Abstract
Analysis of the spectra, real or complex, of the waves or oscillations in open guiding structures is much less developed as compared with the theory of shielded waveguides which enters many textbooks and monographs in electromagnetics, e.g., [1,2,3,4]. In fact, the former is possible only within the frames of the spectral theory of open structures [5, 6] involving mathematically correct statements of non-self-adjoint boundary eigenvalue problems with generalized conditions at infinity that enable one to consider complex modes of all types.
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References
M.J. Adams, An Introduction to Optical Waveguide (Wiley, New York, 1981)
A. Snyder, J. Love, Optical Waveguide Theory (Springer, New York, 1983), p. 735
L.A. Vainshtein Electromagnetic Waves (Sovetskoe Radio, 1957) (in Russian)
D. Marcuse Light Transmission Optics (Krieger Pub Co, 1989)
V. Shestopalov, Yu. Shestopalov, Spectral Theory and Excitation of Open Structures (IET, London, 1996)
G. Hanson, A. Yakovlev, Operator Theory for Electromagnetics: An Introduction (Springer, New York, 2002)
W.-P. Yuen, A simple numerical analysis of planar optical waveguides using wave impedance transformation. IEEE Photon. Technol. Lett. 5(8) (1993)
R.E. Smith, S.N. Houde-Walter, G.W. Forbes, Mode determination for planar waveguides using the four-sheeted dispersion relation. IEEE J. Quantum Electron. 28, 1520–1526 (1992)
A.A. Shishegar, A. Safavi-Naeini, A hybrid analysis method for planar lens-like structures, in IEEE Antennas and Propagation Society International Symposium (1996)
R. Collin, Field Theory of Guided Waves (IEEE Press, Piscataway, 1991), p. 852
L.B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice Hall, Englewood Cliffs, 1973)
Y.G. Smirnov, E.Y. Smolkin, Discreteness of the spectrum in the problem on normal waves in an open inhomogeneous waveguide. Differ. Equ. 53(10), 1168–1179 (2018)
Y.G. Smirnov, E. Smolkin, M.O. Snegur, Analysis of the spectrum of azimuthally symmetric waves of an open inhomogeneous anisotropic waveguide with longitudinal magnetization. Comput. Math. Math. Phys. 58(11), 1887–1901 (2018)
Y.G. Smirnov, E. Smolkin, Operator function method in the problem of normal waves in an inhomogeneous waveguide. Differ. Equ. 54(9), 1262–1273 (2017)
Y.G. Smirnov, E. Smolkin, Investigation of the spectrum of the problem of normal waves in a closed regular inhomogeneous dielectric waveguide of arbitrary cross section. Dokl. Math. 97(1), 86–89 (2017)
Y.G. Smirnov, Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides. Comput. Math. Math. Phys. 55(3), 461–469 (2015)
G.W. Hanson, A.B. Yakovlev, Investigation of mode interaction on planar dielectric waveguides with loss and gain. Radio Sci. 34, 1349–1359 (1999)
A.N. Tikhonov, A.A. Samarskii, On the excitation of radio waves. I. Zh. Tekh. Fiz. 17, 1283–1296 (1947)
A.N. Tikhonov, A.A. Samarskii, On the excitation of radio waves. II. Zh. Tekh. Fiz. 17, 1431–1440 (1947)
A.N. Tikhonov, A.A. Samarskii, On the representation of the field in a waveguide as a sum of the fields TE and TM. Zh. Tekh. Fiz. 18, 959–970 (1948)
Y. Shestopalov, Y. Smirnov, Eigenwaves in waveguides with dielectric inclusions: spectrum. App. Anal. 93(2), 408–427 (2014)
Y.V. Shestopalov, Y.G. Smirnov, Eigenwaves in waveguides with dielectric inclusions: completeness. Appl. Anal. 93(9), 1824–1845 (2014)
Y.V. Shestopalov, E. Kuzmina, On a rigorous proof of the existence of complex waves in a dielectric waveguide of circular cross section. PIER B 82, 137–164 (2018)
N. Marcuvitz, On field representations in terms of leaky modes or eigenmodes. IRE Trans. Antennas Propag. 4(3), 192–194 (1956)
A.A. Oliner, Leaky waves: basic properties and applications. Proc. Asia-Pacific Microw. Conf. 1, 397–400 (1997)
F. Monticone, A. Alu, Leaky-wave theory, techniques, and applications: from microwaves to visible frequencies. Proc. IEEE 103(5), 793–821 (2015)
G.A. Korn, T.M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (General Publishing Company, 2000)
R. Adams, Sobolev Spaces (Academic Press, New York, 1975)
I. Gohberg, M. Krein, Introduction to the Theory of Linear Nonself-adjoint Operators in Hilbert Space, vol. 18 (American Mathematical Society, 1969)
Y.G. Smirnov, E.Y. Smolkin, On the existence of an infinite number of leaky complex waves in a dielectric layer. Dokl. Math. 101(1), 53–56 (2020)
Y.G. Smirnov, E.Y. Smolkin, Complex waves in dielectric layer. Lobachevskii J. Math. 41(7), 1396–1403 (2020)
Y.G. Smirnov, Mathematical Methods for Electromagnetic Problems (Penza State University Press, Penza, 2009)
T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1980)
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Shestopalov, Y., Smirnov, Y., Smolkin, E. (2022). Planar Waveguide. In: Optical Waveguide Theory. Springer Series in Optical Sciences, vol 237. Springer, Singapore. https://doi.org/10.1007/978-981-19-0584-1_3
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