Vectorial wave-matching mode analysis of integrated optical waveguides

For mode fields of integrated optical waveguides with piecewise constant and rectangular permittivity profile, Maxwell's equations reduce to the two-dimensional Helmholtz wave equation, supplemented by continuity requirements on the boundaries between different media. Two basic components of the mode field are expanded into factorizing harmonic or exponential functions, separately on each rectangular region. We determine approximations for guided modes and propagation constants by means of a minimization procedure based on a least squares expression for the mismatch in the continuity requirements. Results for the hybrid mode fields of typical sample waveguides classify this approach as competitive with and superior to alternative methods for vectorial mode analysis, although some open questions remain.