Edge states in coupled periodic dielectric waveguides induced by long-range interaction
https://doi.org/10.17586/2220-8054-2018-9-6-716-723
Abstract
We study the properties of coupled periodic dielectric nanowaveguides and reveal that finite arrays of equally spaced waveguides with certain parameters support edge modes, which originate due to the presence of the long-range interactions between the waveguides. We provide a simple model of the coupled waveguides with next-to-nearest neighbors interaction that captures the main properties of the considered system including the formation of the edge states. The predicted results suggest that the arrays of periodic dielectric nanowaveguides may serve as a fruitful system for studying the discrete coupled systems with long-range interaction and realizing optical metasurfaces with novel functionalities for guiding surface waves.
Supporting agencies: This work was supported by the Russian Foundation for Basic Research, according to the research project No. 16-37-60092 mol a dk, and the Grant from the President of the Russian Federation (MK-381.2017.2).
References
1. Christodoulides D., Lederer F., Silberberg Y. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature, 2003, 424, P. 817–823.
2. Malkova N., Hromada I., Wang X., Bryant G., Chen Z. Transition between Tamm-like and Shockleylike surface states in optically induced photonic superlattices. Phys. Rev. A., 2009, 80, P. 043806.
3. Blanco-Redondo A., Andonegui I., Collins M.J., Harari G., Lumer Y., Rechtsman M.C., Eggleton B.J., Segev M. Topological Optical Waveguiding in Silicon and the Transition between Topological and Trivial Defect States. Phys. Rev. Lett. 2016, 116, P. 163901.
4. Kraus Y.E., Lahini Y., Ringel Z., Verbin M., Zilberberg O. Topological States and Adiabatic Pumping in Quasicrystals. Phys. Rev. Lett., 2012, 109, P. 106402.
5. Sukhorukov A.A., Kivshar Y.S., Eisenberg H.S., Silberberg Y. Spatial optical solitons in waveguide arrays. IEEE Journal of Quantum Electronics, 2003, 39, P. 31–50.
6. Fleischer J.W., Bartal G., Cohen O., Schwartz T., Manela O., Freedman B., Segev M., Buljan H., Efremidis N.K. Spatial photonics in nonlinear waveguide arrays. Opt. Express, 2005, 13, P. 1780–1796.
7. Peschel U., Pertsch T., Lederer F. Optical Bloch oscillations in waveguide arrays. Opt. Lett., 1998, 23, P. 1701–1703.
8. Pertsch T., Dannberg P., Elflein W., Brauer A., Lederer F. Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays.¨ Phys. Rev. Lett., 1999, 83, P. 4752–4755.
9. Morandotti R., Peschel U., Aitchison J.S., Eisenberg H.S., Silberberg Y. Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations. Phys. Rev. Lett., 1999, 83, P. 4756–4759.
10. Longhi S. Optical Zener-Bloch oscillations in binary waveguide arrays. EPL (Europhysics Letters), 2006, 76, P. 416.
11. Trompeter H., Krolikowski W., Neshev D.N., Desyatnikov A.S., Sukhorukov A.A., Kivshar Y.S., Pertsch T., Peschel U., Lederer F. Bloch Oscillations and Zener Tunneling in Two-Dimensional Photonic Lattices. Phys. Rev. Lett., 2006, 96, P. 053903.
12. Lahini Y., Avidan A., Pozzi F., Sorel M., Morandotti R., Christodoulides D.N., Silberberg Y. Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices. Phys. Rev. Lett., 2008, 100, P. 013906.
13. Martin L., Giuseppe G.D., Perez-Leija A., Keil R., Dreisow F., Heinrich M., Nolte S., Szameit A., Abouraddy A.F., Christodoulides D.N., Saleh B.E.A. Anderson localization in optical waveguide arrays with off-diagonal coupling disorder. Opt. Express, 2011, 19, P. 13636–13646.
14. Cherpakova Z., Bleckmann F., Vogler T., Linden S. Transverse Anderson localization of surface plasmon polaritons. Opt. Lett., 2017, 42, P. 2165–2168.
15. Longhi S. Quantum-optical analogies using photonic structures. Laser and Photonics Reviews, 2009, 3(3), P. 243–261.
16. Garanovich I.L., Longhi S., Sukhorukov A.A., Kivshar Y.S. Light propagation and localization in modulated photonic lattices and waveguides. Phys. Rep., 2012, 518, P. 1–79.
17. Fan S., Winn J.N., Devenyi A., Chen J.C., Meade R.D., Joannopoulos J.D. Guided and defect modes in periodic dielectric waveguides. J. Opt. Soc. Am. B., 1995, 12, P. 1267–1272.
18. Du J., Liu S., Lin Z., Zi J., Chui S.T. Dielectric-based extremely-low-loss subwavelength-light transport at the nanoscale: An alternative to surface-plasmon-mediated waveguiding. Phys. Rev. A, 2011, 83, P. 035803.
19. Savelev R.S., Slobozhanyuk A.P., Miroshnichenko A.E., Kivshar Y.S., Belov P.A. Subwavelength waveguides composed of dielectric nanoparticles. Phys. Rev. B, 2014, 89, P. 035435.
20. Bakker R.M., Yu Y.F., Paniagua-Dom´ınguez R., Luk’yanchuk B., Kuznetsov A.I. Resonant Light Guiding Along a Chain of Silicon Nanoparticles. Nano Lett., 2017, 17, P. 3458–3464.
21. Kuznetsov A.I., Miroshnichenko A.E., Brongersma M.L., Kivshar Y.S., Luk’yanchuk B. Optically resonant dielectric nanostructures. Science, 2016, 354.
22. Savelev R.S., Filonov D.S., Kapitanova P.V., Krasnok A.E., Miroshnichenko A.E., Belov P.A., Kivshar Y.S. Bending of electromagnetic waves in all-dielectric particle array waveguides. Appl. Phys. Lett., 2014, 105, P. 181116.
23. Kivshar Y.S. Nonlinear Tamm states and surface effects in periodic photonic structures. Laser Phys. Lett., 2008, 5, P. 703.
24. Garanovich I.L., Sukhorukov A.A., Kivshar Y.S. Defect-Free Surface States in Modulated Photonic Lattices. Phys. Rev. Lett., 2008, 100, P. 203904.
25. Evlyukhin A.B., Reinhardt C., Seidel A., Luk’yanchuk B.S., Chichkov B.N. Optical response features of Si-nanoparticle arrays. Phys. Rev. B, 2010, 82, P. 045404.
26. Evlyukhin A., Reinhardt C., Chichkov B. Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation. Phys. Rev. B, 2011, 23, P. 235429.
27. Novotny L., Hecht B. Principles of Nano-optics. Cambridge University Press, New York, 2006.
28. Su W.P., Schrieffer J.R., Heeger A.J. Solitons in Polyacetylene. Phys. Rev. Lett., 1979, 42, P. 1698–1701.
29. Gorlach M., Slobozhanyuk A. Nonlinear topological states in the Su-Schrieffer-Heeger model. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8, P. 695–700.
30. Plotnik Y., Rechtsman M.C., Song D., Heinrich M., Zeuner J.M., Nolte S., Lumer Y., Malkova N., Xu J., Szameit A., Chen Z., Segev M. Observation of unconventional edge states in “photonic graphene”. Nature Mater., 2013, 13, P. 57–62.
31. Li L., Xu Z., Chen S. Topological phases of generalized Su-Schrieffer-Heeger models. Phys. Rev. B, 2014, 89, P. 085111.
Review
For citations:
Savelev R.S. Edge states in coupled periodic dielectric waveguides induced by long-range interaction. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(6):716–723. https://doi.org/10.17586/2220-8054-2018-9-6-716-723
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