Modeling and Design Optimization of a Resonant Optothermoacoustic Trace Gas Sensor

Trace gas sensors that are compact and portable are being deployed for use in a variety of applications including disease diagnosis via breath analysis, monitoring of atmospheric pollutants and greenhouse gas emissions, control of industrial processes, and for early warning of terrorist threats. One such sensor is based on optothermal detection and uses a modulated laser source and a quartz tuning fork resonator to detect trace gases. In this paper we introduce the first mathematical model of such a resonant optothermoacoustic sensor. The model is solved via the finite element method and couples heat transfer and thermoelastic deformation to determine the strength of the generated signal. Numerical simulations validate the experimental observation that the source location that produces the maximum signal is near the junction of the tines of the tuning fork. Determining an optimally designed sensor requires maximizing the signal as a function of the geometry of the quartz tuning fork (length and width of the tines, etc). To avoid difficulties from numerical differentiation we chose to solve the optimization problem using the derivative-free mesh adaptive direct search algorithm. An optimal tuning fork constrained to resonate at a frequency close to the 32.8 kHz resonance frequency of many commercially available tuning forks produces a signal that is three times larger than the one obtained with the current experimental design. Moreover, the optimal tuning fork found without imposing any constraint on the resonance frequency produces a signal that is 24 times greater than that obtained with the current sensor.