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HIGH-FREQUENCY EXPRESSION FOR THE FIELD IN THE CAUSTIC REGION OF A PEMC GREGORIAN SYSTEM USING MASLOV'S METHOD

By M. A. Fiaz, A. Aziz, C. A. Ghaffar, and Q. A. Naqvi

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Abstract:
Method proposed by Maslov has been used, to remedy the problem of geometrical optics, for a two dimensional Perfect electromagnetic conductor (PEMC) Gregorian system. It generates an integral form of solution near the caustic that can be evaluated analytically/numerically, or withuniform asymptotic techniques. Away from the caustic it recovers the geometrical optics field. Numerical computations are made to calculate the field around the caustic of a Gregorian system.

Citation: (See works that cites this article)
M. A. Fiaz, A. Aziz, C. A. Ghaffar, and Q. A. Naqvi, "High-frequency expression 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
http://www.jpier.org/PIER/pier.php?paper=08010901

References:
1. Lindell, I. V. and A. H. Sihvola, "Perfect electromagnetic conductor," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 7, 861-869, 2005.
doi:10.1163/156939305775468741

2. Lindell, I. V. and A. H. Sihvola, "Realization of the PEMC boundary," IEEE Trans. Antennas Propag., Vol. 53, No. 9, 3012-3018, 2005.
doi:10.1109/TAP.2005.854524

3. Dechamps, G. A., Electromagnetics and differential forms, Proc. IEEE, Vol. 69, 676-696, 1981.

4. Lindell, I. V., Differential Forms in Electromagnetics, Willey IEEE press, New York, 2004.

5. Gizesik, J. A., "Focusing properties of a three-parameter class of oblate, Luneberg-like inhomogeneous lenses," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 8, 1005-1019, 2005.
doi:10.1163/156939305775526089

6. Nikolic, N., J. S. Kot, and S. Vinogradov, "Scattering by a Luneberg Lens partially covered by a metallic cap," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 4, 549-563, 2007.
doi:10.1163/156939307780616856

7. Boutayeb, H., A.-C. Tarot, and K. Mahdjoubi, "Focusing characteristics of a metallic cylindrical electromagnetic band gap structure withdefects," Progress In Electromagnetics Research, Vol. 66, 89-103, 2006.
doi:10.2528/PIER06100504

8. Vinogradov, S. S., P. D. Smith, J. S. Kot, and N. Nikolic, "Radar cross-section studies of spherical lens reflectors," Progress In Electromagnetics Research, Vol. 72, 325-337, 2007.
doi:10.2528/PIER07031206

9. Lindell, I. V. and A. H. Sihvola, "Transformation method for problems involving perfect electromagnetic conductor (PEMC) structures," IEEE Trans. on Antennas and Propagation, Vol. 53, No. 9, 3005-3011, 2005.
doi:10.1109/TAP.2005.854519

10. Lindell, I. V. and A. H. Sihvola, "Losses in PEMC boundary," IEEE Trans. on Antennas and Propagation, Vol. 54, No. 9, 2553-2558, 2006.
doi:10.1109/TAP.2006.880740

11. Lindell, I. V. and A. H. Sihvola, "The PEMC resonator," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 849-859, 2006.
doi:10.1163/156939306776149824

12. Hehl, F. W. and Y. N. Obukhov, "Linear media in classical electrodynamics and post constraint," Phys. Lett. A, Vol. 334, 249-259, 2005.
doi:10.1016/j.physleta.2004.11.038

13. Obukhov, Y. N. and F. W. Hehl, "Measuring a piecewise constant axon field in classical electrodynamics," Phys. Lett. A, Vol. 341, 357-365, 2005.
doi:10.1016/j.physleta.2005.05.006

14. Jancewicz, B., "Plane electromagnetic wave in PEMC," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 5, 647-659, 2006.
doi:10.1163/156939306776137746

15. Ruppin, R., "Scattering of electromagnetic radiation by a perfect electromagnetic conductor sphere," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 12, 1569-1576, 2006.
doi:10.1163/156939306779292390

16. Ruppin, R., "Scattering of electromagnetic radiation by a perfect electromagnetic conductor cylinder," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1853-1860, 2006.
doi:10.1163/156939306779292219

17. Lindell, I. V., A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media, Artech House, Norwood, MA, 1994.

18. Hansen, R. C., Geometrical Theoryof Diffraction, IEEE Press, New York, NY, 1988.

19. Felson, L. B., Hybrid Formulation of Wave Propagation and Scattering, Nato ASI Series, Martinus Nijhoff, Dordrecht, The Netherlands, 1984.

20. Hussain, A. and Q. A. Naqvi, "Perfect electromagnetic conductor (PEMC) and fractional waveguide," Progress In Electromagnetics Research, Vol. 73, 61-69, 2007.
doi:10.2528/PIER07032401

21. Hussain, A., Q. A. Naqvi, and M. Abbas, "Fractional duality and perfect electromagnetic conductor," Progress In Electromagnetics Research, Vol. 71, 85-94, 2007.
doi:10.2528/PIER07020702

22. Ahmed, S. and Q. A. Naqvi, "Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space," Progress In Electromagnetics Research, Vol. 78, 25-38, 2008.
doi:10.2528/PIER07081601

23. Ahmed, S. and Q. A. Naqvi, "Electromagnetic scattering from a parallel perfect electromagnetic conductor cylinders of circular cross-sections using an iterative procedure," Journal of Electromagnetic Waves and Applications, Vol. 22, 987-1003, 2008.
doi:10.1163/156939308784150209

24. Fiaz, M. A., A. Ghaffar, and Q. A. Naqvi, "High frequency expressions for the field in the caustic region of a PEMC cylindrical reflector using Maslov's method," Journal of Electromagnetic Waves and Applications, Vol. 22, 358-397, 2008.
doi:10.1163/156939308784160794

25. 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.

26. 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

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

28. 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

29. 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

30. 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, No. 5, 592-598, 1988.
doi:10.1109/8.192134

31. 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.

32. 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.

33. Hongo, K. and H. Kobayashi, "Radiation characteristics of a plano convex lens antenna," Radio Sci., Vol. 31, No. 5, 1025-1035, 1987.
doi:10.1029/96RS01330

34. 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.
doi:10.2528/PIER07022001

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. Ghaffar, A., Q. A. Naqvi, and K. Hongo, "Focal region fields of three dimensional Gregorian system," Optics Communications, 2007.

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

44. Faryad, M. and Q. A. Naqvi, "Highfrequency field in the caustic region of a parabolic reflector coated withisotropic chiral medium," Journal of Electromagnetic Waves and Applications, Vol. 22, 965-986, 2008.


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