The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.
References
[1]
Farjallah, H., Hassiba, H. and Ghozlen, M.H.B. (2016) Application of the Plane Wave Expansion and Stiffness Matrix Methods to Study Transmission Properties and Guided Mode of Phononic Plates. Wave Motion, 64, 68-78. https://doi.org/10.1016/j.wavemoti.2016.03.001
[2]
Zhou, Y., Chen, H. and Zhou, A. (2019) Plane Wave Methods for Quantum Eigenvalue Problems of Incommensurate Systems. Journal of Computational Physics, 384, 99-113. https://doi.org/10.1016/j.jcp.2019.02.003
[3]
Pan, Y., Dai, X., de Gioronocoli, S., Gong, X., Rignanese, G. and Zhou, A. (2017) A Parallel Orbital-Updated Based Plane-Wave Basis Method for Electronic Structure Calculations. Journal of Computational Physics, 348, 482-492. https://doi.org/10.1016/j.jcp.2017.07.033
[4]
Joannopoulos, J.D., Meade, R.D. and Winn, J.N. (1995) Photonic Crystals Modeling the Flow of Light. Princeton University Press, Princeton.
[5]
Johnson, S.G. and Joannopoulos, J.D. (2002) Photonic Crystal the Road from Theory to Practice. Kluwer Academic Publishing, Boston.
[6]
Sukhoivanov, I.A. and Guryev, I.V. (2009) Photonic Crystals Physics and Practical Modeling. Springer, Berlin.
[7]
Liew, S.F., Knitter, S., Xiong, W. and Cao, H. (2015) Photonic Crystals with Topological Defects. Physical Review A, 91, Article ID: 023811.
[8]
Cornelious, S.R., Sahoo, T., Sujatha, A. and Chelliah, P. (2019) Study of Symmetric and Asymmetric Defect Positions in a Photonic Crystal Supercell. Optics Communications, 450, 22-27. https://doi.org/10.1016/j.optcom.2019.05.014
[9]
Zhang, T., Sun, J., Yang, Y. and Li, Z. (2018) Photonic Crystal Filter Based on Defect Mode and Waveguide Mode Symmetry Matching. Optics Communications, 428, 53-56. https://doi.org/10.1016/j.optcom.2018.07.039
[10]
Mackay, T.G. and Lakhtakia, A. (2019) Electromagnetic Anisotropy and Bianisotropy A Field Guide. Second Edition, World Scientific, London.
[11]
Razzaz, F. and Alkanhal, M.A.S. (2018) Resonances in Bianisotropic Layers. IEEE Photonics Journal, 10, Article ID: 6100112. https://doi.org/10.1109/JPHOT.2017.2782742
[12]
Jakoby, B. and Baghai-Wadji, A. (1996) Analysis of Bianisotropic Layered Structures with Laterally Periodic Inhomogeneities—An Eigenvector Formulation. IEEE Transactions on Antennas and Propagation, 44, 615-626. https://doi.org/10.1109/8.496247
[13]
Kong, J.A. (2008) Electromagnetic Wave Theory. EMW Publishing, Cambridge.
[14]
Post, E.J. (1967) Sagnac Effect. Reviews of Modern Physics, 39, 475-493. https://doi.org/10.1103/RevModPhys.39.475
[15]
Lakhtakia, A. and Mackay, T. (2004) Towards Gravitationally Assisted Negative Refraction of Light in Vacuum. Journal of Physics A: Mathematical and General, 37, L505-L510.
[16]
Ivannenko, Y., Gustafsson, M. and Nordebo, S. (2019) Optical Theorems and Physical Bounds on Absorption in Lossy Media. Optics Express, 27, 34323-34341. https://doi.org/10.1364/OE.27.034323
[17]
Xu, X., Quan, B., Gu, C. and Wang, L. (2006) Bianisotropic Response of Microfrabricated Metamaterials in the Terahertz Region. Journal of the Optical Society of America B, 23, 1174-1180. https://doi.org/10.1364/JOSAB.23.001174
[18]
Mulkey, T., Dillies, J. and Durach, M. (2018) Inverse Problem of Quartic Photonics. Optics Letters, 43, 1266-1229. https://doi.org/10.1364/OL.43.001226
[19]
Gangaraj, A.A.H. and Hanson, G.W. (2017) Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material from a Classical Electromagnetics Perspective. IEEE Journal on Multiscale and Multiphysics Computational Techniques, 2, 3-17. https://doi.org/10.1109/JMMCT.2017.2654962
[20]
Durach, M., Williamson, R., Laballe, M. and Mulkey, T. (2020) Tri- and Tetra-Hyperbolic Iso-Frequency Topologies Complete Classification of Bi-Anisotropic Materials. Applied Sciences, 10, 763. https://doi.org/10.3390/app10030763
[21]
Durach, M. (2020) Tetra-Hyperbolic and Tri-Hyperbolic Optical Phase in Anisotropic Metamaterials without Magnetoelectric Coupling Due to Hybridization of Plasmonic and Magnetic Block High-K Polaritons. Optics Communications, 476, Article ID: 126349.
[22]
Kong, J.A. (1972) Theorems of Bianisotropic Media. Proceedings of the IEEE, 60, 1036-1046. https://doi.org/10.1109/PROC.1972.8851
[23]
Kang, M., Zhang, T., Zhao, B., Sun, L. and Chen, J. (2021) Chirality of Exceptional Points in Bianisotropic Metasurfaces. Optics Express, 29, 11582-11590. https://doi.org/10.1364/OE.419511
[24]
Heiss, W.D. (2004) Exceptional Points of Non-Hermitian Operators. Journal of Physics A: Mathematical and General, 37, 2455-2464. https://doi.org/10.1088/0305-4470/37/6/034
[25]
Miri, M. and Alu, A. (2019) Exceptional Points in Optics and Photonics. Science, 363, eaar7709. https://doi.org/10.1126/science.aar7709
