeneous media are unstable, i.e. they exist only at the critical power.For lower power, the beam still spreads, and for higher power the beam collapses.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons
What the sources say
- Not checked — no full text of the sourcecites [76] source
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As more complex intensity distributions are simply a superposition of a set of single waveguide excitations, this setting therefore allows for the imaging of arbitrary input signals.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“In nonlinear optics, surface waves residing at the interface between naturally uniform materials typically are observed when their power exceeds a certain threshold and are stable under appropriate conditions [84].”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
What the sources say
- Not checked — no full text of the sourcecites [84] Mihalache D, 1989, Prog. Opt. source
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the electronic χ (3) nonlinearity provides an almost instantaneous response of the system, but is rather weak.Therefore, a high input peak power is required for the excitation of discrete solitons in these lattices, so that the experimental analysis relies on powerful laser sources.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 1D discrete solitons
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Propagation bands and bandgaps are a direct consequence of the periodicity of an infinite waveguide array, yielding the existence of discrete solitons when the propagation constant of the travelling modes is shifted by the nonlinear influence from the bands into the bandgaps.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Since this novel method is independent of array boundaries, it therefore provides a versatile method for exact image transmission in a variety of configurations in integrated optics.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Self-imaging in waveguide arrays by segmentation
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The situation completely changes in the presence of a surface, since the periodicity is abruptly interrupted.The former homogeneous band structure is splitting up depending on the distance to the surface, so the simplified picture of shifting the propagation constant from the band into the bandgap is no longer valid.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Furthermore, it is possible to precisely control the properties of every single waveguide, to generate sharply defined surfaces or artificial defects.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“To summarize, it was demonstrated that fabricating complex refractive index landscapes with the fs laser-writing approach has a variety of advantages leaving these structures as an important alternative to common fabrication techniques.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The repulsive character of the interface is preserved but is much weaker than for a surface.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The fs-laser-writing approach for the fabrication of waveguide arrays thereby exhibits a variety of advantages such as the stability and homogeneity of the waveguides and the evanescent coupling, the processing speed and the possibility of fabricating arbitrary 1D and 2D topologies for linear and nonlinear light propagation.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“because nonlinearity increases the refractive index and causes phase matching of both array sections.”
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Particularly, this socalled discrete optics has the potential to mimic many different quantum systems in a fully classical domain.”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
The authors state this as an assumption.
In the coupled mode description, the transverse shape of the modes in individual guides remains constant, so only the amplitudes evolve.
“the transverse shape of the modes in the individual guides is assumed to remain constant, so that only the amplitudes evolve.”
The authors state this as an assumption.
Only coupling to the nearest lattice sites is considered because interaction between waveguides drops exponentially with increasing spacing.
“only coupling to the nearest lattice sites is taken into account.”
The authors state this as an assumption.
For reconstructing the refractive index from near-field distributions, the effective index is taken to equal the bulk index.
“using the assumption n eff = n bulk”
The authors state this as an assumption.
The bending of the waveguides is much smaller than the waveguide spacing.
“Assuming the bending to be much smaller than the waveguide spacing d”
The paper relies on this without support.
A two-dimensional square waveguide lattice can be described as a superposition of horizontal and vertical one-dimensional lattices.
“it can be described by the superposition of horizontal and vertical 1D lattices”
The authors state this as an assumption.
Coupling between waveguides along the diagonal in the two-dimensional square lattice is negligible.
“as long as the impact of coupling between waveguides along the diagonal is negligible”
The authors state this as an assumption.
In a finite waveguide lattice, the influence of the boundary on the propagation of the mode can be neglected.
“when the influence of the boundary on the propagation of the mode can be neglected”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“While it is technologically challenging to modulate the waveguide profile in a way to precisely realize the on-site modulation involved in Thouless' original topological pump model ( 29), the excellent control in the waveguide spacing achievable with femtosecond laser microfabrication technology (Szameit et al., 2007;Szameit and Nolte, 2010) allowed for the emulation of an off-diagonal pump model”
From Topological photonics (2019) · cites this paper as Szameit and Nolte, 2010
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“In previous works, optical diffraction through such an array has been conceptualized in terms of a reduced-dimensionality system [25]: in the paraxial limit, the envelope function of the linearly-polarized electric field, ψ, is found to obey a (2+1)D Schrödinger wave equation”
From Experimental observation of optical Weyl points and Fermi arc-like surface states (2017) · cites this paper as [25]
The cited source says what the claim attributes to it.
In the citing paper
“Such an oscillatory motion has been recently observed in Ref.[38] in binary arrays written in fused silica by the femtosecond laser writing technology [5], providing the first simulation in optics of ZB.”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [5]
The cited source says what the claim attributes to it.
In the citing paper
“by using three-dimensional systems (in particular, arrays of optical waveguides) (Szameit and Nolte, 2010), it is possible to use one of the dimensions as a temporal coordinate and thus observe topological protection in the orthogonal plane (Rechtsman, Zeuner, Plotnik et al., 2013).”
From Topological photonics (2019) · cites this paper as Szameit and Nolte, 2010
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“Thus, a 100% visibility peak (in this case a doubling in the coincidental count rate after the splitter) should ideally be measured when changing from distinguishable to indistinguishable photons [33].”
From Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays (2014) · cites this paper as [33]
Experimental — accuracy not yet measured
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“The maximum visibility of the non-classical interference for these diagonal elements depends solely on the quality of the indistinguishability between the two photons inside the quantum network, irrespective of the network structure and the evolution length of the coupling region.”
From Quantum Walks of Correlated Photon Pairs in Two-Dimensional Waveguide Arrays (2014) · cites this paper as [33]
Experimental — accuracy not yet measuredIn the citing paper
“Such a structure could be realized, for instance, by femtosecond laser writing in fused silica, in which the defect line is readily obtained by varying the writing speed of the laser beam (see, for instance, [6,20]).”
From Photonic Bloch oscillations of correlated particles (2011) · cites this paper as [20]
In the citing paper
“We realize the graph structure by means of a novel hybrid approach: 2D photonic lattices of spatially coupled waveguides are inscribed into fused silica by femtosecond laser writing (32), while one synthetic dimension is encoded in the photons’ polarization.”
From Exploring complex graphs using three-dimensional quantum walks of correlated photons (2021) · cites this paper as [32]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Discrete optics in femtosecond-laserwritten photonic structures > 2D discrete solitons at surfaces and interfaces
“for low peak power P peak = 40 kW the light is almost confined to the square region since it is reflected at the interface (figure 32(a)).”
§ Discrete optics in femtosecond-laserwritten photonic structures > Conclusion
“The input power is (a) 62 kW, (b) 1.4 MW, (c) 2 MW, (d) 2.3 MW, (e) 2.7 MW and (f) 3.2 MW.”
Citations
Cites
�ber die Quantenmechanik der Elektronen in Kristallgittern
Bloch, F. (1929) · Zeitschrift f�r Physik · doi:10.1007/bf01339455 · Cited by 3,436
Femtosecond laser micromachining in transparent materials
Gattass, R. R., & Mazur, E. (2008) · Nature Photonics · doi:10.1038/nphoton.2008.47 · Cited by 3,306
Optical multi-mode interference devices based on self-imaging: principles and applications
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Sorted by citations
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Self-citationExceptional topology of non-Hermitian systems
Bergholtz, E. J., Budich, J. C., & Kunst, F. K. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.015005 · Cited by 1,711
“Photonic crystals belong to the larger experimental platform of optical microresonators, also known as microcavities (Vahala, 2003).”
BackgroundTopologically protected bound states in photonic parity–time-symmetric crystals
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Self-citation
Metadata
- Authors
- Szameit, A., & Nolte, S.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Friedrich Schiller University Jena (DE)
- Venue
- Journal of Physics B: Atomic, Molecular and Optical Physics
- Publisher
- IOP Publishing
- Published
- 2010-07-23
- Volume
- 43
- Issue
- 16
- Pages
- 163001
- ISSN
- 0953-4075 (ISSN-L)
- 1361-6455
- OpenAlex
- W2038985364
- Cited by
- 610
- References
- 108
- Citations by year
- 2026: 30 · 2025: 45 · 2024: 40 · 2023: 49 · 2022: 36 · 2021: 40 · 2020: 63 · 2019: 51 · 2018: 33 · 2017: 39 · 2016: 40 · 2015: 27 · 2014: 36 · 2013: 30 · 2012: 33
- FWCI
- 25.48
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics B Atomic Molecular and Optical Physics (publishedVersion)
- Funders
- Deutsche Forschungsgemeinschaft
- Leibniz-Gemeinschaft
- Topics
- Physical Sciences › Engineering › Industrial and Manufacturing Engineering › Laser Material Processing Techniques
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Photonic and Optical Devices
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Nonlinear Optical Materials Studies
- Keywords
- femtosecond laser direct writing, waveguide arrays, evanescently coupled waveguides, photonic structures, quantum-classical analogy, waveguide dispersion, diffraction
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