Perturbational estimation of geometry tolerances for rectangular integrated optics devices

Shifting the location of a dielectric boundary in the cross section of an integrated optical waveguide with piecewise constant refractive index profile results in a permittivity perturbation in a layer along the discontinuity line. On the basis of these thin layer perturbations, we discuss perturbational expressions for the derivatives of the propagation constants with respect to geometry parameters, both for fully vectorial, hybrid and for semivectorial approximations to the basic mode fields. The expressions are numerically verified by comparison with rigorously calculated data for a common semiconductor rib waveguide. Applied to a more complex device, the perturbational approach allows to estimate its complete set of tolerances for the geometry parameters, including the wavelength, on the basis of a single mode analysis. This is exemplified with a two rib waveguide coupler. By comparison with conventionally computed tolerances we give some assessment for the applicability of the effective perturbational approach.