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Effective Permittivity of a Statistically Inhomogeneous Medium with Strong Permittivity Fluctuations
By
, Vol. 44, 169-195, 2004
Abstract
Most previous multiple-scattering theories for electromagnetic waves in strongly fluctuating media are limited by the assumption of statistical homogeneity of media. In the paper, a lossy electrically isotropic random medium is considered whose mean permittivity distribution, as well as the multipoint permittivity's moments are invariant under arbitrary rotations about and translations along a fixed symmetry axis, and are inhomogeneous in the radial direction. The goal of the paper is to calculate the effective permittivity operator (EPO) for such medium in the case of strong permittivity fluctuations. For this purpose, one has to eliminate the secular terms from the spectral representation of the-EPO in the basis set of waves suited to a statistically inhomogeneous medium. This is achieved via a renormalization approach which takes into proper account a delta function singularity of the spectral Green's function (rather than that of the spatial Green's function accounted for in the past) referring to a spatially inhomogeneous electrically anisotropic background medium. On this basis, the permittivity matrix of the background medium is explicitly found, a full perturbation series solution and a bilocal approximation for the EPO are derived, the macroscopic properties of the spatially dispersive effective medium are studied, and a perturbative solution for the propagation constants of guided modes of the mean field is obtained.
Citation
, "Effective Permittivity of a Statistically Inhomogeneous Medium with Strong Permittivity Fluctuations," , Vol. 44, 169-195, 2004.
doi:10.2528/PIER03033001
http://www.jpier.org/PIER/pier.php?paper=0303301
References

1. Rytov, S. M., Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics, Vols. I-IV, Springer, Berlin, 1987.

2. Lifshitz, I. M, M. I. Kaganov, and V. M. Tsukernick, "Propagation of electromagnetic oscillations in inhomogeneous anisotropic media," Ucheniye Zapiski Kharkovckogo Gosuniversiteta. Trudy fiz. Otdeleniya Fizmat Fakulteta, Vol. 35, 41-54, 1950.

3. Ryzhov, Y. A., V. V. Tamoikin, and V. I. Tatarskii, "Spatial dispersion of inhomogeneous media," Soviet Phys. JETP, Vol. 21, 433-438, 1965.

4. Ryzhov, Y. A. and V. V. Tamoikin, ''Radiation and propagation of electromagnetic waves in randomly inhomogeneous media, Vol. 13, 273-300, '' Radiophys. Quantum Electron, Vol. 13, 273-300, 1973.

5. Tsang, L. and J. Kong, "Scattering of electromagnetic waves from random media with strong permittivity fluctuations," Radio Sci., Vol. 16, 303-320, 1981.

6. Tsang, L., J. Kong, and R. Newton, "Application of strong fluctuation random medium theory to scattering of electromagnetic waves from a half-space of dielectric mixture," IEEE Trans. Antennas Propagat., Vol. 30, 292-302, 1983.
doi:10.1109/TAP.1982.1142774

7. Zhuck, N. P., "Strong fluctuation theory for a mean electromagnetic field in a statistically homogeneous random medium with arbitrary anisotropy of electrical and statistical properties," Phys. Rev. B, Vol. 50, 15636-15645, 1994.
doi:10.1103/PhysRevB.50.15636

8. Zhuck, N. P. and A. S. Omar, "Calculation of the effective constitutive parameters of a disordered biisotropic medium using renormalization method," IEEE Trans. Antennas Propagat., Vol. 44, 1142-1149, 1996.
doi:10.1109/8.511823

9. Zhuck, N. P., "Wave propagation in statistically irregular layered waveguides," Cand. Phys. & Math. Sci. degree dissertation, 1982.

10. Danilevich, S. B., N. P. Zhuck, and O. A. Tret'yakov, "Equivalent parameters of waveguiding structures with random volume perturbations," Radiotekhnika (Kharkov), No. 75, 17-25, 1985.

11. Zhuck, N. P., "The effective permittivity of strongly fluctuating statistically layered medium with arbitrary anisotropy of electromagnetic properties," J. Electrmagnetic Waves Appl., Vol. 7, 1653-1681, 1993.

12. Felsen, L. and N. Marcuvitz, Radiation and Scattering of Waves, Prentice-Hall, Englewood Cliff, New York, 1973.

13. Friedman, B., Principles and Techniques of Applied Mathematics, Wiley, New York, 1956.

14. Shevchenko, V. V., Continuous Transitions in Open Waveguides, Golem, Boulder, CO, 1971.

15. Gel'fand, I. M. and G. E. Shilov, Generalized Functions, Vol. I, Academic, New York, 1964.

16. Zhuck, N. P. and O. A. Tret'yakov, "Equivalent para neters of an optical waveguide with random volume perturbation," Soviet J. Communications Technology and Electronics, Vol. 31, 38-44, 1986.

17. Marcuse, D., "Coupled mode theory of round optical fibers," The Bell Syst. Tech. J., 817-842, 1973.

18. Agranovich, V. M. and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons, Springer, Berlin, 1984.

19. Gakhov, F. D., Boundary Value Problems, Pergamon, Oxford, 1966.