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

Displacement as a basic physical quantity often serves as the intermediate physical quantity of various sensors in terms of its excellent testability. Most sensors transform the quantity to be measured, including force, deformation, acceleration, angle, etc., into the detectable displacement, thus completing the measurement or perception. Therefore, a displacement sensing unit with high accuracy and compactness is the cornerstone of precision sensing and advanced manufacturing and plays an important role in fundamental research and industrial production.

Optical displacement sensors, especially the Fabry-Perot cavity-based sensor, have found great success in dozens of application scenarios due to their high optical finesse and promise of miniaturization. Optical displacement sensors pursue higher light-displacement sensitivity, optical contrast, and larger linear range.

Regarding a Fabry-Perot cavity-based displacement sensor, people always manipulate the response and finesse by adjusting the cavity mirrors. Although there have been a series of theories and models that can successfully predict the optical response, the inverse problem, e.g., the design of an optical cavity with a designated response, was extremely difficult in the past because of the unaffordable cost of computation. Conventional displacement-sensitive cavity design historically relies on intuition-based approaches, which cannot simultaneously tune multiple parameters and optimize interdependent characteristics.

Advances in the development of algorithms and increased computing power have enabled inverse designs of a mount of nanophotonic structures with desired functional characteristics. However, the inverse design of the displacement-sensitive cavity is a typical multi-objective optimization problem. The problem involving how to realize high sensitivity, linearity, and technical feasibility remains open. In addition, common numerical methods are more like fuzzy operations that cannot help understand physics and cost substantially more compared with simple formula calculation. It is fair to say that the inverse design of a cavity-based displacement sensing unit, which allows a large degree of freedom in the light-displacement response control, is of considerable scientific and practical value.

The authors of an article now published in Opto-Electronic Advances combined the characteristic matrix method and mixed-discrete variables algorithm-enabled inverse design to establish a path toward an arbitrary response of an optical cavity-based displacement transducer. This work uses the characteristic matrix method to build the connection between the variable parameters and output response of the cavity, and this method is demonstrated to be concise and trustable by benchmarking other numerical methods.

A modified mixed-discrete genetic algorithm is used to optimize the variable parameters of the optical cavity by constructing a self-built fitness function. The algorithm is fit for discrete variables such as the material index number (each material's complex refractive index is numbered, termed MI) to greatly improve the speed. The fitness function contains the evaluation factors of optical contrast, intensity, linearity, and symmetry and is moderately adjusted. Single-layer and multi-layers systems are both considered, and the optimal results in turn pass through tolerance analysis to maintain high process feasibility.

This work presents two specific cavity designs to illustrate the effectiveness of the inverse design, where the cavities have a designated sawtooth-like light-displacement response and a highly symmetric response, respectively. Such designs are verified by experiments, which demonstrate that they have high contrast and good consistency. This makes the compact cavities promising candidates for displacement transducers aiming at high sensitivity and other performances.

Furthermore, the semi-analytical inverse design-based flow, including theoretical model setup, mixed-discrete variables evolutionary algorithm, and Monte Carlo method-based tolerance analysis, allows a specific design of displacement-sensitive optical cavities and further opens avenues for the universal design of stratified devices.