Fourier decomposition method applied to mapped infinite domains:scalar analysis of dielectric waveguides down to modal cutoff

By transforming the infinite x-y plane onto a unit square and using two-dimensional Fourier series expansions, the modal fields and propagation constants of dielectric waveguides are accurately determined within the scalar (weak-guidance) regime. The new method is reliable down to modal cutoff and gives cutoff V-values directly. Numerical cutoff values for the LP₁₁ modes of square- and rectangular-core waveguides are determined as a function of core aspect ratio, and are found to agree with those obtained by the finite element method to within 0.1%