Rough Fabry-Perot cavity: a vastly multi-scale numerical problem

A commercial Fabry-Perot laser diode is characterized by highly disproportionate dimensions, which poses a significant numerical challenge, even for state-of-the-art tools. This challenge is exacerbated when one of the cavity mirrors is roughened, as is the case when fabricating random laser diodes. Such a system involves length scales from several hundred micrometres (length) to a few nanometres (roughness) all of which are relevant when studying optical properties in the visible. While involving an extreme range of dimensions, these cavities cannot be treated through statistical approaches such as those used with self-similar fractal structures known to show well-studied properties. Here we deploy numerical methods to compute cavity modes and show how random corrugations of the Fabry-Perot cavity wall affect statistical proper-ties of their spectral features. Our study constitutes a necessary first step in developing technologically essential devices for photonic computation and efficient speckle-free illumination.