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SIMPLE RELATIONS BETWEEN A UNIAXIAL MEDIUM AND AN ISOTROPIC MEDIUM

By S. G. Sen

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Abstract:
In this article, in a simple way, simple relations are derived between the electric field components of an electrically uniaxial medium and those of an isotropic medium. The permittivity of the isotropic medium is the same as the permittivity of the uniaxial medium that is common to the axes transverse to the optic axis. Using the spectral representation, the vector wave equation for the electric field intensity vector of the uniaxial medium is solved for the x directed, y directed and z directed point sources. For the x directed and y directed point sources, the electric field components transverse to the optic axis are written in terms of the corresponding components of the isotropic medium plus some other terms. Part of these terms are closed forms expressions, and the rest are Sommerfeld type integrals. Elements of each group are related to each other by coordinate transformations. The electric field components parallel to the optic axis are shown to be obtained from the isotropic medium components using coordinate transformations. The relations between the uniaxial medium and isotropic medium field components are verified by comparing the results of a previous study in the literature to the results obtained using the relations in this study. Good agreement is achieved between these results.

Citation:
S. G. Sen, "Simple Relations Between a Uniaxial Medium and an Isotropic Medium," Progress In Electromagnetics Research B, Vol. 60, 79-93, 2014.
doi:10.2528/PIERB14041311

References:
1. Clemmow, P. C., "The theory of electromagnetic waves in a simple anisotropic medium," Proceedings IEE, Vol. 110, 101-106, Jan. 1963.

2. Felsen, L. B. and N. Marcuwitzv, Radiation and Scattering of Waves, Wiley-IEEE Press, New Jersey, 2003.

3. Chen, H. C., Theory of Electromagnetic Waves, McGraw-Hill, New York, 1983.

4. Weiglhofer, W. S., "Dyadic Green's functions for general uniaxial media," Proceedings IEE, Vol. 137, 5-10, Feb. 1990.

5. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.

6. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, 1986.

7. Born, M., E. Wolf, and , "Principles of Optics," Cambridge University Press, 1999.

8. Lakhtakia, A., V. K. Varadan, and V. V. Varadan, "Radiation and canonical sources in uniaxial dielectric media," International Journal of Electronics, Vol. 65, No. 6, 1171-1175, 1988.
doi:10.1080/00207218808945319

9. Lakhtakia, A., V. V. Varadan, and V. K. Varadan, "Time-harmonic and time-dependent dyadic Green's functions for some uniaxial gyro-electromagnetic media," Applied Optics, Vol. 28, No. 6, 1049-1052, 1989.
doi:10.1364/AO.28.001049

10. Weiglhofer, W., "Analytic methods and free-space dyadic Green-functions," Radio Science, Vol. 28, No. 5, 847-857, 1993.
doi:10.1029/93RS00903

11. Weiglhofer, W. S. and I. V. Lindell, "Analytic solution for the dyadic Green-function of a non-reciprocal uniaxial bianisotropic medium," International Journal of Electronics and Communications, Vol. 48, No. 2, 116-119, Mar. 1994.

12. Weiglhofer, W. S., "Dyadic Green-function for unbounded general uniaxial bianisotropic medium," International Journal of Electronics, Vol. 77, No. 1, 105-115, Jul. 1994.
doi:10.1080/00207219408926039

13. Weiglhofer, W. S. and A. Lakhtakia, "New expressions for depolarization dyadics in uniaxial dielectric-magnetic media," International Journal of Infrared and Millimeter Waves, Vol. 17, No. 8, 1365-1376, Aug. 1996.
doi:10.1007/BF02068788

14. Olyslager, F. and B. Jakoby, "Time-harmonic two- and three-dimensional Green dyadics for a special class of gyrotropic bianisotropic media," IEE Proceedings --- Microwaves Antennas and Propagation, Vol. 143, No. 5, 413-416, Oct. 1996.
doi:10.1049/ip-map:19960589

15. Marklein, R., K. J. Langenberg, and T. Kaczorowski, "Electromagnetic and elastodynamic point source excitation of unbounded homogeneous anisotropic media," Radio Science, Vol. 31, No. 6, 1919-1930, 1996.
doi:10.1029/96RS02155

16. Lindell, I. V., "Decomposition of electromagnetic fields in bi-anisotropic media," Journal of Electromagnetic Waves and Applications, Vol. 11, No. 5, 645-657, 1997.
doi:10.1163/156939397X00882

17. Cheng, D., J, W. Ren, and Y. Q. Jin, "Green dyadics in uniaxial bianisotropic-ferrite medium by cylindrical vector wavefunctions," Journal of Physics A --- Mathematical and General, Vol. 30, No. 2, 573-585, 1997.
doi:10.1088/0305-4470/30/2/020

18. Olyslager, F. and I. V. Lindell, "Green's dyadics for a class of bi-anisotropic media with nonsymmetric bi-anisotropic dyadics," AEU --- International Journal of Electronics and Communications, Vol. 52, No. 1, 32-36, 1998.

19. Weiglhofer, W. S., "New expressions for depolarization dyadics in an axially uniaxial bianisotropic medium," International Journal of Infrared and Millimeter Waves, Vol. 19, No. 7, 993-1005, Jul. 1998.
doi:10.1023/A:1022631609746

20. Weiglhofer, W. S., "Scalar Hertz potentials for nonhomogeneous uniaxial dielectric-magnetic mediums," International Journal of Applied Electromagnetics and Mechanics, Vol. 11, No. 3, 131-140, 2000.

21. Liu, S. H., L. W. Li, M. S. Leong, and T. S. Yeo, "Field representations in general rotationally uniaxial anisotropic media using spherical vector wave functions," Microwave and Optical Technology Letters, Vol. 25, No. 3, 159-162, 2000.
doi:10.1002/(SICI)1098-2760(20000505)25:3<159::AID-MOP2>3.0.CO;2-F

22. Weiglhofer, W. S., "The connection between factorization properties and closed-form solutions of certain linear dyadic diĀ®erential operators," Journal of Physics A --- Mathematical and General, Vol. 33, No. 35, 6253-6261, 2000.
doi:10.1088/0305-4470/33/35/312

23. Li, L. W., N. H. Lim, M. S. Leong, T. S. Yeo, and J. A. Kong, "Cylindrical vector wave function representation of Green's dyadics for uniaxial bianisotropic media," Radio Science, Vol. 36, No. 4, 517-523, 2001.
doi:10.1029/2000RS002557

24. Li, K., S. O. Park, H. J. Lee, and W. Y. Pan, "Dyadic Green's function for an unbounded gyroelectric chiral medium in cylindrical coordinates," 3rd International Symposium on Electromagnetic Compatibility, 668-671, Beijing, 2002.

25. Tan, E. L., "Vector wave function expansions of dyadic Green's functions for bianisotropic media," IEE Proceedings --- Microwaves Antennas and Propagation, Vol. 149, No. 1, 57-63, Feb. 2002.
doi:10.1049/ip-map:20020292

26. Olyslager, F. and I. V. Lindell, "Electromagnetics and exotic media: A quest for the holy grail," IEEE Antennas and Propagation Magazine, Vol. 44, No. 2, 48-58, 2002.
doi:10.1109/MAP.2002.1003634

27. Lakhtakia, A. and T. G. Mackay, "Simple derivation of dyadic green functions of a simply moving, isotropic, dielectric-magnetic medium," Microwave and Optical Technology Letters, Vol. 48, No. 6, 1073-1074, 2006.
doi:10.1002/mop.21604

28. Havrilla, M. J., "Scalar potential depolarizing dyad artifact for a uniaxial medium," Progress In Electromagnetics Research, Vol. 134, 151-168, 2013.
doi:10.2528/PIER12101214


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