Analytical calculations in maple to implement the method of adiabatic modes for modelling smoothly irregular integrated optical waveguide structures

This paper presents analytical calculations in CAS Maple. The calculations are used for the method of adiabatic waveguide modes, applied in mathematical modeling of smoothly irregular integrated-optical waveguides. Such structures drew researchers' attention at the end of the 20th century, when several models were proposed to describe the coherent laser radiation in such structures. But these models could not adequately characterize the phenomena of depolarization and hybridization of guided modes. The proposed model of adiabatic waveguide modes, on the contrary, describes these experimentally observed phenomena, but on the other hand, we have more complicated analytical expressions. So we have developed a special program in Maple to computerize analytical calculations. The program is presented in this work. © 2014 Springer International Publishing.