2 Modeling and Numerical Investigation of Photoacoustic Resonators Bernd Baumann 1 , Bernd Kost 1 , Marcus Wolff 1,2 and Hinrich Groninga 2 1 Hamburg University of Applied Sciences, 2 PAS-Tech GmbH, Hamburg Germany 1. Introduction Photoacoustic spectroscopy is based on the photoacoustic effect, that was discovered in 1880 by A. G. Bell (Bell, 1880). One year later, W. C. Röntgen published a paper on the application of photoacoustic spectroscopy on gas (Röntgen, 1881). Sensors based on the photoacoustic effect are devices which allow the detection of molecules of very low concentration. It is even possible to discriminate different isotopes of one molecule. In a photoacoustic sensor (PAS) a gas sample contained in the measuring cell is subjected to a laser beam. The wavelength of the laser is tuned to a vibrational or rotational line of the searched molecules. The technique takes advantage of the fact, that absorbed electromagnetic radiation is due to non-radiant transitions partially transferred into thermal energy of the surrounding molecules. This leads to an increase of the pressure in the sample. A modulated emission generates a sound wave. The resulting acoustic wave is detected by a microphone and phase-sensitively measured. A typical set-up for photoacoustic investigation is shown in Figure 1. To detect low molecule concentrations one enhances the microphone signal by utilizing the acoustic resonances of the measuring chamber. The achievable amplification depends on the shape of the resonator and on the precise coupling of the laser profile and the acoustic modes. Experimental investigations of different PAS set-ups are very time consuming and expensive. Addressing the related questions numerically is much more efficient. The theoretical treatment of PAS has a long history. Analytical calculations have been performed for cylinder shaped resonators, which play an important role among the variety of measuring chambers. Resonator shapes of higher complexity, however, are not amenable to these methods. Numerical techniques like the finite element method (FEM) represent a suitable tool to investigate such systems. Generally, the investigation of the excited gas requires the solution of a system of coupled partial differential equations. The FEM allows the treatment of such coupled problems. However, this is rather computer time consuming and, considering the numerous design variants, should be avoided. In literature, methods are discussed, that allow to circumvent the coupled problem. We combine these methods with the FEM and are now able to calculate the photoacoustic signal for arbitrary resonator shapes. This offers the possibility