An Ab Initio, Fully Coherent, Semi-Analytical Model of Surface-Roughness-Induced Scattering

Integrated optics and silicon photonics is a rapidly maturing technology and is progressing in telecom, computation, and sensing. Surface-roughness-induced scattering is the primary source of optical loss in any photonic integrated circuit, and as such, ultimately limits the performance of any of its applications. However, a closed form description for arbitrary refractive index profiles remains lacking, even though such a one is essential to enable an objective-oriented design of the waveguide platform. We present an ab initio, fully coherent, analytical model based on the volume current method that uses the surface roughness' autocorrelation function and the unperturbed mode's electromagnetic fields to predict the loss coefficient in closed form. An improved expression for the perturbation facilitates the application also to high-index-contrast systems. Hence, it is flexible concerning wavelength, materials, fabrication process, geometry and mode. Consequently, our model may be seamlessly integrated into electromagnetic simulation software suites, once the surface roughness is known for the utilized fabrication process. To verify our model, we compare the calculated scattering losses to measured propagation losses and established models for a wide range of waveguide systems in literature. We find that the previously neglected correlation along the waveguide height significantly impacts the scattering, which necessitates the holistic statistical analysis of the surface roughness. We believe these comprehensive prediction capabilities to be a useful tool for the optimization of silicon photonics design and fabrication, especially for low-confinement applications like sensors.