Browse > Article
http://dx.doi.org/10.5515/JKIEES.2012.12.1.45

A Uniform Asymptotic Solution for Transmitted Waves through a Plane Dielectric Interface from a Denser to a Rarer Mediums by Using Parabolic Cylinder Functions  

Quang, Dinh Trong (Dept. of Communication Engineering, National Defense Academy)
Goto, Keiji (Dept. of Communication Engineering, National Defense Academy)
Kawano, Toru (Dept. of Communication Engineering, National Defense Academy)
Ishihara, Toyohiko (Dept. of Communication Engineering, National Defense Academy)
Publication Information
Journal of electromagnetic engineering and science / v.12, no.1, 2012 , pp. 45-54 More about this Journal
Abstract
When the cylindrical wave is incident on a plane dielectric interface from a denser medium to a rarer one, the asymptotic solution for the transmitted wave in the near region is different from the one in the far region. In this paper, we have derived a novel uniform asymptotic solution represented by using the parabolic cylinder function for the transmitted and scattered waves observed in the rarer medium when the cylindrical wave is incident on the plane dielectric interface from the denser medium. The validity of the uniform asymptotic solution has been confirmed by comparing with the reference solution calculated numerically. It has been clarified that the transition wave plays an important role to connect smoothly the asymptotic solution in the near region to the one in the far region through the transition region. We have shown the very interesting phenomenon that the lateral wave type transmitted wave is observed in the far and shallow region.
Keywords
Parabolic Cylinder Function; Plane Dielectric Interface; Transmitted Wave; Uniform Asymptotic Solution;
Citations & Related Records
연도 인용수 순위
  • Reference
1 D. R. Smith, D. Schurig, and J. B. Pendry, "Negative refraction of modulated electromagnetic waves," Applied Physics Letters, vol. 81, no. 15, pp. 2713-2715, Oct. 2002.   DOI   ScienceOn
2 P. M. Valanju, R. M. Walser, and A. P. Valanju, "Wave refraction in negative-index media: always positive and very inhomogeneous," Physical Review Letters, vol. 88, no. 18, pp. 187401-1-187-401-4, May 2002.   DOI   ScienceOn
3 J. R. Thomas, A. Ishimaru, "Wave packet on negative index media," IEEE Trans. on Antennas and Propag., vol. 53, no. 5, pp. 1591-1599, May 2005.   DOI   ScienceOn
4 T. Kawano, K. Goto, and T. Ishihara, "High-frequency asymptotic analysis for scattered fields over half-space metamaterials," The Paper of Technical Meeting on Electromagnetic Theory, IEE Japan, EMT-10-131, pp. 165-170, Nov. 2010.
5 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "Asymptotic analysis of transmitted wave in transition region through a plane dielectric interface," The Paper of Technical Meeting on Electromagnetic Theory, IEE Japan, EMT-10-129, pp. 153-157, Nov. 2010.
6 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "A novel asymptotic analysis for transmitted waves through a plane dielectric interface," The Paper of Technical Meeting on Electromagnetic Theory, IEE Japan, EMT-11-055, pp. 57-62, May 2011
7 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "Novel asymptotic solution in the transition region for transmitted wave through a plane dielectric interface," IEEE AP-S Int. Symp., CD-ROM (ISBN:978-1-4244-9561-0), Spokane, USA, Jul. 2011.
8 B. R. Horowitz, T. Tamir, "Unified theory of total reflection phenomena at a dielectric interface," Appl. Phys., 1, pp. 31-38, vol. 1, 1973.   DOI
9 S. Kozaki, H. Sakurai, "Characteristics of a Gaussian beam at a dielectric interface," J. Opt Soc. Am., vol. 68, no. 4, pp. 508-514, Apr. 1978.   DOI
10 L. M. Brekhovskikh, Waves in Layered Media, 2nd ed., chaps. 1 and 4, Academic Press, New York, USA, 1980.
11 E. K. Westwood, "Complex ray methods for acoustic interaction at a fluid-fluid interface," J. Acoust. Soc. Am., 85(5), pp. 1872-1884, May 1989.   DOI
12 W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd Ed., sec. 9.5, Cambridge University Press, Cambridge, England, 1992.
13 E. T. Whittaker, G. N. Watson, A Course in Modern Analysis, 4th eds., pp. 347-351, Cambridge University Press, Cambridge, 1927.
14 M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions, pp. 686-720, Dover, New York, 1972.
15 J. P. Tignol, Galois' Theory of Algebraic Equations, chap. 3, World Scientific Publishing, Toh Tuck Link, Singapore, 2001.
16 L. B. Felsen, N. Marcuvitz, eds., Radiation and Scattering of Waves, chap. 4, IEEE Press (Classic Reissue), New Jersey, USA, 1994.
17 M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions, p. 10, Dover, New York, 1972.
18 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "A novel uniform asymptotic solution for reflection of a Gaussian beam at a dielectric interface," IEICE Electron. Express, vol. 8, no. 6, pp. 397-403, Mar. 2011.   DOI
19 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "A uniform asymptotic solution for transmitted waves through a plane dielectric interface from a denser to a rarer mediums," Proc. of International Symposium on Antennas and Propagation (ISAP) 2011, ISBN: 978-89-5708-211-9 Jeju, Korea, Oct. 2011.
20 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "Asymptotic analysis of transmitted waves through a plane dielectric interface by using parabolic cylinder function," The Paper of Technical Meeting on Electromagnetic Theory, IEE Japan, EMT-11-130, pp. 13-19, Nov. 2011.
21 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "A uniform asymptotic solution for reflection and beam shift of a Gaussian beam at a plane dielectric interface," IEICE Trans. Electron., vol. E95-C, no. 1, pp. 16-26, Jan. 2012.   DOI
22 D. T. Quang, K. Goto, T. Kawano, and T. Ishihara, "A novel uniform asymptotic solution for transmitted wave through a plane dielectric interface," IEICE Electron. Express, vol. 8, no. 23, pp. 1989-1995, Dec. 2011.   DOI
23 H. L. Bertoni, L. B. Felsen, and J. W. Ra, "Evanescent fields produced by totally reflected beams," IEEE Trans. on Antennas and Propag., pp. 730-732, Sep. 1973.
24 Q. Li, R. J. Vernon, "Theoretical and experimental investigation of Gaussian beam transmission and reflection by a dielectric slab at 110 GHz," IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3449-3457, Nov. 2006.   DOI   ScienceOn
25 H. K. V. Lotsch, "Beam displacement at total reflection: The Goos-Hänchen effect I," Optik, vol. 32, no. 2, pp. 116-137, Apr. 1970.
26 B. R. Horowitz, T. Tamir, "Lateral displacement of light beam at a dielectric interface," J. Opt. Soc. Am., vol. 61, no. 5, pp. 586-594, May 1971.   DOI
27 H. Yamada, T. Kawano, K. Goto, and T. Ishihara, "A uniform asymptotic solution for lateral displacement of a Gaussian beam at a dielectric interface," Proc. of International Symposium on Antennas and Propagation (ISAP) 2007, CD-ROM (ISBN: 978-4- 88552-223-9C3055@IEICE), Niigata, Japan, Aug. 2007.
28 M. Hashimoto, "The law of total reflection in geometrical optics based on wave-normal rays," IEICE Trans. Electron. C-I, vol. J72-C-I, no. 3, pp. 131- 138, Mar. 1989.
29 H. Shirai, "Transient scattering responses from a plane interface between dielectric half space," IEICE Trans. Electron. C-I, vol. J78-C-I, no. 3, pp. 125- 133, Mar. 1995.