Consider a plane wave incident on a multilayered planar anisotropic structure composed of conventional materials and metamaterials and surround by two half-spaces. In this paper, we aim to prove three theorems which indicate a kind of duality in these structures. Assume an arbitrarily polarized plane wave obliquely incident on the structures. Theorem 1: Assume that an arbitrarily polarized plane wave is obliquely incident on the structure. Now each layer is filled with by dual media according to the interchanges DPS ↔ DNG and ENG ↔ MNG. Then, the reflection (R) and transmission (T) coefficients of the structure become the complex conjugates of their counterparts. Consequently, the reflected power and transmitted power from the structure are the same for the two dual cases of anisotropic media. Theorem 2: If the interchanges DPS ↔ DNG and ENG ↔ MNG are made in all the layers except in the half spaces on the two sides of the multilayer structure (which is more realizable), then the reflection coefficients become complex conjugates and the reflected power remains the same. Theorem 3: If the structure is backed by a perfect electric conductor and the media interchanges DPS ↔ DNG and ENG ↔ MNG are made in the layers, then the reflection coefficients of the two dual structures become complex conjugates of each other, and the reflected powers are equal. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, these theorems hold true in case of any change in any of these conditions. In the last section, some examples are provided to verify the validity of the proposed theorems.
1. Teitler, S. and B. W. Henvis, "Refraction in stratified anisotropic media," J. Opt. Soc. Am., Vol. 60, 830-834, Jun. 1970. doi:10.1364/JOSA.60.000830
2. Berreman, D. W., "Optic in stratified and anisotropic media: 4 x 4 matrix formulation," J. Opt. Soc. Am., Vol. 62, 502-510, Apr. 1972. doi:10.1364/JOSA.62.000502
3. Barkovskii, L. M. and G. N. Borzdov, "Electromagnetic waves in absorbing plane-layered anisotropic and gyrotropic media," J. Appl. Spectrosc., Vol. 23, 985-991, Sept. 1976. doi:10.1007/BF00608828
4. Barkovskii, L. M. and G. N. Borzdov, "Reflection of electromagnetic waves from layered continuously inhomogeneous anisotropic media: Multiple reflection method," Opt. Spectrosc. (USSR), Vol. 45, 701-705, Oct. 1978.
5. Graglia, R. D. and P. L. E. Uslenghi, "Electromagnetic scattering from anisotropic materials, part I: General theory," IEEE Trans. Antennas Propagat., Vol. 32, 867-869, Aug. 1984. doi:10.1109/TAP.1984.1143422
6. Morgan, M. A., et al., "Electromagnetic scattering by stratified inhomogeneous anisotropic media," IEEE Trans. Antennas Propagat., Vol. 35, 191-198, Feb. 1987. doi:10.1109/TAP.1987.1144069
7. Graglia, R. D., et al., "Reflection and transmission for planar structures of bianisotropic media," Electromagnetics, Vol. 11, 193-208, 1991. doi:10.1080/02726349108908273
8. Titchener, J. B. and J. R. Willis, "The reflection of electromagnetic waves from stratified anisotropic media," IEEE Trans. Antennas Propagat., Vol. 39, 35-40, Jan. 1991. doi:10.1109/8.64432
9. Tsalamengas, J. L., "Interaction of electromagnetic waves with general bianisotropic slabs," IEEE Trans. Microwave Therory Tech., Vol. 40, 1870-1879, Oct. 1992. doi:10.1109/22.159623
10. Lindell, I. V., et al., "Vector Transmission-line and circuit theory for bi-isotropic layered structures," Journal of Electromagnetic Waves and Applications, Vol. 7, 147-173, 1993. doi:10.1163/156939393X01119
11. Yang, H. D., "A spectral recursive transformation method for electromagnetic waves in generalized anisotropic layered media," IEEE Trans. Antennas Propagat., Vol. 45, 520-527, Mar. 1997. doi:10.1109/8.558667
12. Ning, J. and E. L. Tan, "Hybrid matrix method for stable analysis of electromagnetic waves in stratified bianisotropic media," IEEE Microwave Wireless Comp. Lett., Vol. 18, 653-656, Oct. 2008. doi:10.1109/LMWC.2008.2003446
13. Kong, J. A., "Theory of Electromagnetic Waves," EMW Publishing, 2005.
14. Oraizi, H. and A. Abdolali, "Design and optimization of planar multilayer antireflection meta-material coatings at Ku band under circularly polarized oblique plane wave incidence," Progress In Electromagnetics Research C, Vol. 3, 1-18, 2008. doi:10.2528/PIERC08021906
15. Ziolkowski, R. W. and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E, tat. Phys. Plasmas Fluids Relat., Vol. 64, No. 5, 617-625, 2001.
16. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress In Electromagnetics Research, Vol. 35, 1-52, 2002. doi:10.2528/PIER01082101
17. Oraizi, H. and A. Abdolali, "Mathematical formulation for zero reflection from multilayer metamaterial structures and their notable applications," IET Microwaves, Antennas & Propagation, Vol. 3, No. 6, 987-996, Sep. 2009. doi:10.1049/iet-map.2008.0281
18. Oraizi, H. and A. Abdolali, "Several theorems for reflection and transmission coefficients of plane wave incidence on planar multilayer metamaterial structures," IET Microwaves, Antennas & Propagation Journal, Vol. 4, No. 11, 1870-1879, Nov. 2010. doi:10.1049/iet-map.2009.0468
19. Su, H. L. and K. H. Lin, "Design of an anisotropic quarter-wave polariser without insertion loss caused by mismatch," IEE Proc .--- Microw. Antennas Propag., Vol. 153, No. 3, 253-258, Jun. 2006. doi:10.1049/ip-map:20045144
20. Yang, H. D., "A spectral recursive transformation method for electromagnetic waves in generalized anisotropic layered media," IEEE Trans. Antennas Propagat., Vol. 45, 520-527, Mar. 1997. doi:10.1109/8.558667
21. Ning, J. and E. L. Tan, "Hybrid matrix method for stable analysis of electromagnetic waves in stratified bianisotropic media," IEEE Microwave Wireless Comp. Lett., Vol. 18, 653-656, Oct. 2008.