volume | PIER Journals

Abstract

A geometrical high-frequency approximation method for solving the propagation of electromagnetic wave through the quartic Wood lens into an uniaxial crystal is presented in this paper. Caustic problem of electromagnetic wave is translated into non-caustic problem by using the hybrid space. The drawback that the solution in the caustic region cannot be obtained with geometrical optics is overcome by this method known as Maslov's method. The high-frequency approximation solution that is valid around caustic region is obtained by using this method which combines the simplicity of ray and generality of the transform method. And the results are compared with those obtained by Huygens-Kirchhoff's expression.

1. Keller, J. B. and J. S. Papadakis, Wave Propagation and Underwater Acoustics, Springer-Verlag, 1977.

2. Kline, M. and I. Kay, Electromagnetic Theory and Geometrical Optics, Interscience, 1965.

3. Budden, K., The Propagation of Radio Waves, Cambridge University Press, 1985.

4. Maslov, V. and M. Fedoriuk, Semiclassical Approximation in Quantum Mechanics, Reidel Publications Co., 1981.

5. Klauder, J., Ann. Phys., 108-180, N.Y., 1987. Google Scholar

6. Kravtsov, Y. A. and Y. I. Orlov, Caustics, Catastrophes, and Wave Fields, 2nd Ed., Springer-Verlag, 1998.

7. Zhu, T., "A ray-Kirchhoff method for body-wave calculations in inhomogeneous media: Theory," Geophys. J., Vol. 92, 181-193, 1988.
doi:10.1111/j.1365-246X.1988.tb01133.x Google Scholar

8. Maslov, V. P., Perturbation Theory and Asymptotic Method, Gos. Univ., 1965 (in Russia). (Translated into Japanese by Ouchi et al., Iwanami, Tokyo, 1976.).

9. Kravtsov, Y. A., "Two new methods in the theory of wave propagation in inhomogeneous media (review)," Sov. Phys. Acoust., Vol. 14, No. 1, 1-17, 1968. Google Scholar

10. Kravtsov, Y. A. and Y. I. Orlov, Caustics, Catastrophes, and Wave Fields, 306, Springer-Verlag, 1993, 2nd edition, 1997.

11. Kravtsov, Y. A. and Y. I. Orlov, Geometrical Optics in Inhomogeneous Media, 312, Springer-Verlag, 1990.

12. Kravtsov, Y. A. and Y. I. Orlov, "Geometrical optics in engineering physics," Alpha Science, International Ltd., UK, 2005. 1990. Google Scholar

13. Gorman, A. D., S. P. Anderson, and R. B. Mohindra, "On caustic related to several common indices of refraction," Radio Sci., Vol. 21, 434-436, 1986.
doi:10.1029/RS021i003p00434 Google Scholar

14. Gorman, A. D., "Vector field near caustics," J. Math. Phys., Vol. 26, 1404-1407, 1985.
doi:10.1063/1.526954 Google Scholar

15. Ziolkowski, R. W. and G. A. Deschamps, "Asymptotic evaluation of high frequency field near a caustic: An introduction to Maslov's method," Radio Sci., Vol. 19, 1001-1025, 1984.
doi:10.1029/RS019i004p01001 Google Scholar

16. Hongo, K., Y. Ji, and E. Nakajimi, "High-frequency expression for the field in the caustic region of a reflector using Maslov's method," Radio Sci., Vol. 21, No. 6, 911-919, 1986.
doi:10.1029/RS021i006p00911 Google Scholar

17. Hongo, K. and Y. Ji, "High-frequency expression for the field in the caustic region of a cylindrical reflector using Maslov's method," Radio Sci., Vol. 22, No. 3, 357-366, 1987.
doi:10.1029/RS022i003p00357 Google Scholar

18. Hongo, K. and Y. Ji, "Study of the field around the focal region of spherical reflector antenna by Maslov's method," IEEE Trans. Antennas Propagat., Vol. 36, 592-598, May 1988.
doi:10.1109/8.192134 Google Scholar

19. Ji, Y. and K. Hongo, "Field in the focal region of a dielectric spherical by Maslov's method," J. Opt. Soc. Am. A, Vol. 8, 1721-1728, 1991.
doi:10.1364/JOSAA.8.001721 Google Scholar

20. Ji, Y. and K. Hongo, "Analysis of electromagnetic waves refracted by a spherical dielectric interface by Maslov's method," J. Opt. Soc. Am. A, Vol. 8, 541-548, 1991.
doi:10.1364/JOSAA.8.000541 Google Scholar

21. Ghaffar, A., Q. A. Naqvi, and K. Hongo, "Analysis of the fields in three dimensional Cassegrain system," Progress In Electromagnetics Research, Vol. 72, 215-240, 2007.
doi:10.2528/PIER07031602 Google Scholar

22. Ghaffar, A., A. Hussain, Q. A. Naqvi, and K. Hongo, "Radiation characteristics of an inhomogeneous slab," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2, 301-312, 2008.
doi:10.1163/156939308784160695 Google Scholar

23. Ghaffar, A., Q. A. Naqvi, and K. Hongo, "Study of focusing of field refracted by a cylindrical plano-convex lens into a uniaxial crystal by using Maslov's method," Journal of Electromagnetic Waves and Applications, Vol. 22, 665-679, 2008.
doi:10.1163/156939308784159499 Google Scholar

24. Ghaffar, A., Q. A. Naqvi, and K. Hongo, "Focal region fields of three dimensional Gregorian system," Optics Communications, Vol. 281, 1343-1353, 2008.
doi:10.1016/j.optcom.2007.11.011 Google Scholar

25. Ghaffar, A. and Q. A. Naqvi, "Focusing of electromagnetic plane wave into uniaxial crystal by a three dimensional plano convex lens," Progress In Electromagnetics Research, Vol. 83, 25-42, 2008.
doi:10.2528/PIER08041404 Google Scholar

26. Ghaffar, A. and Q. A. Naqvi, "Study of focusing of field refracted by an inhomogeneous slab into uniaxial crystal by using Maslov's method," Journal of Modern Optics. Google Scholar

27. Ghaffar, A. and Q. A. Naqvi, "Focusing of electromagnetic plane wave into uniaxial crystal by a Wood lens," Central European Journal of Physics.. Google Scholar

28. Ashraf, M. R., A. Ghaffar, and Q. A. Naqvi, "Fields in the focal space of symmetrical hyperbolic focusing lens," Journal of Electromagnetic Waves and Applications, Vol. 22, 815-828, 2008.
doi:10.1163/156939308784159480 Google Scholar

29. Fiaz, M. A., A. Ghaffar, and Q. A. Naqvi, "High-frequency expressions for the field in the caustic region of a PEMC cylinderical reflector using Maslov's method," Journal of Electromagnetic Waves and Applications, Vol. 22, 385-397, 2008.
doi:10.1163/156939308784160794 Google Scholar

30. Fiaz, M. A., A. Ghaffar, and Q. A. Naqvi, "High-frequency expressions for the field in the caustic region of a PEMC Gregorian system using Maslov's method," Progress In Electromagnetics Research, Vol. 81, 135-148, 2008.
doi:10.2528/PIER08010901 Google Scholar

31. Aziz, A., Q. A. Naqvi, and K. Hongo, "Analysis of the fields in two dimensional Cassegrain system," Progress In Electromagnetics Research, Vol. 71, 227-241, 2007. Google Scholar

32. Aziz, A., A. Ghaffar, Q. A. Naqvi, and K. Hongo, "Analysis of the fields in two dimensional Gregorian system," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 1, 85-97, 2008.
doi:10.1163/156939308783122733 Google Scholar

33. Faryad, M. and Q. A. Naqvi, "Highfrequency expressions for the field in the caustic region of a cylindrical reflector placed in chiral medium," Progress In Electromagnetics Research, Vol. 76, 153-182, 2007.
doi:10.2528/PIER07070401 Google Scholar

34. Faryad, M. and Q. A. Naqvi, "Cylindrical reflector in chiral medium supporting simultaneously positive phase velocity and negative phase velocity," Journal of Electromagnetic Waves and Applications, Vol. 22, 563-572, 2008.
doi:10.1163/156939308784150344 Google Scholar

35. Hussain, A., Q. A. Naqvi, and K. Hongo, "Radiation characteristics of the Wood lens using Maslov's method," Progress In Electromagnetics Research, Vol. 73, 107-129, 2007.
doi:10.2528/PIER07030302 Google Scholar

36. Stamnes, J. J., Waves in Focal Regions, Adam Hilger, 1986.

37. Stamnes, J. J. and G. C. Sherman, "Radiation of electromagnetic fields in uniaxially anisotropic media," J. Opt. Soc. Am., Vol. 66, No. 8, 780-788, 1976.
doi:10.1364/JOSA.66.000780 Google Scholar

38. Stamnes, J. J. and D. Jiang, "Focusing of electromagne waves into a uniaxial crystal," Opt. Comm., Vol. 150, 251-262, 1998.
doi:10.1016/S0030-4018(98)00055-8 Google Scholar

39. Jiang, D. and J. J. Stamnes, "Numerical and asymptotic results for focusing of two-dimensional electromagnetic waves in uniaxial crystals," Opt. Comm., Vol. 163, 55-71, 1999.
doi:10.1016/S0030-4018(99)00101-7 Google Scholar

Dr. Abdul Ghaffar

Dr. M. Sajjad

Dr. Qaisar Abbas Naqvi