Self-imaging and modulational instability in an array of periodically curved waveguides
Abstract
Linear and nonlinear light propagation in an array of waveguides with a periodically bent axis is theoretically investigated. In the linear propagation regime, it is shown that a self-imaging effect at periodic planes may occur, a phenomenon analogous to that of dynamic localization observed when an electron in a periodic potential is subjected to an ac field. In the nonlinear propagation regime, it is shown that periodic waveguide bending under the self-imaging condition inhibits the phenomenon of discrete modulational instability.
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Photonic structures allow simulation of such external potentials in curved waveguide arrays and resolution of the evolution dynamics.
“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].”
From Discrete optics in femtosecond-laser-written photonic structures (2010) · cites this paper as [33]
After every full period, an effective coupling constant c_eff = c J0(2πωA0/z0) can be defined.
“One can formally show [25,33,47] that after every full period z → z + z 0 , an effective coupling constant”
From Discrete optics in femtosecond-laser-written photonic structures (2010) · cites this paper as [33]
Cites
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Quantum-optical analogies using photonic structures
Longhi, S. (2009) · Laser & Photonics Reviews · doi:10.1002/lpor.200810055 · Cited by 725 · see citing works
Self-citationDiscrete 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
Observation of Dynamic Localization in Periodically Curved Waveguide Arrays
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Self-citationYuan, L., & Fan, S. (2016) · Optica · doi:10.1364/optica.3.001014 · Cited by 136 · see citing works
“For example, with a different choice of parameters, an effect of dynamic localization [29,35,38,39] in the frequency domain may be achieved.”
BackgroundImaging 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
Self-citationSpectral resolved dynamic localization in curved fs laser written waveguide arrays
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Classical simulation of relativistic quantum mechanics in periodic optical structures
Longhi, S. (2011) · Applied Physics B · doi:10.1007/s00340-011-4628-7 · Cited by 72 · see citing works
Self-citationDiffraction control in periodically curved two-dimensional waveguide arrays
Garanovich, I. L., Szameit, A., Sukhorukov, A. A., Pertsch, T., Krolikowski, W., Nolte, S., Neshev, D., Tuennermann, A., & Kivshar, Y. S. (2007) · Optics Express · doi:10.1364/oe.15.009737 · Cited by 50 · see citing works
Optical Zener-Bloch oscillations in binary waveguide arrays
Longhi, S. (2006) · Europhysics Letters (EPL) · doi:10.1209/epl/i2006-10301-8 · Cited by 45 · see citing works
Self-citationNonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays
Garanovich, I. L., Sukhorukov, A. A., & Kivshar, Y. S. (2007) · Optics Express · doi:10.1364/oe.15.009547 · Cited by 26 · see citing works
Polychromatic optical Bloch oscillations
Longhi, S. (2009) · Optics Letters · doi:10.1364/ol.34.002174 · Cited by 11 · see citing works
Self-citationDirac Dynamics in Waveguide Arrays: From Zitterbewegung to Photonic Topological Insulators
Dreisow, F., Rechtsman, M. C., Zeuner, J. M., Plotnik, Y., Keil, R., Nolte, S., Segev, M., & Szameit, A. (2017) · Quantum Science and Technology · doi:10.1007/978-3-319-52025-4_8 · Cited by 4 · see citing works
- Authors
- Longhi, S.
- Affiliations
- Istituto di Fotonica e Nanotecnologie (IT)
- Corresponding author
- Longhi, Stefano
- ORCID
- Longhi, Stefano
- Venue
- Optics Letters
- Publisher
- Optica Publishing Group
- Published
- 2005-08-15
- Volume
- 30
- Issue
- 16
- Pages
- 2137
- ISSN
- 0146-9592 (ISSN-L)
- 1539-4794
- OpenAlex
- W2011967582
- Cited by
- 84
- References
- 14
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 3 · 2023: 1 · 2022: 3 · 2021: 3 · 2019: 4 · 2018: 1 · 2017: 2 · 2016: 4 · 2015: 2 · 2014: 2 · 2013: 6 · 2012: 2
- FWCI
- 5.66
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Optics Letters (publishedVersion)
- PubMed (publishedVersion)
- Virtual Community of Pathological Anatomy (University of Castilla La Mancha) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Random lasers and scattering media
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photorefractive and Nonlinear Optics
- Keywords
- self-imaging, modulational instability, waveguide arrays, nonlinear light propagation, dynamical localization
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