Method of adiabatic modes in research of smoothly irregular integrated optical waveguides: zero approximation

We consider the application of the method of adiabatic waveguide modes for calculating the propagation of electromagnetic radiation in three-dimensional (3D) irregular integrated optical waveguides. The method of adiabatic modes takes into account a three-dimensional distribution of quasi-waveguide modes and explicit ('inclined') tangential boundary conditions. The possibilities of the method are demonstrated on the example of numerical research of two major elements of integrated optics: a waveguide of 'horn' type and a thin-film generalised waveguide Luneburg lens by the methods of adiabatic modes and comparative waveguides.