Diffraction control in periodically curved two-dimensional waveguide arrays
Open accessAbstract
We study propagation of light beams in two-dimensional photonic lattices created by periodically curved waveguide arrays. We demonstrate that by designing the waveguide bending, one can control not only the strength and sign of the beam diffraction, but also to engineer the effective geometry and even dimensionality of the two-dimensional photonic lattice. We reveal that diffraction of different spectral components of polychromatic light can display completely different patterns in the same periodically modulated structure, e.g. one-dimensional, hexagonal, or rectangular. Our results suggest novel opportunities for efficient self-collimation, focusing, and reshaping of light beams in two-dimensional photonic structures.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
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 basic idea relies on the fact that the resonance condition has infinite solutions.
“The basic idea relies on the fact that equation ( 23) has infinite solutions as sketched in figure 18(a) [56].”
From Discrete optics in femtosecond-laser-written photonic structures (2010) · cites this paper as [56]
For d = 26 μm and design λ = 550 nm, the first section has A1 = 56 μm and z1 = 63 mm, and the second has A2 = 86 μm and z2 = 42 mm.
“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.”
From Discrete optics in femtosecond-laser-written photonic structures (2010) · cites this paper as [56]
Cites
Discretizing light behaviour in linear and nonlinear waveguide lattices
Christodoulides, D. N., Lederer, F., & Silberberg, Y. (2003) · Nature · doi:10.1038/nature01936 · Cited by 1,692 · see citing works
Self-collimating phenomena in photonic crystals
Kosaka, H., Kawashima, T., Tomita, A., Notomi, M., Tamamura, T., Sato, T., & Kawakami, S. (1999) · Applied Physics Letters · doi:10.1063/1.123502 · Cited by 691 · see citing works
Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations
Morandotti, R., Peschel, U., Aitchison, J. S., Eisenberg, H. S., & Silberberg, Y. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.4756 · Cited by 626 · see citing works
Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays
Pertsch, T., Dannberg, P., Elflein, W., Bräuer, A., & Lederer, F. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.4752 · Cited by 587 · see citing works
Self-citationFemtosecond waveguide writing: a new avenue to three-dimensional integrated optics
Nolte, S., Will, M., Burghoff, J., & Tuennermann, A. (2003) · Applied Physics A: Materials Science & Processing · doi:10.1007/s00339-003-2088-6 · Cited by 545 · see citing works
Self-citationEisenberg, H. S., Silberberg, Y., Morandotti, R., & Aitchison, J. S. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.1863 · Cited by 512 · see citing works
Observation of Dynamic Localization in Periodically Curved Waveguide Arrays
Longhi, S., Marangoni, M., Lobino, M., Ramponi, R., Laporta, P., Cianci, E., & Foglietti, V. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.243901 · Cited by 357 · see citing works
Channel optical waveguide directional couplers
Somekh, S., Garmire, E., Yariv, A., Garvin, H. L., & Hunsperger, R. G. (1973) · Applied Physics Letters · doi:10.1063/1.1654468 · Cited by 275 · see citing works
Bloch Oscillations and Zener Tunneling in Two-Dimensional Photonic Lattices
Trompeter, H., Krolikowski, W. Z., Neshev, D. N., Desyatnikov, A. S., Sukhorukov, A. A., Kivshar, Y. S., Pertsch, T., Peschel, U., & Lederer, F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.053903 · Cited by 275 · see citing works
Self-citationCoupling of Optical Fibers and Scattering in Fibers*
Jones, A. L. (1965) · Journal of the Optical Society of America · doi:10.1364/josa.55.000261 · Cited by 244 · see citing works
Visual Observation of Zener Tunneling
Trompeter, H., Pertsch, T., Lederer, F., Michaelis, D., Streppel, U., Bräuer, A., & Peschel, U. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.023901 · Cited by 233 · see citing works
Self-citationAchieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal
Rakich, P. T., Dahlem, M. S., Tandon, S. N., et al. (2006) · Nature Materials · doi:10.1038/nmat1568 · Cited by 224 · see citing works
Bloch Oscillations in an Array of Curved Optical Waveguides
Lenz, G., Talanina, I., & de Sterke, C. M. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.963 · Cited by 213 · see citing works
Self-guiding in two-dimensional photonic crystals
Chigrin, D. N., Enoch, S., Torres, C. M. S., et al. (2003) · Optics Express · doi:10.1364/oe.11.001203 · Cited by 208 · see citing works
Discrete nonlinear localization in femtosecond laser written waveguides in fused silica
Szameit, A., Blömer, D., Burghoff, J., Schreiber, T., Pertsch, T., Nolte, S., Tünnermann, A., & Lederer, F. (2005) · Optics Express · doi:10.1364/opex.13.010552 · Cited by 160 · see citing works
Self-citationDiscrete diffraction in two-dimensional arrays of coupled waveguides in silica
Pertsch, T., Peschel, U., Lederer, F., Burghoff, J., Will, M., Nolte, S., & Tünnermann, A. (2004) · Optics Letters · doi:10.1364/ol.29.000468 · Cited by 142 · see citing works
Self-citationExact dynamic localization in curved AlGaAs optical waveguide arrays
Iyer, R., Stewart Aitchison, J., Wan, J., Dignam, M. M., & Martijn de Sterke, C. (2007) · Optics Express · doi:10.1364/oe.15.003212 · Cited by 115 · see citing works
Imaging of Bloch oscillations in erbium-doped curved waveguide arrays
Chiodo, N., Della Valle, G., Osellame, R., Longhi, S., Cerullo, G., Ramponi, R., Laporta, P., & Morgner, U. (2006) · Optics Letters · doi:10.1364/ol.31.001651 · Cited by 103 · see citing works
Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity
Kevrekidis, P. G., Malomed, B. A., & Gaĭdideĭ, Y. B. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.66.016609 · Cited by 90 · see citing works
Hexagonal waveguide arrays written with fs-laser pulses
Szameit, A., Blömer, D., Burghoff, J., Pertsch, T., Nolte, S., & Tünnermann, A. (2006) · Applied Physics B · doi:10.1007/s00340-005-2127-4 · Cited by 88 · see citing works
Self-citationSelf-imaging and modulational instability in an array of periodically curved waveguides
Longhi, S. (2005) · Optics Letters · doi:10.1364/ol.30.002137 · Cited by 84 · see citing works
Light evolution in arbitrary two-dimensional waveguide arrays
Szameit, A., Pertsch, T., Dreisow, F., Nolte, S., Tünnermann, A., Peschel, U., & Lederer, F. (2007) · Physical Review A · doi:10.1103/physreva.75.053814 · Cited by 58 · see citing works
Self-citationBroadband diffraction management and self-collimation of white light in photonic lattices
Garanovich, I. L., Sukhorukov, A. A., & Kivshar, Y. S. (2006) · Physical Review E · doi:10.1103/physreve.74.066609 · Cited by 55 · see citing works
Self-citationDynamical localization and AC Bloch oscillations in periodic optical waveguide arrays
Lenz, G., Parker, R., Wanke, M. C., & de Sterke, C. M. (2003) · Optics Communications · doi:10.1016/s0030-4018(03)01172-6 · Cited by 54 · see citing works
Two-dimensional high-precision fiber waveguide arrays for coherent light propagation
Röpke, U., Bartelt, H., Unger, S., et al. (2007) · Optics Express · doi:10.1364/oe.15.006894 · Cited by 45 · see citing works
Soliton dragging by dynamic optical lattices
Kartashov, Y. V., Torner, L., & Christodoulides, D. N. (2005) · Optics Letters · doi:10.1364/ol.30.001378 · Cited by 44 · see citing works
Demonstration of all-optical beam steering in modulated photonic lattices
Rosberg, C. R., Garanovich, I. L., Sukhorukov, A. A., et al. (2006) · Optics Letters · doi:10.1364/ol.31.001498 · Cited by 43 · see citing works
Self-citationDemonstration of all-optical beam steering in modulated photonic lattices
Rosberg, C. R., Garanovich, I. L., Sukhorukov, A. A., et al. (2005) · Cited by 38 · see citing works
Self-citationOptically induced Zener tunneling in one-dimensional lattices
Fratalocchi, A., Assanto, G., Brzdąkiewicz, K. A., & Karpierz, M. A. (2006) · Optics Letters · doi:10.1364/ol.31.000790 · Cited by 30 · see citing works
Soliton control in modulated optically-induced photonic lattices
Garanovich, I. L., Sukhorukov, A. A., & Kivshar, Y. S. (2005) · Optics Express · doi:10.1364/opex.13.005704 · Cited by 24 · see citing works
Self-citationOptical filters based on dynamic localization in curved coupled optical waveguides
Wan, J., Laforest, M., de Sterke, C. M., & Dignam, M. M. (2004) · Optics Communications · doi:10.1016/j.optcom.2004.11.075 · Cited by 18 · see citing works
Han, Y., & Lee, S. B. (2005) · Optics Express · doi:10.1364/opex.13.009224 · Cited by 16 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Quantum-optical analogies using photonic structures
Longhi, S. (2009) · Laser & Photonics Reviews · doi:10.1002/lpor.200810055 · Cited by 725 · see citing works
Discrete optics in femtosecond-laser-written photonic structures
Szameit, A., & Nolte, S. (2010) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/43/16/163001 · Cited by 610 · see citing works
Self-citationPolychromatic dynamic localization in curved photonic lattices
Szameit, A., Garanovich, I. L., Heinrich, M., Sukhorukov, A. A., Dreisow, F., Pertsch, T., Nolte, S., Tünnermann, A., & Kivshar, Y. S. (2009) · Nature Physics · doi:10.1038/nphys1221 · Cited by 159 · see citing works
Self-citation
- Authors
- Garanovich, I. L., Szameit, A., Sukhorukov, A. A., Pertsch, T., Krolikowski, W., Nolte, S., Neshev, D., Tuennermann, A., & Kivshar, Y. S.
- Affiliations
- Australian National University (AU)
- Friedrich Schiller University Jena (DE)
- ORCID
- Venue
- Optics Express
- Publisher
- Optica Publishing Group
- Published
- 2007-07-20
- Volume
- 15
- Issue
- 15
- Pages
- 9737
- ISSN
- 1094-4087 (ISSN-L)
- OpenAlex
- W2088005430
- Cited by
- 50
- References
- 32
- Citations by year
- 2025: 1 · 2024: 1 · 2023: 3 · 2019: 1 · 2018: 2 · 2017: 1 · 2016: 2 · 2015: 6 · 2014: 1 · 2013: 1 · 2012: 5
- FWCI
- 4.69
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Optics Express (publishedVersion)
- PubMed (publishedVersion)
- Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft) (submittedVersion, other-oa)
- ANU Open Research (Australian National University) (submittedVersion)
- Fraunhofer-Publica (Fraunhofer-Gesellschaft) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photonic Crystals and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Photonic and Optical Devices
- Keywords
- two-dimensional photonic lattices, waveguide bends, dimensionality engineering, polychromatic light, self-collimation, beam focusing, beam reshaping, optical beam propagation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
