Thin-film waveguide L¨uneburg lens in the model of adiabatic guided modes

Abstract

A mathematical model is presented that describes the processes of propagation and transformation of coherent electromagnetic radiation in a multilayer three-dimensional (3D) smoothly irregular integrated optical waveguide, called the model of adiabatic guided modes. Its presentation and individual applications in smoothly irregular integrated optical waveguides contain two short stories: • two-dimensional evolution of guided modes is described; • boundary conditions are formed on non-horizontal planes tangent to media interfaces, which lead to the description of hybridization of guided modes and other interesting phenomena. The model of adiabatic guided modes generalizes the cross-section method (reference waveguide method) with nonlocal boundary conditions for the transverse guided mode operator in the reference waveguide cross section to the case of twodimensional evolution, leading to the description of a number of new effects.