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IEEE Transactions on Antennas and Propagation
Volume 47 Number 8, August 1999
Table of Contents for this issue
Complete paper in PDF format
Radiation and Low-Frequency Scattering
of EM Waves in a General Anisotropic
Homogeneous Medium
Nickolay P. Zhuck and Abbas S. Omar
Page 1364.
Abstract:
This paper focuses on a boundless homogeneous medium with
general anisotropy of electromagnetic properties. The explicit exact
form of the four spectral Green's dyads
G
(k) is
obtained and a coordinate-free representation of the four spatial
Green's functions
G
(x- x')
in terms of one scalar potential
W(x - x') is
developed. On this basis, asymptotic expressions for the radiation field
due to arbitrary sources are derived that show that the associated modes
and the eigenmodes determine radiation along a singular optic axis and
in all other directions, respectively. Using an integral equation
approach and the theory of Newtonian potential, the problem of
low-frequency scattering by a small anisotropic ellipsoidal body
immersed into an anisotropic medium is solved
analytically.
References
-
C. T. Tai, Dyadic Green's Functions in
Electromagnetic Theory, 2nd ed.New York: IEEE
Press, 1994.
-
W. S. Weiglhofer, "Analytic methods and free-space dyadic
Green's functions," Radio Sci.,
vol. 28, no. 5, pp. 847-857, Sept./Oct. 1993.
-
S. Przezdziecki and W. Laprus, "On the representation of
electromagnetic fields in gyrotropic media in terms of scalar
potentials," J. Math. Phys.,
vol. 23, no. 9, pp. 1708-1712, Sept. 1982.
-
W. Weiglhofer and W. Papousek, "Skalare Hertzsche Potentiale
für anisotrope Medien,"
AEÜ, B. 39, H. 6, S.
343-346, Nov./Dec. 1985.
-
D. I. Kaklamani and N. K. Uzunoglu, "Radiation of a dipole
in an infinite triaxial anisotropic medium,"
Electromagn., vol. 12, no. 3, pp.
231-245, May/June 1992.
-
A. Lakhtakia and W. S. Weiglhofer, "Source-region
electromagnetic field in an affinely transformable AUBM,"
Int. J. Infrared Millimeter Waves,
vol. 19, no. 1, pp. 95-106, Jan. 1998.
-
F. Olyslager and I. V. Lindell, "Closed form Green's dyadics
for a class of bi-anisotropic media with axial bi-anisotropy,"
Rep. 244, Electromagn. Lab., Helsinki Univ. Technol., Apr. 1997.
-
N. P. Zhuck and A. S. Omar, "EM wave excitation and
propagation in a generally anisotropic homogeneous medium: A
coordinate-free approach," in IEEE Antennas
Propagat. Soc. Int. Symp., Newport Beach, CA, June
1995, vol. 1, pp. 756-759.
-
B. Jakoby and F. Olyslager, "Asymptotic expansions for
Green's dyadics in bianisotropic media," in
Progress in Electromagnetic
Research.Cambridge, MA: EMW, 1996, vol. 12,
pp. 277-302.
-
A. Sihvola and I. V. Lindell, "Electromagnetic Green dyadics
of bi-anisotropic media in spectral domain--The six-vector
approach," Rep. 240, Electromagn. Lab., Helsinki Univ. Technol.,
Mar. 1997.
-
F. V. Bunkin, "On radiation in anisotropic media,"
Zh. eksp. teor. fiz., vol. 32, no. 2,
pp. 338-344, Aug. 1957 (in Russian); English transl.
Sov. Phys.--JETP, vol. 5, no. 2,
pp. 277-283, Sept. 1957.
-
V. Daniele, "The use of dyadic Green's functions for wave
propagation in anisotropic media," in Selected
Papers URSI Symp. Electromagn. Waves, Stresa, Italy,
June 1968; Alta Frequenza, vol. 38,
no. 5, pp. 16-19, May 1969.
-
B. Jakoby and F. Olyslager, "Quasistatic asymptotics of
dynamic Green dyadics for general bianisotropic media,"
AEÜ, vol. 50, no. 3, pp.
189-195, May/June 1996.
-
N. P. Zhuck and A. S. Omar, "Low-frequency interaction of EM
waves with an anisotropic ellipsoid in an anisotropic medium," in
IEEE Antennas Propagat. Soc. Int.
Symp., Montreal, Canada, July 1997, vol. 3, pp.
2092-2094.
-
R. C. Jones, "A generalization of the dielectric ellipsoid
problem," Phys. Rev., vol. 68,
nos. 3/4, pp. 93-96, Aug. 1945.
-
A. H. Sihvola, "On the dielectric problem of isotropic
sphere in anisotropic medium," Rep. 217, Electromagn. Lab.,
Helsinki Univ. Technol., Mar. 1996.
-
A. Lakhtakia and W. S. Weiglhofer, "Scattering by an
electrically small bianisotropic sphere in a gyroelectromagnetic
uniaxial medium," Proc. Inst. Elect.
Eng., vol. 139, pt. H, pp. 217-220, 1992.
-
A. H. Sihvola and I. V. Lindell, "Electrostatics of an
anisotropic ellipsoid in an anisotropic environment,"
AËU, vol. 50, no. 5, pp.
281-284, Sept./Oct. 1996.
-
N. A. Khizhnyak, "Application of integral equations to
solving diffraction problems," Trudy radiofiz.
fakulteta Kharkovskogo gosuniversiteta, vol. 2, pp.
13-22, 1957 (in Russian).
-
N. A. Khizhnyak, "Green's function of Maxwell's equations
for inhomogeneous media," Zh. tekhn.
fiz., vol. 28, no. 7, pp. 1592-1609, July 1958
(in Russian).
-
Ya. N. Feld, "Uniqueness of solutions to Maxwell's equations
for complex amplitudes at settled harmonic oscillations,"
Zh. eksp. teor. fiz., vol. 8, no. 6,
p. 754, 1938 (in Russian).
-
F. I. Fedorov, Optics of Anisotropic
Media.Minsk, Russia: Izd. AN BSSR, 1958 (in
Russian).
-
H. C. Chen, Theory of Electromagnetic Waves. A
Coordinate-Free Approach.New York:
McGraw-Hill, 1983.
-
V. M. Agranovich and V. L. Ginzburg, Crystal
Optics with Spatial Dispersion, and
Excitons.Berlin, Germany: Springer-Verlag,
1984.
-
I. M. Lifshitz and L. N. Rosenzveig, "On the development of
Green's tensor for the fundamental equation of the theory of elasticity
in the case of an unbounded elastic anisotropic medium,"
Zh. eksp. teor. fiz., vol. 17, no. 9,
pp. 783-791, Sept. 1947 (in Russian).
-
A. Stogryn, "A note on the singular part of the dyadic
Green's function in strong fluctuation theory,"
Radio Sci., vol. 18, no. 6, pp.
1283-1286, Nov./Dec. 1983.
-
G. Strang, Linear Algebra and Its
Applications.San Diego, CA: Harcourt Brace
Jovanovich, 1988.
-
R. Z. Muratov, Potentials of the
Ellipsoid.Moscow, Russia: Atomizdat, 1976 (in
Russian).