No Access

QUASI-NONUNIQUENESS IN THE SCATTERED FIELD OF A DIELECTRIC CIRCULAR CYLINDER

T. M. DUNSTER

Department of Mathematical Sciences, San Diego State University, San Diego, California 92182-7720, USA

https://doi.org/10.1142/S0219530510001515Cited by:2 (Source: Crossref)

Abstract

It is well known that the scattered field of a z polarized plane wave incident on a dielectric circular cylinder can be expanded as an infinite series involving Hankel functions. From numerical calculations of this expansion, Lam and Yedlin [5] observed that the mean square measure, over all space, of the difference of the scattered fields from two or more distinct values of the dielectric constant of the cylinder can take very small values, thereby almost contradicting the uniqueness property. We investigate this phenomenon rigorously using uniform asymptotic expansions of Bessel functions, and from our analysis we determine the spurious values of the dielectric constant which lead to this quasi-nonuniqueness.

Keywords:

AMSC: 78A45, 33C10, 34E20

References

M. Abramowitz and I. Stegun (eds.) , Handbook of Mathematical Functions ( Dover , 1965 ) . Google Scholar
T. M. Dunster, M. Yedlin and K. Lam, Anal. Appl. 4, 311 (2006), DOI: 10.1142/S0219530506000796. Link, Web of Science, Google Scholar
T. M. Dunster, Anal. Appl. 7, 73 (2009), DOI: 10.1142/S0219530509001281. Link, Web of Science, Google Scholar
R. F. Harrington , Time-Harmonic Electromagnetic Fields , IEEE Press Series on Electromagnetic Wave Theory ( Wiley , New York , 2001 ) . Crossref, Google Scholar
K. Lam and M. Yedlin, Monochromatic nonuniqueness in plane-wave inverse scattering, Antennas and Propagation Society International Symposium, 2005 IEEE2A (IEEE Press, 2005) pp. 123–126. Google Scholar
F. W. J. Olver , Asymptotics and Special Functions ( Academic Press , New York , 1974 ) . Google Scholar
P. A. Tipler and G. Mosca, Physics for Scientists and Engineers, 6th edn. (W. H. Freeman, 2008). Google Scholar
J. E. Wilkins, Bull. Amer. Math. Soc. 54, 232 (1948). Crossref, Web of Science, Google Scholar