Thin-film waveguide Liineburg lens in the model of adiabatic guided modes

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 two-dimensional evolution, leading to the description of a number of new effects.