Fresnel coefficients for three-layered uniaxially anisotropic media with arbitrarily oriented optic axes have been obtained using half-space reflection and transmission coefficients. The optic axes of the anisotropic media are assumed to be tilted at different angles ((Ψi, χi), i = 1,2). This gives arbitrary orientation for anisotropic medium in the stratified configuration. The half space coefficients are derived at the boundary surfaces of two different media including isotropic-anisotropic, anisotropic-anisotropic, anisotropic-isotropic interfaces with the application of boundary conditions. The interface between two media for the three-layered media leads to four different cases of wave propagation, which are analyzed in detail. The results are compared with the existing results in the limiting cases analytically. The results presented in this paper can be used to establish dyadic Green's functions, which can be used to calculate radiation and scattering from the stratified structure.
2. Kong, J. A., Theory of Electromagnetic Waves, 1st Ed., Wiley-Interscience, New York, 1975.
3. Landau, L. D., L. P. Pitaevski, and E. M. Lifshitz, Electrodynamics of Continous Media, 2nd Ed., Butterworth-Heinemann, 1984.
4. Eroglu, A. and J. K. Lee, "Far field radiation from an arbitrarily orientated Hertzian dipole in the presence of layered anisotropic medium ," IEEE Trans. on Antennas and Propag., Vol. 53, 2005.
doi:10.1109/TAP.2005.859749
5. Lee, J. K. and J. A. Kong, "Dyadic Green's functions for layered anisotropic medium," Electromagnetics, Vol. 3, 111, 1983.
doi:10.1080/02726348308915180
6. Wheeland, S., A. V. Amirkhizi, and S. Nemat-Nasser, "Soft-focusing in anisotropic indefinite media through hyperbolic dispersion," Progress In Electromagnetic Research, Vol. 132, 389-402, 2012.
7. Choudhury, P. K. and W. K. Soon, "On the tapered optical fibers with radially anisotropic liquid crystal clad," Progress In Electromagnetic Research, Vol. 115, 461-475, 2011.
8. Gajewski, D., "Radiation from point sources in general anisotropic media," Geophysical Journal International, Vol. 113, 299, 2007.
doi:10.1111/j.1365-246X.1993.tb00889.x
9. Cakoni, F., D. Colton, P. Monk, and J. Sun, "The inverse electromagnetic scattering problem for anisotropic media," Inverse Problems, Vol. 26, 1, 2010.
10. Yuan, J., C. Gu, and Z. Li, "Electromagnetic scattering by arbitrarily shaped stratified anisotropic media using the equivalent dipole moment method ," International Journal of RF and Microwave Computer-aided Eng., Vol. 20, 416, 2010.
doi:10.1002/mmce.20446
11. Geng, Y.-L., X.-B. Wu, and B. Guan, "Electromagnetic scattering from an anisotropic uniaxial-coated conducting sphere," PIERS Proceedings, 403-407, Hangzhou, China, Aug. 22-26, 2005.
12. Wong, K. and H. Chen, "Electromagnetic scattering by a uniaxially anisotropic sphere," IEE Proceedings H Microwaves, Antennas and Propagation, Vol. 139, No. 314, 1992.
13. Varadan, V. V., A. Lakhtakia, and V. K. Varadran, "Scattering by three-dimensional anisotropic scatterers," IEEE Trans. on Antennas and Propag., Vol. 37, 800, 1989.
doi:10.1109/8.29369
14. Slawinski, M. A., R. A. Slawinski, and R. J. Brown, "A generalized form of Snell's law in anisotropic media," Geophysics, Vol. 65, 632-637, Mar.-Apr. 2000.
15. Smith, D. R. and D. Shurig, "Electromagneticwave propagation in media with indefinite permittivity and permeability tensors materials ," Phys. Rev. Lett., Vol. 90, 077 405-1-4, Feb. 2003.
16. Landry, G. D. and T. A. Maldonado, "Complete method to determine transmission and reflection characteristics at a planar interface between arbitrarily oriented biaxial media," J. Opt. Soc. Am. A, Vol. 12, No. 9, 2048-2063, Sep. 1995.
doi:10.1364/JOSAA.12.002048
17. Stamnes, J. J. and G. S. Sithambaranathan, "Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating isotropic and biaxial medium," J. Opt. Soc. Am. A, Vol. 18, No. 12, 3119-3129, Dec. 2001.
doi:10.1364/JOSAA.18.003119
18. Grzegorczyk, T. M., M. Nikku, X. Chen, B.-I.Wu, and J. A. Kong, "Refraction laws for anisotropic media and their application to left-handed metamaterials," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 4, 1443-1450, 2005.
doi:10.1109/TMTT.2005.845206
19. Grzegorczyk, T. M., X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, Vol. 51, 83-113, 2005.
doi:10.2528/PIER04040901
20. Barkovskii, L. M., G. N. Borzdov, and A. V. Lavrinenko, "Fresnel's reflection transmission operators for stratified gyroanisotropic media," J. Phys. A: Math. Gen., Vol. 20, 1095-1106, 1987.
doi:10.1088/0305-4470/20/5/021
21. Furs, A. N. and T. A. Alexeeva, "Reflection and transmission of weakly inhomogeneous anisotropic and bianisotropic layers calculated by perturbation method," J. Phys. A: Math. Theor., Vol. 41, No. 6, 065203, 2008.
doi:10.1088/1751-8113/41/6/065203
22. Zhukovsky, S. V. and V. M. Galynsky, "Spectral and polarization effects in deterministically non-periodic multilayers containing optically anisotropic and gyrotropic materials," J. Opt. A: Pure Appl. Opt., Vol. 8, 489-500, 2006.
doi:10.1088/1464-4258/8/6/001
23. Golden, K. M. and S. F. Ackley, "Modeling of anisotropic electromagnetic reflection from sea ice," J. Geophys. Res., Vol. 86, No. c9, 8107-8116, Sep. 1981.
doi:10.1029/JC086iC09p08107
24. Nghiem, S. V., M. Borgreaud, J. A. Kong, and R. T. Shin, "Polarimetric remote sensing of geophysical media with layer random medium model ," Progress In Electromagnetic Research, Vol. 3, 1-73, 1990. Polarimetric Remote Sensing, J. A. Kong, Ed., Chapter 1, 1-73, Elsevier, Amsterdam, 1990.
25. Noble, B. and J. W. Daniel, Applied Linear Algebra, 3rd Ed., Chapter 3, Prentice-Hall, 1988.
26. Eroglu, A., Y. H. Lee, and J. K. Lee, "Dyadic Green's functions for multi-layered uniaxially anisotropic media with an arbitrarily oriented optic axes ," IET Microwaves, Antennas and Propagation, Vol. 5, No. 15, 1779-1788, Dec. 2011.
doi:10.1049/iet-map.2010.0499
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