Optical Zener-Bloch oscillations in binary waveguide arrays
Open accessAbstract
Zener tunneling in a binary array of coupled optical waveguides with transverse index gradient is shown to produce a sequence of regular or irregular beam splitting and beam recombination events superimposed to Bloch oscillations. These periodic or aperiodic Zener-Bloch oscillations provide a clear and visualizable signature in an optical system of coherent multiband dynamics encountered in solid-state or matter-wave systems.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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?
For α > 0, G(β_x d) moves with constant velocity α/λ towards +β_x d during propagation.
“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].”
From Discrete optics in femtosecond-laser-written photonic structures (2010) · cites this paper as [35]
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)
Experimental — accuracy not yet measuredIn binary arrays, Bloch oscillations are not damped, which significantly simplifies observation of Bloch-Zener dynamics.
“The benefit is that the Bloch oscillations are not damped which significantly simplifies the observation of Bloch-Zener dynamics [35].”
From Discrete optics in femtosecond-laser-written photonic structures (2010) · cites this paper as [35]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Dynamics of Bose-Einstein condensates in optical lattices
Morsch, O., & Oberthaler, M. K. (2006) · Reviews of Modern Physics · doi:10.1103/revmodphys.78.179 · Cited by 1,618 · 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
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
Self-citationWannier–Stark resonances in optical and semiconductor superlattices
Glück, M. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00142-4 · Cited by 340 · see citing works
Optical Bloch oscillations in waveguide arrays
Peschel, U., Pertsch, T., & Lederer, F. (1998) · Optics Letters · doi:10.1364/ol.23.001701 · Cited by 328 · 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
Optical Analogue of Electronic Bloch Oscillations
Sapienza, R., Costantino, P., Wiersma, D., Ghulinyan, M., Oton, C. J., & Pavesi, L. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.263902 · Cited by 265 · 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
Spatial optical solitons in waveguide arrays
Sukhorukov, A. A., Kivshar, Y. S., Eisenberg, H. S., & Silberberg, Y. R. (2003) · IEEE Journal of Quantum Electronics · doi:10.1109/jqe.2002.806184 · Cited by 219 · 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
Zener Tunneling of Light Waves in an Optical Superlattice
Ghulinyan, M., Otón, C. J., Gaburro, Z., Pavesi, L., Toninelli, C., & Wiersma, D. S. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.127401 · Cited by 143 · see citing works
Discrete gap solitons in modulated waveguide arrays
Sukhorukov, A. A., & Kivshar, Y. S. (2002) · Optics Letters · doi:10.1364/ol.27.002112 · Cited by 130 · see citing works
Bloch Oscillations, Zener Tunneling, and Wannier-Stark Ladders in the Time Domain
Rotvig, J., Jauho, A., & Smith, H. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.1831 · Cited by 113 · see citing works
Self-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
Self-citationObservation of an optical Wannier-Stark ladder
de Sterke, C. M., Bright, J. N., Krug, P. A., & Hammon, T. E. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.2365 · Cited by 76 · see citing works
Observation of discrete gap solitons in binary waveguide arrays
Morandotti, R., Mandelik, D., Silberberg, Y., Aitchison, J. S., Sorel, M., Christodoulides, D. N., Sukhorukov, A. A., & Kivshar, Y. S. (2004) · Optics Letters · doi:10.1364/ol.29.002890 · Cited by 66 · see citing works
Dynamical 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
Time-periodic behavior of multiband superlattices in static electric fields
Hone, D. W., & Zhao, X.-G. (1996) · Physical review. B, Condensed matter · doi:10.1103/physrevb.53.4834 · Cited by 35 · see citing works
Light propagation through a nonlinear defect: symmetry breaking and controlled soliton emission
Fratalocchi, A., & Assanto, G. (2006) · Optics Letters · doi:10.1364/ol.31.001489 · Cited by 32 · see citing works
Callaway, J. (1974) · Elsevier eBooks · doi:10.1016/b978-0-12-155202-2.50008-5 · Cited by 4 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- Callaway J., Quantum Theory of the Solid State (Academic Press, New York) 1974, pp. 465- 478.
- Sukhorukov A. A., Kivshar Y. S., Eisenberg H. S. and Silberberg Y., IEEE J. Quantum Electron., 39 (2003) 31.
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
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
Synthetic dimension in photonics
Yuan, L., Lin, Q., Xiao, M., & Fan, S. (2018) · Optica · doi:10.1364/optica.5.001396 · Cited by 545 · see citing works
Light propagation and localization in modulated photonic lattices and waveguides
Garanovich, I. L., Longhi, S., Sukhorukov, A. A., & Kivshar, Y. S. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.03.005 · Cited by 502 · see citing works
Self-citationHigh-harmonic generation from Bloch electrons in solids
Wu, M., Ghimire, S., Reis, D. A., Schäfer, K. J., & Gaarde, M. B. (2015) · Physical Review A · doi:10.1103/physreva.91.043839 · Cited by 377 · see citing works
Bloch-Zener Oscillations in Binary Superlattices
Dreisow, F., Szameit, A., Heinrich, M., Pertsch, T., Nolte, S., Tünnermann, A., & Longhi, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.076802 · Cited by 213 · see citing works
Self-citationNon-Bloch-Band Collapse and Chiral Zener Tunneling
Longhi, S. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.066602 · Cited by 148 · see citing works
Self-citationYuan, L., & Fan, S. (2016) · Optica · doi:10.1364/optica.3.001014 · Cited by 136 · see citing works
Optical Bloch Oscillations and Zener Tunneling with Nonclassical Light
Longhi, S. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.193902 · Cited by 81 · see citing works
Self-citationClassical 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-citationClassical simulation of relativistic quantum mechanics in periodic optical structuresPreprint
Longhi, S. (2011) · Cited by 47 · see citing works
Self-citationLonghi, S. (2010) · Physical Review A · doi:10.1103/physreva.81.022118 · Cited by 25 · see citing works
Self-citationBloch-Zener oscillations of strongly correlated electrons
Longhi, S. (2012) · Physical Review B · doi:10.1103/physrevb.86.075144 · Cited by 24 · see citing works
Self-citationWang, Z., Yang, B., Hu, D., Chen, X., Xiong, H., Wu, B., & Zhou, X. (2016) · Physical Review A · doi:10.1103/physreva.94.033624 · Cited by 22 · see citing works
Quantum optics as a tool for photonic lattice design
Rodríguez-Lara, B. M., Soto, F., & Christodoulides, D. N. (2015) · Physica Scripta · doi:10.1088/0031-8949/90/6/068014 · Cited by 21 · see citing works
Guiding and confining of light in a two-dimensional synthetic space using electric fields
Chalabi, H., Barik, S., Mittal, S., Murphy, T. E., Hafezi, M., & Edo Waks, A. (2020) · Optica · doi:10.1364/optica.386347 · Cited by 21 · see citing works
Caetano, R. A., & Lyra, M. L. (2011) · Physics Letters A · doi:10.1016/j.physleta.2011.06.002 · Cited by 20 · see citing works
Complex Berry phase and imperfect non-Hermitian phase transitions
Longhi, S., & Feng, L. H. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.085122 · Cited by 18 · see citing works
Self-citationTunable hybridization at midzone and anomalous Bloch–Zener oscillations in optical waveguide ladders
Zheng, M., Wang, G., & Yu, K. W. (2010) · Optics Letters · doi:10.1364/ol.35.003865 · Cited by 10 · see citing works
Internal dynamics of a polaron uniformly moving along a molecular chain in a constant electric field
Korshunova, A. N., & Lakhno, V. D. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114786 · Cited by 10 · see citing works
Longhi, S. (2012) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/45/22/225504 · Cited by 9 · see citing works
Self-citationChiral Zener tunneling in non-Hermitian frequency lattices
Zheng, L., Wang, B., Qin, C., Zhao, L., Chen, S., Liu, W., & Lu, P. (2022) · Optics Letters · doi:10.1364/ol.470880 · Cited by 10 · see citing works
Classical and quantum interference in multiband optical Bloch oscillations
Longhi, S. (2009) · Physical Review B · doi:10.1103/physrevb.79.245108 · Cited by 9 · see citing works
Self-citationPlasmonic Zener tunneling in binary graphene sheet arrays
Yang, F., Wang, B., Wang, K., Long, H., & Lu, P. (2016) · Optics Letters · doi:10.1364/ol.41.002978 · Cited by 8 · see citing works
Non-Hermitian Bloch–Zener phase transition
Longhi, S. (2022) · Optics Letters · doi:10.1364/ol.478059 · Cited by 7 · see citing works
Self-citationClassical realization of two-site Fermi-Hubbard systems
Longhi, S., Valle, G. D., & Foglietti, V. (2011) · Physical Review B · doi:10.1103/physrevb.84.033102 · Cited by 7 · see citing works
Self-citationLi, Z., Pang, X.-N., Dong, J., & Wang, H. (2011) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/95/36004 · Cited by 6 · see citing works
Bloch oscillations of polaritons of an atomic ensemble in magnetic fields
Zhang, H. R., & Sun, C. P. (2010) · Physical Review A · doi:10.1103/physreva.81.063427 · Cited by 6 · see citing works
Tran, M. C., & Tran, T. X. (2025) · Physical Review A · doi:10.1103/physreva.111.033525 · Cited by 4 · see citing works
The Optical Bloch oscillation in chirped one-dimensional superconducting photonic crystal
Zhang, Z., Long, Y., Zhang, L., Yin, P., & Xue, C. (2017) · Physica B Condensed Matter · doi:10.1016/j.physb.2017.06.049 · Cited by 4 · see citing works
Photonic Bloch–dipole–Zener oscillations in binary parabolic optical waveguide arrays
Zheng, M., Chan, Y. S., & Yu, K. W. (2011) · Journal of the Optical Society of America B · doi:10.1364/josab.28.001339 · Cited by 4 · see citing works
Talbot effect in binary waveguide arrays
Tran, M. C., & Tran, T. X. (2025) · Journal of the Optical Society of America B · doi:10.1364/josab.559693 · Cited by 3 · see citing works
Bykov, N. V., & Maimistov, A. I. (2016) · Bulletin of the Russian Academy of Sciences Physics · doi:10.3103/s106287381607008x · Cited by 2 · see citing works
Verbitskiy, A., Yulin, A. V., & Balanov, A. G. (2023) · Physical Review A · doi:10.1103/physreva.107.053519 · Cited by 2 · see citing works
Suppression of space broadening of exciton polariton transport by Bloch oscillation effect
Duan, X., Zou, B., & Zhang, Y. (2015) · Journal of Optics · doi:10.1088/2040-8978/17/12/125401 · Cited by 2 · see citing works
Amplitude modulated Bloch oscillations of photon probability distribution in a cavity–atom system
Zhang, G., Hu, W., & Song, Z. (2015) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/48/7/075402 · Cited by 2 · see citing works
Verbitskiy, A., & Yulin, A. V. (2024) · Журнал Экспериментальной и Теоретической Физики · doi:10.31857/s0044451024040011 · Cited by 1 · see citing works
Discrete gap solitons in nonlinear binary plasmonic waveguide arrays
Yan, J.-Y. (2015) · Physical Review A · doi:10.1103/physreva.91.033806 · Cited by 1 · see citing works
Dispersive bands of bound states in the continuum
Longhi, S. (2021) · Nanophotonics · doi:10.1515/nanoph-2021-0260 · Cited by 10 · see citing works
Self-citationBloch-Zener dynamics in binary waveguide arrays
Dreisow, F., Szameit, A., Heinrich, M., Nolte, S., Tünnermann, A., & Longhi, S. (2009) · Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) · doi:10.1109/cleoe-eqec.2009.5192912
Self-citationKerr nonlinearity effect on the stability of Wannier-Stark states in active optical systems
Verbitskiy, A., & Yulin, A. V. (2024) · Photonics and Nanostructures - Fundamentals and Applications · doi:10.1016/j.photonics.2024.101316
Talbot effect in nonlinear binary waveguide arrays
Tran, M. C., Nguyen, H. M., Duong, D. C., Nguyen-The, Q., & Tran, T. X. (2026) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2026.135231
Combination of the discrete Talbot effect with Bloch-Zener oscillations in binary waveguide arrays
Tran, M. C., Nguyen, H. M., Nguyen, T. X., & Tran, T. X. (2026) · Physical Review A · doi:10.1103/5qdn-xpwb
Narrow-peaked localized defect modes in binary waveguide arrays
Tran, M. C., Hue, N., Nguyen, T., Nguyen-The, Q., & Tran, T. (2026) · Journal of the Optical Society of America B · doi:10.1364/josab.599133
- Authors
- Longhi, S.
- Affiliations
- Istituto di Fotonica e Nanotecnologie (IT)
- Corresponding author
- Longhi, S
- ORCID
- Longhi, S
- Venue
- Europhysics Letters (EPL)
- Publisher
- IOP Publishing
- Published
- 2006-11
- Volume
- 76
- Issue
- 3
- Pages
- 416-421
- ISSN
- 0295-5075 (ISSN-L)
- 1286-4854
- OpenAlex
- W2033357739
- Cited by
- 45
- References
- 21
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 3 · 2023: 2 · 2022: 2 · 2021: 2 · 2020: 2 · 2018: 1 · 2017: 1 · 2016: 4 · 2015: 5 · 2012: 3
- FWCI
- 1.10
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Europhysics Letters (EPL) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Random lasers and scattering media
- Keywords
- Zener tunneling, Bloch oscillations, coupled optical waveguides, beam splitting, beam recombination, solid-state systems
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