Numerical shape optimization of photoacoustic resonators

The sensitivity of photoacoustic sensors strongly depends on the shape of the acoustical resonator. Up to now, mainly photoacoustic sensors consisting of a number of cylindrical parts have been investigated (cylinder cells, H cells, T cells etc.). In this paper, a numerical shape optimization of the resonator cell of photoacoustic sensors is described. The approach considers all shapes that can be represented by a number of axisymmetrical truncated cones which are connected in a continuous way. In addition, the geometry of the cell is subjected to certain constraints, e.g. the laser beam should not be blocked during its passage through the cell. The purpose is to maximize the sensor's signal strength. The acoustic pressure at the position of the microphone represents the objective function and is calculated using an eigenmode expansion combined with a finite element calculation. The solution of a 17-dimensional nonlinear optimization problem is a resonator shape with a substantial quality improvement with reference to the well-known H cell.