Advances in Modeling, Design, and Fabrication of Deep-Etched Multilayer Resonators

We present recent advances in modeling, design, and fabrication of in-plane multilayer optical resonators fabricated by high aspect ratio etching of silicon. We first revisit the model of Gaussian beam divergence proposed by A. Lipson to correct a mistake that leads to an underestimation of the losses affecting this type of resonator. Secondly, we discuss the influence of surface roughness at the silicon-air interfaces of multilayered structures. Roughness profiles-measured by white light interferometry on the sidewalls of silicon trenches etched by deep reactive ion etching (DRIE)-are presented. The single absorbing layer model of Carniglia is used to predict the influence of the measured roughness ( nm RMS). This model is combined with the corrected model for Gaussian beam divergence and is compared with recent experimental results obtained for a new generation of deep-etched Fabry-Perot refractive index sensors. These sensors are fabricated using the contour lithography method, which is demonstrated to greatly improve the predictability of their optical characteristics. The combined model for roughness and divergence is found to correspond remarkably well with the experimental results, with predictions of loss and finesse of the resonances within an average error of 1.3 dB and 25%, respectively. We therefore expect the models and the simulations presented in this article to become a useful tool for the design of devices based on deep-etched multilayer resonators.