References
- Samarskiy AA, Tikhonov AN. O predstavlenii polya v volnovode v vide summy poley TE i TM [Representation of the field in the waveguide as a sum of TE and TM fields]. Zhurnal tehnicheskoy fiziki. 1948;18(7):959–970. Russian.
- Ilyinsky AS, Slepyan GYa, Slepyan AYa. Propagation, scattering and dissipation of electromagnetic waves. London: Peter Peregrinus IET; 1993.
- Chew WC. Lectures on theory of microwave and optical waveguides. 2012;362. Available from http://wcchew.ece.illinois.edu/chew/course/tgwAll20121211.pdf
- Werner P. Resonanzphänomene in akustischen und elektromagnetischen wellenleitern. [Resonance phenomena in acoustic and electromagnetic waveguides]. ZAMM. 1987;67(4):42–54. German.
- Sevastyanov LA, Egorov AA. Theoretical analysis of the waveguide propagation of electromagnetic waves in dielectric smoothly-irregular integrated structures. Opt Spectrosc. 2008;105(4):576–584.
- Egorov AA, Sevastyanov LA. Structure of modes of a smoothly irregular integrated-optical four-layer three-dimensional waveguide. Kvantovaya Elektronika. 2009;39(6):566–574.
- Egorov AA, Lovetskii KP, Sevastyanov LA, et al. Simulation of guided modes (eigenmodes) and synthesis of a thin-film generalised waveguide Luneburg lens in the zero-order vector approximation. Kvantovaya Elektronika. 2010;40(9):830–836.
- Sevastianov LA, Egorov AA, Sevastyanov AL. Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures. Phys At Nuclei. 2013;76(2):224–239.
- Schelkunoff SA. Conversion of Maxwell’s equations into generalized telegraphist’s equations. Bell Syst Tech J. 1955;34(5):995–1043.
- Snyder W. Coupled-mode theory for optical fibers. J Opt Soc Am. 1972;62(11):1267–1277.
- Marcuse D. Coupled mode theory of round optical fibers. Bell Syst Tech J. 1973;52(6):817–843.
- Yariv A. Coupled-mode theory for guided-wave optics. IEEE J Quantum Electron. 1973;9(9):919–933.
- Kogelnik H. Theory of dielectric waveguides. In: Tamir T, editor. Integrated optics. New York (NY): Springer-Verlag; 1975. p. 13–81.
- Hardy A, Streifer W. Coupled mode theory of parallel waveguides. J Lightwave Technol. 1985;3(5):1135–1146.
- Kawakami S, Haus HA. Continuum analog of coupled multiple waveguides. J Lightwave Technol. 1986;4(2):160–168.
- Berk AD. Variational principles for electromagnetic resonators and waveguides. IRE Trans Antennas Propag. 1956;4(2):104–111.
- Haus HA. Electron beam waves in microwave tubes. Proceedings of the symposium on electronic waveguides. New York (NY): Polytechnic Institute of Brooklyn; 1958.
- Wei-P Huang. Mu J. Complex coupled-mode theory for optical waveguides. Opt Express. 2009;17(21):19134–19152.
- Xu J. Chen Yu. General coupled mode theory in non-Hermitian waveguides. Opt Express. 2015;23(17):22619–22627.
- Stevenson AF. General theory of electromagnetic horns. J Appl Phys. 1951;22(12):1447–1460.
- Stevenson AF. Exact and approximate equations for wave propagation in acoustic horns. J Appl Phys. 1951;22(12):1461–1463.
- Katsenelenbaum BZ. Neregulyarnyye volnovody s medlenno menyayushchimisya parametrami [Irregular waveguides with slowly varying parameters]. Doklady AN SSSR. 1955;102(4):711–714. Russian.
- Lyubarskiy GYa, Povzner AYa. K teorii rasprostraneniya voln v neregulyarnykh volnovodakh [On the theory of wave propagation in irregular waveguides]. Zhurnal tehnicheskoy fiziki. 1959;29(2):170–179. Russian.
- Mal’tsev NE. Nekotoryye modifikatsii metoda poperechnykh secheniy [Some modifications of the cross-section method]. Akusticheskiy zhurnal. 1970;16(1):102–109. Russian.
- Sveshnikov AG. Priblizhennyy metod rascheta slabo neregulyarnogo volnovoda [Approximate method for calculating a weakly irregular waveguide]. Doklady AN SSSR. 1956;110(2):197–199. Russian.
- Il’inski AS, Sveshnikov AG. Methods for investigating irregular waveguides. USSR Comput Math Math Phys. 1968;8(2):167–180.
- Fedoryuk MV. A justification of the method of transverse sections for an acoustic wave guide with nonhomogeneous content. USSR Comput Math Math Phys. 1973;13(1):162–173.
- Sveshnikov AG. The basis for a method of calculating irregular waveguides. USSR Comput Math Math Phys. 1963;3(1):219–232.
- Sveshnikov AG. A substantiation of a method for computing the propagation of electromagnetic oscillations in irregular waveguides. USSR Comput Math Math Phys. 1963;3(2):413–429.
- Bogolyubov AN, Sveshnikov AG. Investigation of plane waveguides with an inhomogeneous filling using an iterative method. USSR Comput Math Math Phys. 1974;14(4):125–133.
- Bogolyubov AN, Erokhin AI, Mogilevskii IE. Mathematical simulation of an irregular waveguide with reentering edges. Comput Math Math Phys. 2012 June;52(6):932–936.
- Chiang KS. Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides. Opt Quantum Electron. 1994;26:S113–S134. doi:10.1007/BF00384667.
- Wang YEH, Zhang X. Generalized Fourier series expansion method for determining cutoffs in optical waveguides. Int J Infrared Millimeter Waves. 1997;18(9):1731–1737.
- Gaal S, Lorincz E, Richter PI, et al. Assessment of the point matching method for waves in uniaxially anisotropic materials. Opt Commun. 1998;155:368–375.
- Kim J, Kim DY. Dispersion calculation method for axially symmetric optical fibers. Fiber Integr Opt. 2002;21(1):13–29.
- Malykh MD, Nikolaev NE, Sevastianov LA. The geometrical description of electromagnetic radiation. J Electromagn Waves Appl. 2016 Oct;30(15):2055–2066.
- Zhang K, Li D. Electromagnetic theory for microwaves and optoelectronics. Berlin: Springer; 2007.
- Menachem Z, Tapuchi S. Influence of rectangular and periodic rectangular profiles in the cross section of the straight waveguide on the output field. J Electromagn Waves Appl. 2016 Feb;30(4):536–552.
- Marcuse D. Solution of the vector wave equation for general dielectric waveguides by the Galerkin method. IEEE J Quantum Electron. 1992 Feb;28(2):459–465.
- Lo KM, Li EH. Solutions of the quasi-vector wave equation for optical waveguides in a mapped infinite domains by the Galerkin’s method. J Lightwave Technol. 1998;16(5):937–944.
- Huang C-C, Huang C-C. An efficient and accurate semivectorial spectral collocation method for analyzing polarized modes of rib waveguides. J Lightwave Technol. 2005;23(7):2309–2317.
- Chaudhuri PR, Ghatak AK, Pal BP, et al. Fast convergence and higher-order mode calculation of optical waveguides: perturbation method with finite difference algorithm. Opt Laser Technol. 2004;37:61–67.
- Hsiao CS, Chiang YJ, Wang L, et al. An efficient numerical full-vectorial mode solver based on Fourier series expansion method. IEEE Photonics J. 2014 Aug;6(4):1–17. doi:10.1109/JPHOT.2014.2335714.
- Love AEH. A treatise on the mathematical theory of elasticity. Cambridge: Cambridge University Press; 1927.
- Bogolyubov AN, Malykh MD. Remark on the radiation conditions for an irregular waveguide. Comput Math Math Phys. 2003;43(4):560–563.
- Bogolyubov AN, Delitsyn AL, Sveshnikov AG. On the completeness of the set of eigen- and associated functions of a waveguide. Comput Math Math Phys. 1998;38(11):1815–1823.
- Pashaie R. Fourier decomposition analysis of anisotropic inhomogeneous dielectric waveguide structures. IEEE Trans Microwave Theory Tech. 2007 Aug;55(8):1689–1696.
- Courant R, Hilbert D. Methods of mathematical physics. vol. 1--2, Berlin: Wiley-VCH; 1989.
- SageMath [Internet]. Available from: http://www.sagemath.org