Dynamic and spectral responses of a micromachined Fabry-Perot interferometer-based spectrometer

The dynamic and spectral responses of a micromachined Fabry-Perot interferometer (FPI) subjected to an electrostatic force have been simulated. The FPI features a circular corrugated diaphragm supporting a flat thin film coated optical mirror that can be driven by four electrodes. These four electrodes serve not only to fine adjust the parallelism but also to tune the air gap between the mirrors and hence the characteristic wavelengths of the interferometer. Regarding to the dynamics response of the flat diaphragm, we consider a force balance among the squeezing-film damping, the spring force of the corrugated diaphragm, the inertia force of the flat diaphragm, and the electrostatic attraction force. The spectral response of a novel FPI based spectrometer that consists of two FPIs in tandem has been modeled and simulated. Contrary to the second-order oscillation normally existed in a mass-spring-damper system, for the current system, the dynamic of the optical mirror released from a pre-deflection displays an over-damping effect, which depicts the simulated mirror deflection as a function of time relaxing from a 6 μm pre-deflection. This interesting phenomenon may exist pervasively in various micro-systems due to its higher area to mass ratio compared to that of the macro-systems. Our simulated result demonstrates that the tandem FPI based spectrometer, in principle, is able to obtain a spectral response with high accuracy from a light source having continuous spectrum.