Zero approximation of vector model for smoothly-irregular optical waveguide

On the base of adiabatic representation for eigenmodes of integrated-optical multilayer waveguide are presented differential equations and boarder conditions to vertical distribution of electromagnetic field in the waveguide. To smoothly-irregular waveguides an asymptotic method is applied and zero approximation parts of differential equations and boarder conditions are determined. Exact expressions are considered for vertical distribution of electromagnetic field in a waveguide and for boarder conditions. Finally the problem is reduced to the solution of homogeneous system of linear algebraic equations depending on a spectral parameter and to the search of the parameter values. The method and algorithms of calculating vertical dispersion of adiabatic modes are considered in conclusion.