Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory

Abstract: Alteration of a geometry parameter in the cross section of a dielectric waveguide with piecewise constant permittivity profile can be regarded as a refractive index perturbation in a layer along a dielectric discontinuity line. Starting from these thin layer perturbations, we derive explicit expressions for partial derivatives of propagation constants with respect to the transverse waveguide dimensions, both for hybrid modes and for fields calculated in the semivectorial approximation. The perturbational formulas allow to estimate fabrication tolerances for realistic integrated optics devices at almost no extra computational cost. We demonstrate this by the example of a simple directional coupler and compare the perturbational results to numerically calculated tolerances.