Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8813Research ArticleModeling in the Adiabatic Waveguide Modes Model of Amplitude-Phase Transformation of the Electromagnetic Field by a Thin-Film Generalized Waveguide Luneburg LensSevastyanovA LTelecommunication System Departmentalsevastyanov@gmail.comKulyabovD STelecommunication System Departmentdharma@sci.pfu.edu.ruSevastyanovL ATelecommunication System Departmentleonid.sevast@gmail.comPeoples’ Friendship University of Russia15042013413214208092016Copyright © 2013,2013R.K. Luneburg proposed a model of the three-dimensional propagation of electromagnetic radiation. V. Guillemin and S. Sternberg showed that the basic equations of Luneburg, which are the Lagrange equations, correspond to Hamilton’s equations on the cotangent bundle over a three-dimensional conﬁguration space. The model described is a “close relative” of the adiabatic guided modes model, proposed by the authors. In this model similary, two-dimensional ray equations for integrated optical waveguide correspond to Hamilton’s equations on four-dimensional phase space. In this model, the construction of quasi-classical solutions is the phase function of the Hamilton–Jacobi, for the initial phase function the initial Lagrangian manifold is constructed, which is transformed by means of the Hamiltonian ﬂow. As long as the Lagrangian manifold occurred in this process is uniquely projected on the conﬁguration space, we ﬁnd the phase function by calculating the action along the path.Maxwell’s equationsequations of Lagrangeequations of Hamiltonintegrated-optical waveguidesmethod of adiabatic waveguide modesamplitude- phase transformationFourier transformуравнения Максвеллауравнения Лагранжауравнения Гамильтонаинтегрально-оптические волноводыметод адиабатических волноводных модамплитудно-фазовое преобразованиепреобразование Фурье