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Optical and Quantum Electronics

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01-06-2019

Analyzing honeycomb photonic crystal waveguides by Dirichlet-to-Neumann maps

Authors: Mengmeng Wang, Zhen Hu

Published in: Optical and Quantum Electronics | Issue 6/2019

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Abstract

As an analog to graphene, honeycomb photonic crystals (PhCs) have attracted a great deal of interest in recent years. The additional degrees of freedom in a honeycomb PhC are useful in designing and optimizing waveguides, can be used to control the symmetry of the system and to realize novel optical devices. In this paper, we present an efficient numerical method for analyzing two-dimensional honeycomb PhC waveguides. Our method is based on a special supercell that covers one period of the honeycomb PhC waveguide and the so-called Dirichlet-to-Neumann map of the supercell. The method gives rise to a linear eigenvalue value problem with relatively small matrices, and it is validated by comparing with previous works. As an application of the method, we calculate edge modes for a few different PhCs. For a honeycomb PhC with dielectric rods in air, we found an edge mode at the zigzag edge, without using special modified rods at the edge. For a honeycomb PhC with air holes, we found a new edge mode when the PhC is bounded by a perfectly electric conductor.

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Adibi, A., Xu, Y., Lee, R.K., Yariv, A., Scherer, A.: Properties of the slab modes in photonic crystal optical waveguides. J. Lightwave Technol. 18(11), 1554–1564 (2000)ADSCrossRef

Ao, X., Lin, Z., Chan, C.: One-way edge mode in a magneto-optical honeycomb photonic crystal. Phys. Rev. B 80(3), 033105 (2009)ADSCrossRef

Axmann, W., Kuchment, P.: An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. scalar case. J. Comput. Phys. 150(2), 468–481 (1999)ADSMathSciNetCrossRef

Cassagne, D., Jouanin, C., Bertho, D.: Photonic band gaps in a two-dimensional graphite structure. Phys. Rev. B 52(4), R2217–R2220 (1995)ADSCrossRef

David, A., Benisty, H., Weisbuch, C.: Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape. Phys. Rev. B 73(7), 075107 (2006)ADSCrossRef

Dossou, K., Byrne, M.A., Botten, L.C.: Finite element computation of grating scattering matrices and application to photonic crystal band calculations. J. Comput. Phys. 219(1), 120–143 (2006)ADSMathSciNetCrossRef

Escalante, J.M., Martínez, A., Laude, V.: Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs. J. Appl. Phys. 115(6), 064302 (2014)ADSCrossRef

Haldane, F., Raghu, S.: Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100(1), 013904 (2008)ADSCrossRef

Hu, Z., Lu, Y.Y.: Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps. Opt. Express 16(22), 17383–17399 (2008)ADSCrossRef

Hu, Z., Lu, Y.Y.: Efficient numerical modeling of photonic crystal heterostructure devices. J. Lightwave Technol. 33(10), 2012–2018 (2015)ADSCrossRef

Huang, Y., Lu, Y.Y.: Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps. J. Lightwave Technol. 24(9), 3448–3453 (2006)ADSCrossRef

Huang, Y., Lu, Y.Y., Li, S.: Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps. JOSA B 24(11), 2860–2867 (2007)ADSCrossRef

Jia, H., Yasumoto, K.: Rigorous analysis of guided modes of two-dimensional metallic electromagnetic crystal waveguides. J. Electromag. Waves Appl. 19(14), 1919–1933 (2005)CrossRef

Joannopoulos, J.D., Johnson, S.G., Winn, J.N., Meade, R.D.: Photonic Crystals: Molding the Flow of Light, 2nd edn. Princeton University Press, Princeton, NJ (2008)MATH

Ma, P., Jäckel, H.: Low crosstalk waveguide intersections in honeycomb lattice photonic crystals for tm-polarized light. J. Opt. 13(9), 095501 (2011)ADSCrossRef

Ma, P., Kaspar, P., Fedoryshyn, Y., Strasser, P., Jäckel, H.: Inp-based planar photonic crystal waveguide in honeycomb lattice geometry for tm-polarized light. Opt. Lett. 34(10), 1558–1560 (2009)ADSCrossRef

Novoselov, K.S., Geim, A.K., Morozov, S., Jiang, D., Katsnelson, M., Grigorieva, I., Dubonos, S., Firsov, A.: Two-dimensional gas of massless dirac fermions in graphene. Nature 438(7065), 197–200 (2005)ADSCrossRef

Novoselov, K.S., Fal, V., Colombo, L., Gellert, P., Schwab, M., Kim, K.A.: Roadmap for graphene. Nature 490(7419), 192–200 (2012)ADSCrossRef

Ochiai, T., Onoda, M.: Photonic analog of graphene model and its extension: dirac cone, symmetry, and edge states. Phys. Rev. B 80(15), 155103 (2009)ADSCrossRef

Ouyang, C., Xiong, Z., Zhao, F., Dong, B., Hu, X., Liu, X., Zi, J.: Slow light with low group-velocity dispersion at the edge of photonic graphene. Phys. Rev. A 84(1), 015801 (2011)ADSCrossRef

Pendry, J.B.: Calculating photonic band structure. J. Phys. Condens. Matter 8(9), 1085–1108 (1996)ADSCrossRef

Polini, M., Guinea, F., Lewenstein, M., Manoharan, H.C., Pellegrini, V.: Artificial honeycomb lattices for electrons, atoms and photons. Nature Nanotechnol. 8(9), 625–633 (2013)ADSCrossRef

Poo, Y., Wu, Rx, Lin, Z., Yang, Y., Chan, C.: Experimental realization of self-guiding unidirectional electromagnetic edge states. Phys. Rev. Lett. 106(9), 093903 (2011)

Prather, D.W., Sharkawy, A., Shi, S., Murakowski, J., Schneider, G.: Photonic Crystals: Theory, Applications, and Fabrication. Wiley, Hoboken, NJ (2009)

Puerto, D., Griol, A., Escalante, J.M., Pennec, Y., Djafari-Rouhani, B., Beugnot, J.C., Laude, V., Martínez, A.: Honeycomb photonic crystal waveguides in a suspended silicon slab. IEEE Photon. Technol. Lett. 24(22), 2056–2059 (2012)ADSCrossRef

Sepkhanov, R., Bazaliy, Y.B., Beenakker, C.: Extremal transmission at the dirac point of a photonic band structure. Phys. Rev. A 75(6), 063813 (2007)ADSCrossRef

Wen, F., David, S., Checoury, X., El Kurdi, M., Boucaud, P.: Two-dimensional photonic crystals with large complete photonic band gaps in both te and tm polarizations. Opt. Express 16(16), 12278–12289 (2008)ADSCrossRef

Wu, H., Citrin, D., Jiang, L., Li, X.: Polarization-independent single-mode waveguiding with honeycomb photonic crystals. IEEE Photon. Technol. Lett. 27(8), 840–843 (2015)ADSCrossRef

Xu, X., Gu, H., Zheng, Y., Wei, M., Zheng, D., Xiao, R., Qiang, Z.: Polarization beam splitter based on honeycomb-lattice photonic crystal ring resonators. J. Mod. Opt. 61(5), 373–378 (2014)ADSCrossRef

Ye, C., Hu, Z.: Computing equifrequency contours of two-dimensional photonic crystals by Dirichlet-to-Neumann maps. J. Mod. Opt. 64(2), 196–204 (2017)ADSMathSciNetCrossRef

Yu, C.P., Chang, H.C.: Applications of the finite difference mode solution method to photonic crystal structures. Opt. Quantum Electron. 36(1–3), 145–163 (2004)CrossRef

Yuan, J., Lu, Y.Y.: Photonic bandgap calculations with Dirichlet-to-Neumann maps. JOSA A 23(12), 3217–3222 (2006)ADSMathSciNetCrossRef

Yuan, J., Lu, Y.Y.: Computing photonic band structures by Dirichlet-to-Neumann maps: the triangular lattice. Opt. Commun. 273(1), 114–120 (2007)ADSCrossRef

Zoli, R., Gnan, M., Castaldini, D., Bellanca, G., Bassi, P.: Reformulation of the plane wave method to model photonic crystals. Opt. Express 11(22), 2905–2910 (2003)ADSCrossRef

Title: Analyzing honeycomb photonic crystal waveguides by Dirichlet-to-Neumann maps
Authors: Mengmeng Wang
Zhen Hu
Publication date: 01-06-2019
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 6/2019
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-019-1890-0

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