In-Depth Optical Characterization of Femtosecond-Written Waveguides in Silicon

We analyze the properties of femtosecond-laser-written waveguides in silicon. By using a mix of semianalytical and numerical methods, we find that the transverse index profile is accurately modeled by a W-shaped function supporting nonleaky guided modes. The maximum change in the refractive index is about $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, whereas the central lobe is about 2.5 $\ensuremath{\mu}\mathrm{m}$ wide for a writing wavelength of 1.55 $\ensuremath{\mu}\mathrm{m}$. Waveguide shape and maximum index variation both saturate for input pulse energies larger than 100 nJ and a pulse duration of 860 fs. We find that the performance of the waveguides are limited by the presence of randomly distributed scattering centers situated in the waveguide core. To confirm our findings, we probed the waveguide response as the input beam is kept normal at the input interface but shifted perpendicularly to the waveguide axis, resulting in a variable offset with respect to the center of the waveguide. The behavior of the energy coupled in the waveguide versus the beam shift is in agreement with theoretical predictions. We also used a simple analytical model to describe the nonlinear propagation of the writing beam.