Inverse design and realization of an optical cavity-based displacement transducer with arbitrary responses

Optical cavity has long been critical for a variety of applications ranging from precise measurement to spectral analysis. A number of theories and methods have been successful in describing the optical response of a stratified optical cavity, while the inverse problem, especially the inverse design of a displacement sensitive cavity, remains a significant challenge due to the cost of computation and comprehensive performance requirements. This paper reports a novel inverse design methodology combining the characteristic matrix method, mixed-discrete variables optimization algorithm, and Monte Carlo method-based tolerance analysis. The material characteristics are indexed to enable the mixed-discrete variables optimization, which yields considerable speed and efficiency improvements. This method allows arbitrary response adjustment with technical feasibility and gives a glimpse into the analytical characterization of the optical response. Two entirely different light-displacement responses, including an asymmetric sawtooth-like response and a highly symmetric response, are dug out and experimentally achieved, which fully confirms the validity of the method. The compact Fabry-Perot cavities have a good balance between performance and feasibility, making them promising candidates for displacement transducers. More importantly, the proposed inverse design paves the way for a universal design of optical cavities, or even nanophotonic devices.