PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 83 > pp. 25-42

FOCUSING OF ELECTROMAGNETIC PLANE WAVE INTO UNIAXIAL CRYSTAL BY A THREE DIMENSIONAL PLANO CONVEX LENS

By C. A. Ghaffar and Q. A. Naqvi

Full Article PDF (721 KB)

Abstract:
A three dimensional plano-convex lens which is placed at a certain distance from a plane uniaxial interface has been considered. High frequency fields refracted by the geometry are derived. The treatment is based on Maslov's method. The method combines the simplicity of asymptotic ray theory and generality of the transform method to remedy the problem of geometrical optics around the caustic point of a focusing system. Field patterns are obtained which includes the observation points around the caustic region. The results are found in good agreement with obtained using Huygens-Kirchhoff Principle.

Citation:
C. A. Ghaffar 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
http://www.jpier.org/PIER/pier.php?paper=08041404

References:
1. Hansen, R. C., Geometrical Theory of Diffraction, IEEE Press, New York, NY, 1988.

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

3. Dou, W. B., Z. L. Sun, and X. Q. Tan, "Fields in the focal space of symmetrical hyperbolic focusing lens," Progress In Electromagnetics Research, Vol. 20, 213-226, 1998.
doi:10.2528/PIER98021300

4. Dou, W. B., Z. L. Sun, and X. Q. Tan, "Diffraction fields in the focal space of symmetrical hyperbolic focusing lens," International Journal of Infrared and Millimeter Waves, Vol. 20, No. 10, 1843-1854.
doi:10.1023/A:1021721917087

5. 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

6. 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

7. Jiang, D. and J. J. Stamnes, "Numerical and experimental results for focusing of two-dimensional electromagnetic waves into uniaxial crystals," Opt. Com., Vol. 174, 321-334, 2000.
doi:10.1016/S0030-4018(99)00671-9

8. 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

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

10. Maslov, V. P., Perturbation Theory and Asymptotic Method, Moskov, Gos. Univ., Moscow, 1965.

11. Ziolkowski, R. W. and G. A. Deschamps, "Asymptotic evaluation of high frequency fields near a caustic: An introduction to Maslov's method," Radio Sci., Vol. 19, No. 4, 1001-1025, 1984.
doi:10.1029/RS019i004p01001

12. 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.

13. 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

14. 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

15. 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, 1988.
doi:10.1109/8.192134

16. 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.

17. 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.

18. 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

19. 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.

20. 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

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

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

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

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

25. 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

26. 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

27. Faryad, M. and Q. A. Naqvi, "High frequency 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

28. 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

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

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

31. Lindell, I. V. and S. Ilvonen, "Waves in a slab of uniaxial BW medium," Journal of Electromagnetic Waves and Applications, Vol. 16, 303-318, 2002.
doi:10.1163/156939302X01164

32. Saraei, R. and Rashed-Mohassel, "The theory of uniaxial bi-anisotropic media: The quasi-static case," Journal of Electromagnetic Waves and Applications, Vol. 17, 1075-1086, 2003.
doi:10.1163/156939303322519171

33. Li, K., S.-O. Park, and H.-S. Lee, "Analytical evaluation of the asymptotic impedance matrix of a uniaxial substrate withro of-top functions," Journal of Electromagnetic Waves and Applications, Vol. 17, 957-968, 2003.

34. Liu, S., L. W. Li, M. S. Leong, and T. S. Yeo, "Scattering by an arbitrarily shaped rotationally uniaxial anisotropic object: Electromagnetic fields and dyadic Green's functions," Journal of Electromagnetic Waves and Applications, Vol. 14, 903-904, 2000.

35. Lindell, I. V. and F. Olyslager, "Decomposition of electromagnetic sources in axially chiral uniaxial anisotropic media," Journal of Electromagnetic Waves and Applications, Vol. 10, 51-59, 1996.
doi:10.1163/156939396X00207

36. Lindell, I. V. and F. Olyslager, "Electromagnetic source decomposition in bi-anisotropic media," Journal of Electromagnetic Waves and Applications, Vol. 12, 1-21, 1998.
doi:10.1163/156939398X00016

38. Lilonga-Boyenga, D., C. N. Mabika, and G. Okoumou-Moko, "Rigorous analysis of uniaxial discontinuities microwave components using a new multimodal variational formulation," Progress In Electromagnetics Research B, Vol. 2, 61-71, 2008.
doi:10.2528/PIERB07102403

39. Gavrilenko, V. G., G. V. Jandieri, A. Ishimaru, and V. G. Jandieri, "Peculiarities of spatial spectrum of scattered electromagnetic waves in anisotropic inhomogeneous medium," Progress In Electromagnetics Research B, Vol. 7, 191-208, 2008.

40. Kokkorakis, G. C., "Scalar equations for scattering by rotationally symmetric radially inhomogeneous anisotropic sphere," PIER Letters, Vol. 3, 179-186, 2008.

41. Kukharchik, P. D., V. M. Serdyuk, and J. A. Titovitsky, "Diffraction of hybrid modes in a cylindrical cavity resonator by a transverse circular slot witha plane anisotropic dielectric layer," Progress In Electromagnetics Research B, Vol. 3, 73-94, 2008.
doi:10.2528/PIERB07112502


© Copyright 2014 EMW Publishing. All Rights Reserved