Strain-induced birefringence in Si1−xGex optical waveguides

For the design of Si1−xGex optical waveguide devices, one of the most important material parameters is the refractive index difference, δn, between the alloy layer and the silicon substrate. We have measured δn for pseudomorphic waveguide layers with germanium fractions between 1% and 9% by fitting measured mode profiles to theoretical mode shapes for a wavelength of 1.3 μm. For transverse electric modes, the measured δn varied with composition as δn=(0.34±0.05)x. Transverse magnetic modes were more tightly confined to the waveguide layer and the index was determined to be δn=(0.55±0.05)x. The large difference between the two polarizations results from strain-induced birefringence. Bulk photoelastic theory, using constants appropriate for pure silicon, predicts strain contributions to the index of −0.080x and +0.095x for light polarized parallel and perpendicular, respectively, to the substrate plane, consistent with experimental observations.