This paper presents a stabilized scheme that solves the wave propagation problem in a general bianisotropic, stratified medium. The method utilizes the concept of propagators, i.e., the wave propagation operators that map the total tangential electric and magnetic fields from one plane in the slab to another. The scheme transforms the propagator approach into a scattering matrix form, where a spectral decomposition of the propagator enables separation of the exponentially growing and decaying terms in order to obtain a well-conditioned formulation. Multilayer structures can be handled in a stable manner using the dissipative property of the Redheffer star product for cascading scattering matrices. The reflection and transmission dyadics for a general bianisotropic medium with an isotropic half space on both sides of the slab are presented in a coordinate-independent dyadic notation, as well as the reflection dyadic for a bianisotropic slab with perfect electric conductor backing (PEC). Several numerical examples that illustrate the performance of the stabilized algorithm are presented.
2. Clemmow, P. C., The Plane Wave Spectrum Representation of Electromagnetic Fields, Pergamon Press, New York, 1966.
3. Digani, J., P. W. Hon, and A. R. Davoyan, "Framework for expediting discovery of optimal solutions with blackbox algorithms in non-topology photonic inverse design," ACS Photonics, Vol. 9, No. 2, 432-442, 2022.
doi:10.1021/acsphotonics.1c01819
4. Hale, N., I. Simonsen, C. Brune, and M. Kildemo, "Use of 4 x 4 transfer matrix method in the study of surface magnon polaritons via simulated attenuated total re ection measurements on the antiferromagnetic semiconductor mnf 2," Physical Review B, Vol. 105, No. 10, 104421, 2022.
doi:10.1103/PhysRevB.105.104421
5. Ji, W., T. Cai, Z. Xi, and P. Urbach, "Highly efficient and broadband achromatic transmission metasurface to refract and focus in microwave region," Laser & Photonics Reviews, Vol. 16, No. 1, 2100333, 2022.
doi:10.1002/lpor.202100333
6. Ko, D. Y. K. and J. Sambles, "Scattering matrix method for propagation of radiation in strati ed media: Attenuated total reflection studies of liquid crystals," JOSA A, Vol. 5, No. 11, 1863-1866, 1988.
doi:10.1364/JOSAA.5.001863
7. Kohlberger, C. and A. Stelzer, "Multi-modal scattering and propagation through several close periodic grids," IEEE Transactions on Antennas and Propagation, Vol. 70, No. 7, 5758-5769, 2022.
doi:10.1109/TAP.2022.3161327
8. Kristensson, G., S. Poulsen, and S. Rikte, "Propagators and scattering of electromagnetic waves in planar bianisotropic slabs --- An application to frequency selective structures," Progress In Electromagnetics Research, Vol. 48, 1-25, 2004.
doi:10.2528/PIER04031503
9. Kristensson, G., Scattering of Electromagnetic Waves by Obstacles. Mario Boella Series on Electromagnetism in Information and Communication, SciTech Publishing, Edison, NJ, USA, 2016.
doi:10.1049/SBEW524E
10. Kumar, N. and J. Saraf, "Tunable reflectance characteristics of magnetized cold plasma based one-dimensional defective photonic crystal," Optik, Vol. 252, 168577, 2022.
doi:10.1016/j.ijleo.2022.168577
11. Li, B. and Z. Shen, "Wideband 3d frequency selective rasorber," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 12, 6536-6541, 2014.
doi:10.1109/TAP.2014.2361892
12. Li, L., "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," JOSA A, Vol. 13, No. 5, 1024-1035, 1996.
doi:10.1364/JOSAA.13.001024
13. Li, Z.-Y. and L.-L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Physical Review E, Vol. 67, No. 4, 046607, 2003.
doi:10.1103/PhysRevE.67.046607
14. Lindell, I. V., A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media, Artech House, Boston, MA, 1994.
15. Luque-Raigon, J. M., J. Halme, H. Miguez, and G. Lozano, "Symmetry analysis of the numerical instabilities in the transfer matrix method," Journal of Optics, Vol. 15, No. 12, 125719, 2013.
doi:10.1088/2040-8978/15/12/125719
16. Marigo, J.-J. and A. Maurel, "Second order homogenization of subwavelength strati ed media including nite size effect," SIAM Journal on Applied Mathematics, Vol. 77, No. 2, 721-743, 2017.
doi:10.1137/16M1070542
17. Menzel, C., J. Sperrhake, and T. Pertsch, "Efficient treatment of stacked metasurfaces for optimizing and enhancing the range of accessible optical functionalities," Physical Review A, Vol. 93, No. 6, 063832, 2016.
doi:10.1103/PhysRevA.93.063832
18. Michalski, K. A., "Modal transmission line theory of plane wave excited layered media with multiple conductive anisotropic sheets at the interfaces," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 226, 19-28, 2019.
doi:10.1016/j.jqsrt.2019.01.010
19. Ning, J. and E. L. Tan, "Hybrid matrix method for stable analysis of electromagnetic waves in strati ed bianisotropic media," IEEE Microwave and Wireless Components Letters, Vol. 18, No. 10, 653-655, 2008.
doi:10.1109/LMWC.2008.2003446
20. Norgren, M., "Optimal design using strati ed bianisotropic media: Application to anti-re ection coatings," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 7, 939-959, 1998.
doi:10.1163/156939398X01178
21. Norgren, M., "Wave-splitting approaches to direct and inverse frequency-domain scattering of electromagnetic waves from strati ed bianisotropic materials,", Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden, 1996.
doi:10.1163/156939398X01178
22. Orfanidis, S., Electromagnetic Waves and Antennas, Sophocles J. Orfanidis, 2016.
23. Ourir, A., Y. Gao, A. Maurel, and J.-J. Marigo, "Homogenization of thin and thick metamaterials and applications," Metamaterials --- Devices and Applications, 149-165, 2017.
24. Pendry, J., "Photonic band structures," Journal of Modern Optics, Vol. 41, No. 2, 209-229, 1994.
doi:10.1080/09500349414550281
25. Pozar, D. M., Microwave Engineering, John Wiley & Sons, New York, NY, 1998.
26. Ranjbar, A. and A. Grbic, "Analysis and synthesis of cascaded metasurfaces using wave matrices," Physical Review B, Vol. 95, No. 20, 205114, 2017.
doi:10.1103/PhysRevB.95.205114
27. Redheffer, R., "On the relation of transmission-line theory on scattering and transfer," J. Math. Phys., Vol. 41, 1-41, 1962.
doi:10.1002/sapm19624111
28. Riga, J. and R. Seviour, "Electromagnetic analogs of quantum mechanical tunneling," Journal of Applied Physics, Vol. 132, No. 20, 200901, 2022.
doi:10.1063/5.0118308
29. Rikte, S., M. Andersson, and G. Kristensson, "Homogenization of woven materials," Arch. Elektron. Ubertragungstech, Vol. 53, No. 5, 261-271, 1999.
30. Rikte, S., G. Kristensson, and M. Andersson, "Propagation in bianisotropic media --- Reflection and transmission," IEE Proc. Microwaves Antennas and Propag., Vol. 148, No. 1, 29-36, 2001.
doi:10.1049/ip-map:20010215
31. Rumpf, R. C., "Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention," Progress In Electromagnetics Research B, Vol. 35, 241-261, 2011.
doi:10.2528/PIERB11083107
32. Silveirinha, M. G. and C. A. Fernandes, "Homogenization of metamaterial surfaces and slabs: The crossed wire mesh canonical problem," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 1, 59-69, 2005.
doi:10.1109/TAP.2004.840538
33. Sjoberg, D., "Analysis of wave propagation in strati ed structures using circuit analogs, with application to electromagnetic absorbers," Eur. J. Phys., Vol. 29, 721-734, 2008.
doi:10.1088/0143-0807/29/4/007
34. Sjoberg, D., "Circuit analogs for wave propagation in strati ed structures," Wave Propagation in Materials for Modern Applications, 489-508, A. Petrin (ed.), InTech, 2010.
35. Sperrhake, J., M. Decker, M. Falkner, S. Fasold, T. Kaiser, I. Staude, and T. Pertsch, "Analyzing the polarization response of a chiral metasurface stack by semi-analytic modeling," Optics Express, Vol. 27, No. 2, 1236-1248, 2019.
doi:10.1364/OE.27.001236
36. Yang, H.-Y. D., "A spectral recursive transformation method for electromagnetic waves in generalized anisotropic layered media," IEEE Trans. Antennas Propag., Vol. 45, No. 3, 520-526, 1997.
doi:10.1109/8.558667
37. Yu, Y., G. Q. Luo, A. A. Omar, X. Liu, W. Yu, Z. C. Hao, and Z. Shen, "3d absorptive frequency selective re ection and transmission structures with dual absorption bands," IEEE Access, 72880-72888, 2018.
doi:10.1109/ACCESS.2018.2881744
38. Zaky, Z. A., A. Panda, P. D. Pukhrambam, and A. H. Aly, "The impact of magnetized cold plasma and its various properties in sensing applications," Scienti c Reports, Vol. 12, No. 1, 1-12, 2022.
doi:10.1038/s41598-021-99269-x
Submit
