Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8353Research ArticleCalculating Phase Retardation Field in Smoothly Irregular Integrated-Optical Waveguide (Using Thin-Film Generalized Waveguide Luneburg Lens)SevastyanovL ATelecommunication Systems Departmentleonid.sevast@gmail.comKulyabovD STelecommunication Systems Departmentdharma@sci.pfu.edu.ruSevastyanovA LTelecommunication Systems Departmentalsevastyanov@gmail.comPeoples’ Friendship University of Russia15022014213314108092016Copyright © 2014,2014Maxwell’s equations are extremely simple and elegant. However, the specific calculations require much more sophisticated approaches. Thus, in the problems of calculation of nonregular integrated optical waveguides a few basic techniques are used. The authors propose to use the method of adiabatic waveguide modes. This method follows in the footsteps of Luneburg works. Moreover, the method has a clear geometric interpretation. As well as Luneburg equations, the equations obtained by this correspond to the Hamilton equations on the cotangent bundle over the configuration space. Moreover, to calculate ray paths a simple geometrization is used, when the refractive index is represented as a metric of some efficient space. Thus, the phase function is evaluated as an action along the trajectory. Thin-film Luneburg lens is an interesting object in the general theoretical sense as well as in practical one. Its study allows to further describe a class of objects, but it is an essential element for the construction of a purely optical control devices. Thus, the authors consider the method of adiabatic modes most suitable for studies of such object as a thin-film generalized waveguide Luneburg lens.Maxwell’s equationsequations of Lagrangeequations of Hamiltonintegrated-optical waveguidesmethod of adiabatic waveguide modesуравнения Максвеллауравнения Лагранжауравнения Гамильтонаинтегрально-оптические волноводыметод адиабатических волноводных мод