Abstract
The paper presents the formulation of the dispersion relations for regular planar waveguides and smoothly irregular integrated optical waveguides in forms of elementary continuous functions. The stable algorithm for computing the roots of the dispersion relations for regular and irregular waveguides, which is applicable in the case of real and complex coefficients of the phase retardation of waveguide modes, is developed. The theoretical and numerical method for studying the characteristics of inhomogeneous waveguide modes in the overcritical regimes is elaborated.
In contrast to the zero approximation of the adiabatic modes method, and moreover to the method of comparison waveguides, the fields of irregular waveguide modes of an integrated optical waveguide in the first approximation are described by a pair of equations of coupled oscillators allowing resonance solutions.
Keywords
- irregular integrated optical waveguide
- method of adiabatic modes
- complex-valued dispersion relatieus
- stable numerical algorithm
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References
Adams, A.: Introduction to the theory of optical waveguides. Mir Publ., Moscow (1984) (in Russian)
Ayrjan, E.A., Egorov, A.A., Michuk, E.N., Sevastyanov, A.L., Sevastyanov, L.A., Stavtsev, A.V.: Representations of guided modes of integrated-optical multilayer thin-film waveguides. Preprint JINR, Dubna, E11-2011-31, 56 (2011)
Ayrjan, E.A., Egorov, A.A., Sevastyanov, A.L., Lovetskiy, K.P., Sevastyanov, L.A.: Zero Approximation of Vector Model for Smoothly Irregular Optical Waveguide. Preprint JINR, Dubna, E11-2009-120, 22 (2009) (in Russian)
Egorov, A.A., Lovetskii, K.P., Sevastyanov, A.L., Sevastyanov, L.A.: Simulation of guided modes (eigenmodes) and synthesis of a thin-film generalised waveguide Luneburg lens in the zero-order vector approximation. Quantum Electronic 40(9), 830–836 (2010)
Egorov, A.A., Sevastyanov, L.A.: Structure of modes of a smoothly irregular integrated-optical four-layer three-dimensional waveguide. Quantum Electronics 39(6), 566–574 (2009)
Egorov, A.A., Sevastyanov, A.L., Ayrjan, E.A., Lovetskiy, K.P., Sevastyanov, L.A.: Zero approximation of vector model for smoothly-irregular optical waveguide. Matematicheskoe Modelirovanie 22(8), 42–54 (2010) (in Russian)
Egorov, A.A., Sevastyanov, A.L., Lovetskiy, K.P.: Zero Approximation Model of Integrated-Optical Generalized Luneburg Lens. Bulletin of PFUR. Series Mathematics. Computer science. Physics. (3), 55–64 (2009) (in Russian)
Egorov, A.A., Sevastyanov, L.A., Sevastyanov, A.L.: Investigation of electrodynamic properties of a planar thin-film Luneberg lens. Journ. of Radioelectronics (6), 1–20 (2008)
Egorov, A.A., Sevastyanov, L.A., Sevastyanov, A.L., Lovetski, K.P.: Propagation of electromagnetic waves in thin-film structures with smoothly irregular sections. In: ICO Topical Meeting on Optoinformatics/Information Photonics, September 15–18, pp. 231–234. ITMO, St. Petersburg (2008)
Hunsperger, R.G.: Integrated Optics: Theory and Technology. Springer, New York (1984)
Il’insky, A.S., Kravtsov, V.V., Sveshnikov, A.G.: Mathematical models of electrodynamics. Vysshaya schkola, Moscow (1991) (in Russian)
Marcuse, D.: Light Transmission Optics. Van Nostrand, New York (1972)
Romanenko, A.A., Sotsky, A.B.: The solution of the dispersion relations for planar waveguides in the case of complex roots. Journ. Techn. Phys. 68(4), 88–95 (1998)
Sevastyanov, L.A.: A complete system of modes of open planar waveguide. In: Proc. VI Internat. Sci.-Tech. Conf. “Lasers in Sci., Tech. and Med.”, pp. 72–76. IRE RAN Publ., Suzdal (1995)
Sevastyanov, L.A., Egorov, A.A.: Theoretical analysis of the waveguide propagation of electromagnetic waves in dielectric smoothly-irregular integrated structures. Optics and Spectroscopy 105(4), 576–584 (2008)
Shevchenko, V.V.: On the spectral decomposition in eigenfunctions and associated functions of a nonself-adjoint Sturm-Liouville problem on the whole axis. Diff. Eqs. 15, 2004–2020 (1979)
Snyder, A., Love, J.: Optical Waveguide Theory. Radio Commun., Moscow (1987) (in Russian)
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Ayryan, E.A., Egorov, A.A., Sevastyanov, L.A., Lovetskiy, K.P., Sevastyanov, A.L. (2012). Mathematical Modeling of Irregular Integrated Optical Waveguides. In: Adam, G., Buša, J., Hnatič, M. (eds) Mathematical Modeling and Computational Science. MMCP 2011. Lecture Notes in Computer Science, vol 7125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28212-6_12
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DOI: https://doi.org/10.1007/978-3-642-28212-6_12
Publisher Name: Springer, Berlin, Heidelberg
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