PIER B
 
Progress In Electromagnetics Research B
ISSN: 1937-6472
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 49 > pp. 429-455

GEOMETRICALLY LIT REGION ANALYSIS OF THE SINGLE-RAY DEBYE TERMS FOR THE TRANSMISSION OF A HIGH FREQUENCY PLANE WAVE INTO A DOUBLE-NEGATIVE CYLINDER BY THE MODIFIED WATSON TRANSFORMATION AND DEBYE SERIES EXPANSION

By S. G. Sen

Full Article PDF (1,193 KB)

Abstract:
The Debye expansion integrals obtained by application of the Modified Watson Transformation and Debye series expansion to the Mie series for the high frequency plane wave transmitted into a double negative(DNG) cylinder are solved in the geometrically lit regions of the corresponding Debye series terms. The Debye series expansion is made up to the possible maximum term after which double ray field formation is first observed. Using the steepest descent method and the geometrical optics approximation, the role of the lower ray in the double-ray field formation is pointed out. For refractive indices satisfying |n| ≥ 10, it is shown that the maximum Debye series term index up to which simple single-ray tracing can be performed is bigger for a DNG cylinder than that for a DPS cylinder and the difference between the term indices incrases as |n| increases.

Citation:
S. G. Sen, "Geometrically Lit Region Analysis of the Single-Ray Debye Terms for the Transmission of a High Frequency Plane Wave into a Double-Negative Cylinder by the Modified Watson Transformation and Debye Series Expansion," Progress In Electromagnetics Research B, Vol. 49, 429-455, 2013.
doi:10.2528/PIERB13012909

References:
1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Soviet Physics Uspekhi, Vol. 10, No. 4, Jan.-Feb. 1968.

2. Pendry, J. B., A. J. Holden, D. J. Robbins, W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Transactions on Microwave Theory and Techniques, Vol. 47, 2075-2084, Nov. 1999.

3. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Physical Review Letters, Vol. 76, 4773, Jun. 17, 1996.

4. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Physical Review Letters, Vol. 84, 4184, May 1, 2000.

5. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, Apr. 6, 2001.

6. Rahim, M. K. A., et al., "Left-handed metamaterial structure incorporated with microstrip antenna,", Vol. 54, No. 12, 2828-2832, Dec. 2012.

7. Han, X., et al., "A novel structure for a broadband left-handed metamaterial," Chinese Physics B, Vol. 21, No. 9, Sep. 2012.

8. Wang, J., et al., "Achieving all-dielectric left-handed metamaterials via single-sized dielectric resonators," Journal of Applied Physics, Vol. 111, No. 4, Feb. 2012.

9. Sabah, C., "Novel, dual band, single and double negative metamaterials: Nonconcentric delta loop resonators," Progress In Electromagnetics Research B, Vol. 25, 225-239, 2010.
doi:10.2528/PIERB10080302

10. Mok, S., S. Kahng, and Y. Kim, "A wide band metamaterial ZOR antenna of a patch coupled to a ring mushroom," Journal of Electromagnetic Waves and Applications, Vol. 26, No. 13, 1667-1774, 2012.
doi:10.1080/09205071.2012.708965

11. Yoon, K.-C., J. H. Kim, and J.-C. Lee, "Band-pass filter with broad-side coupled triple split-ring resonator using left-handed metamaterial," Microwave and Optical Technology Letters, Vol. 53, No. 9, 2174-2177, Sep. 2011.
doi:10.1002/mop.26219

12. Alhawari, A. R. H., et al., "Miniaturized ultra-wideband antenna using microstrip negative index metamaterial," Electromagnetics, Vol. 31, No. 6, 404-418, 2011.
doi:10.1080/02726343.2011.590961

13. Ng Mou Kehn, M., "Spherical slotted antenna coated with double layer of materials having combinations of singly and doubly negative parameters and consequences of mode resonances," Progress In Electromagnetics Research B, Vol. 45, 223-249, 2012.

14. Cojocaru, E., "Waveguides filled with bilayers of double-negative (DNG) and double-positive (DPS) metamaterials," Progress In Electromagnetics Research B, Vol. 32, 75-90, 2011.
doi:10.2528/PIERB11050604

15. Watson, G. N., "The diffraction of electric waves by the earth," Proceedings of the Royal Society of London, Vol. 95, No. 666, 83-99, 1918.
doi:10.1098/rspa.1918.0050

16. Li, M. K. and W. C. Chew, "A new Sommerfeld-Watson transformation in 3-D," IEEE Antennas and Wireless Propagation Letters, Vol. 3, 75-78, Dec. 2004.

17. Valagiannopoulos, C. A., "An overview of the Watson transformation presented through a simple example," Progress In Electromagnetics Research, Vol. 75, 137-152, 2007.
doi:10.2528/PIER07052502

18. Sha, , W. E. I. and W. C. Chew, "High frequency scattering by an impenetrable sphere," Progress In Electromagnetics Research,, Vol. 97, 291-325, 2009.
doi:10.2528/PIER09100102

19. Debye, P., "Das elektromagnetische feld um ein zylinder und die theorie des regenbogens," Physik. Z., Vol. 9, 775, 1908.

20. Ducasse, E. and M. Deschamps, "A nonstandard wave decomposition to ensure the convergence of Debye series for modelling wave propagation in an immersed anisotropic elastic plate," Wave Motion, Vol. 49, No. 8, 745-764, Dec. 2012.
doi:10.1016/j.wavemoti.2012.05.001

21. Li, R., X. Han, and K. Ren, "Generalized Debye series expansion of electromagnetic plane wave scattering by an infinite multilayered cylinder at oblique incidence," Physical Review E, Vol. 79, No. 3, Mar. 2009.

22. ussenzweig, H. M., "High-frequency scattering by an impenetrable sphere," Annals of Physics, Vol. 34, 23-95, 1965.

23. Nussenzweig, H. M., "High-frequency scattering by a transparent sphere. 1. Direct re°ection and transmission," Journal of Mathematical Physics, Vol. 10, No. 1, 82-124, Jan. 1969.
doi:10.1063/1.1664764

24. Inada, H., "Diffracted field computations by a series expansion," Radio Science, Vol. 10, 205-220, Feb. 1975.
doi:10.1029/RS010i002p00205

25. Sen, S. G. and M. Kuzuoglu, "Analysis of high frequency plane wave scattering from a double negative cylinder via the modified Watson transformation and Debye expansion," Progress In Electromagnetics Research, Vol. 84, 55-92, 2008.

26. Sen, S. G, "Analysis of high frequency plane wave transmission into a double negative cylinder by the modified Watson transformation and Debye series expansion: First term of the Debye series," Progress In Electromagnetics Research, Vol. 112, 397-414, 2011.


© Copyright 2010 EMW Publishing. All Rights Reserved