Numerical and Experimental Investigation for a Resonant Optothermoacoustic Sensor N. Petra 1 , A. A. Kosterev 2 , J. Zweck 1 , S. E. Minkoff 1 , and J.H. Doty III 2 1 Department of Mathematics and Statistics University of Maryland Baltimore County, Baltimore, MD 21250 2 Department of Electrical and Computer Engineering Rice University, Houston, TX 77005 E-mail: znoemi1@umbc.edu Abstract: A theoretical study of a resonant optothermoacoustic sensor employing a laser source and a quartz tuning fork receiver validates experimental results showing that the source should be positioned near the base of the receiver. c  2010 Optical Society of America OCIS codes: (110.5125) Photoacoustics; (300.6340) Spectroscopy, infrared 1. Introduction Cost-effective sensor systems with the ability to identify trace gases with sensitivities in the ppm to ppb range are becoming essential tools for environmental monitoring, medical diagnostics, and homeland security. Quartz-enhanced photoacoustic spectroscopy sensors (QEPAS) hold great promise for such sensor systems because of their simple design, compact size, and potentially low cost [1], [2]. Recently, Kosterev et al. [3] proposed a related sensing method – resonant optothermoacoustic detection (ROTADE) – which could further increase wavelength selectivity and sensitivity. Like QEPAS sensors, ROTADE sensors employ a quartz tuning fork (QTF) as a resonant transducer. With the ROTADE technique there is the possibility of performing measurements at lower pressure than for QEPAS sensor, which allows for higher spectral resolution. As in the case of QEPAS, to detect the presence of a trace gas, a modulated laser beam is directed between the tines of a QTF. The interaction of modulated laser radiation with a gas results in periodic heating and cooling. Whereas QEPAS relies on the conversion of thermal disturbances to acoustic pressure waves via V-T relaxation processes, with ROTADE the thermal disturbance is detected directly. The excited molecules diffuse in space, come into contact with a receiver such as a QTF, and transfer their energy directly to the receiver. Because the laser induces a periodic excitation of the gas molecules, the QTF undergoes periodic thermal expansion and contraction cycles. The heating of the QTF is converted via the indirect pyroelectric effect [4] to a mechanical stress and then to an electric charge separation which can be measured. In this paper, we describe a general mathematical model for a ROTADE sensor. We also describe a preliminary study to determine the effect that localized heating of a QTF has on the received signal. For this study we applied heat directly to the surface of the QTF rather than using the heat source to detect a trace gas. The goals of the study are to determine the optimal location of the heat source with respect to the QTF and to provide an initial validation of the model. 2. Mathematical model We use the theory of linear thermoelasticity [5] to develop a two-stage model for the QTF deformation that is induced by a time-harmonic heat source. First, we use the heat equation to model the generation of thermal waves due to the interaction of the laser and the trace gas and the resulting periodic diffusion of heat into the interior of the QTF. Second, we express the mechanical stress, S, produced by the change in temperature, T , via the stress-strain-temperature relation, S = C[E] − C[αT ], where E is the total strain tensor (i.e. the sum of mechanical and thermal strains), C is the elasticity tensor, and α is the thermal expansion tensor. Consequently, the equation that describes the structural deformation of the tuning fork is ∇· C[∇u]+ ρω 2 u = ∇· C[αT ],