Single-mode propagation of adiabatic guided mode in a smooth transition between planar waveguides

The paper considers a model of adiabatic waveguide modes in the zero approximation applied to the numerical solution of the problem of single-mode propagation of guided modes in a smoothly irregular integrated optical waveguide. Within the framework of the model, the solution to the Maxwell system of equations is reduced to a form that is expressed through the solution of a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field. The multilayer structure of waveguides makes it possible to carry out one more stage of reducing the system of equations of the model to a homogeneous system of linear algebraic equations, the condition of nontrivial solvability of which specifies the dispersion equation. Auxiliary eigenvalue and eigenvector problems for describing adiabatic waveguide modes are solved. Example solutions for single-mode propagation of adiabatic waves are presented. © 2022 SPIE.