Abstract
The problem of propagation of electromagnetic waves in an inhomogeneous uniaxial anisotropic medium is discussed. Analytic solutions of Maxwell's equations are found for two particular cases of a plane-layered dielectric. The effect of different parameters of an inhomogeneous distribution of refractive indices on the propagation characteristics of wave beams is analyzed. The corrections of the first approximation of perturbation theory to the propagation constants of natural waves are obtained for a plane-layered focusing medium of general type. This has permitted solving the problem of a distribution of the refractive index which provides for optimal focusing.
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A. M. Goncharenko, V. A. Karpenko, and S. N. Stolyarov, “Waveguide properties of p-n-transitions and the electromagnetic theory of injection lasers,” Institute of Physics of the BSSR Academy of Sciences, Minsk (1970).
A. M. Goncharenko and V. P. Red'ko, Introduction to Integrated Optics [in Russian], Nauka i Tekhnika, Minsk (1975).
F. W. Quelle, Appl. Opt.,5, No. 4, 633 (1966).
I. M. Buzhinskii, E. M. Dianov, S. K. Mamonov, L. M. Mikhailov, and A. M. Prokhorov, Dokl. Akad. Nauk SSSR,190, No. 3, 558 (1970)
Yu. A. Anan'ev and N. I. Grishmanova, Zh. Prikl. Spektrosk.,12, No. 4, 668 (1970).
A. A. Mak, L. N. Soms, A. I. Stepanov, and A. B. Sudakov, Opt. Spektrosk.,30, No. 6, 1081 (1971).
I. P. Kaminow, Appl. Opt.,3, No. 4, 511 (1964).
N. A. Morozov, Inventor's Certificate No. 440630, Byull. Izobret., No. 31 (1974).
M. E. Zhabotinskii, Ch. M. Briskina, and V. F. Zolin, Inventors' Certificate No. 235350, Byull. Izobret., No. 5 (1969).
T. Yasuo, Japanese Patent Class 104A412.6 No. 7597, issued March 16, 1970.
Yu. A. Zaitsev, Yu. A. Kravtsov, and Yu. Ya. Yashin, Izv, Vyssh. Uchebn. Zaved., Radiofiz.,11, No. 12, 1802 (1968).
Yu. A. Kravtsov, Dokl. Akad. Nauk SSSR,183, No. 1, 74 (1968).
M. B. Vinogradova and V. D. Gusev, Radiotekh. Elektron.,19, No. 3, 481 (1974).
F. Ya. Bronfin, V. G. Il'in, G. O. Karapetyan, V. Ya. Livshin, V. I. Maksimov, and D. K. Sattarov, Zh. Prikl. Spektrosk.,18, No. 3, 523 (1973).
E. T. Kornhauser and A. D. Yaghijan, Radio Sci.,2, No. 3, 299 (1967).
G. Bateman and A. Érdein, Higher Transcendental Functions, McGraw-Hill, Vols. 1, 2 (1953).
R. Courant and D. Hilbert, Methods of Mathematical Physics [Russian translation], Gostekhizdat, Moscow (1951).
H. Kogelnik, Bell. Syst. Tech. J.,44, No. 3, 455 (1965).
F. P. Kapron, J. Opt. Soc. Am.,60, No. 11, 1433 (1970).
L. D. Landau and E. M. Lifshits, Quantum Mechanics [in Russian], Nauka, Moscow (1974).
M. Born and E. Wolf, Principles of Optics, Pergamon (1975).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 12, pp. 1812–1821, December, 1978.
In conclusion, the author expresses his gratitude to I. V. Ivanov and N. A. Morozov for their attention to this paper.
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Belokopytov, G.V. Focusing of waves in an anisotropic plane-layered medium. Radiophys Quantum Electron 21, 1262–1269 (1978). https://doi.org/10.1007/BF02121909
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DOI: https://doi.org/10.1007/BF02121909