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.

Micro-Opto-Electro-Mechanical Systems (MOEMS) accelerometer is a new type of accelerometer which combines the merits of optical measurement and Micro-Electro-Mechanical Systems (MEMS) to enable high precision, small volume and anti-electromagnetic disturbance measurement of acceleration. In recent years, with the in-depth research and development of MOEMS accelerometers, the community is flourishing with the possible applications in seismic monitoring, inertial navigation, aerospace and other industrial and military fields. There have been a variety of schemes of MOEMS accelerometers, whereas the performances differ greatly due to different measurement principles and corresponding application requirements. This paper aims to address the pressing issue of the current lack of systematic review of MOEMS accelerometers. According to the optical measurement principle, we divide the MOEMS accelerometers into three categories: the geometric optics based, the wave optics based, and the new optomechanical accelerometers. Regarding the most widely studied category, the wave optics based accelerometers are further divided into four sub-categories, which is based on grating interferometric cavity, Fiber Bragg Grating (FBG), Fabry-Perot cavity, and photonic crystal, respectively. Following a brief introduction to the measurement principles, the typical performances, advantages and disadvantages as well as the potential application scenarios of all kinds of MOEMS accelerometers are discussed on the basis of typical demonstrations. This paper also presents the status and development tendency of MOEMS accelerometers to meet the ever-increasing demand for high-precision acceleration measurement.