Geometry tolerance estimation for rectangular dielectric waveguide devicesby means of perturbation theory

Alteration of a geometry parameter in the cross section of a dielectric wav eguide with piecewise constant permittivity profile can be regarded as a re fractive index perturbation in a layer along a dielectric discontinuity lin e. Starting from these thin layer perturbations, we derive explicit express ions for partial derivatives of propagation constants with respect to the t ransverse waveguide dimensions, both for hybrid modes and for fields calcul ated 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 o f a simple directional coupler and compare the perturbational results to nu merically calculated tolerances. (C) 1999 Elsevier Science B.V. All rights reserved.