We consider the problem of energy transmission from one aperture to another by the wave fields in smoothly inhomogeneous media. The study is performed in the quasioptical and scalar approximations when the aperture sizes significantly exceed the wavelength and there exists a ray connecting the aperture centers. The transmission coefficient is determined using the well-known parabolic equation, which describes the wave-beam propagation in smoothly inhomogeneous media. As in the homogeneous media, the maximum transmission coefficient is shown to be reached when the field structures at the aperture are specified in the form of special functions, namely, the prolate spheroidal angular functions. The maximum achievable transmission coefficient is determined.
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References
Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, Springer-Verlag, Berlin (1990).
V. I. Talanov, Radiophys. Quantum Electron., 28, No. 7, 599 (1985).
V. G. Manishin and G. A. Pasmanik, Radiophys. Quantum Electron., 24, No. 8, 675 (1980).
A. A. Balakin, Radiophys. Quantum Electron., 55, No. 7, 472 2012).
A. A. Balakin, Radiophys. Quantum Electron., 55, No. 8, 502 (2012).
A. A. Balakin, Radiophys. Quantum Electron., 55, No. 9, 556 (2012).
A. A. Balakin, E. D. Gospodchikov, and A. G. Shalashov, JETP Lett., 104, No. 10, 690 (2016).
I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Non-Self-Adjoint Operators in Hilbert Space [in Russian], Nauka, Moscow (1965).
N. G. Bondarenko and V. I. Talanov, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 7, No. 2, 313 (1964).
N. N. Rozanov and V. A. Smirnov, Sov. Tech. Phys. Lett., 5, No. 5, 222 (1979).
G. V. Permitin, Radiophys. Quantum Electron., 16, No. 2, 188 (1973).
I. G. Kondrat’ev, G. V. Permitin, and A. I. Smirnov, Radiophys. Quantum Electron., 23, No. 10, 793 (1980).
G. V. Permitin, and A. I. Smirnov, JETP, 82, No. 3, 395 (1996).
S. N. Vlasov and S. N. Gurbatov, Radiophys. Quantum Electron., 19, No. 8, 811 (1976).
S. N. Vlasov and V. I. Talanov, Self-Focusing of Waves [in Russian], Inst. Appl. Phys., Nizhny Novgorod (1997).
V. I. Talanov, JETP Lett., 11, No. 6, 199 (1970).
J. A. Stratton, P. M. Morse, L. J. Chu, et al., Spheroidal Wave Functions, Technology Press of M.I.T. and Jonh Wiley and Sons, New York (1956).
L. A. Weinstein, Open Resonators and Open Waveguides, Golem Press, Boulder, CO. (1969).
I. V. Komarov, L. I. Ponomarev, and S. Yu. Slavyanov, Spheroidal and Coulomb Spheroidal Functions [in Russian], Nauka, Moscow (1976).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 61, No. 12, pp. 1022–1029, December 2018.
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Vlasov, S.N., Koposova, E.V. Maximum Transmission Coefficient Through a Smoothly Inhomogeneous Medium. Radiophys Quantum El 61, 908–914 (2019). https://doi.org/10.1007/s11141-019-09946-1
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DOI: https://doi.org/10.1007/s11141-019-09946-1