Analytical modeling of the static and dynamic response of thermally actuated optical waveguide circuits

Thermo-optic phase shifters allow one to dynamically tune and control the operation of integrated-optics interferometers. They have been demonstrated nowadays in different waveguide platforms, and their reliable functioning has enabled the realization of reconfigurable circuits of notable complexity. The design approach to such devices is often based on finite-element numerical simulations, which provide accurate descriptions of the underlying thermal phenomena, at the price of long computational times. Here, on the contrary, we devise an analytical model for the heat diffusion in a simplified geometrical configuration. The model describes both static and dynamic regimes, and can be conveniently applied both to three-dimensional waveguide devices inscribed by femtosecond laser pulses and to planar lithographic circuits. The accuracy of the predictions of the model is validated with experimental measurements on Mach-Zehnder interferometers with different geometries, realized in both kinds of platforms.