# Shape Optimization of an Open Photoacoustic Resonator
## 1 Introduction  
Photoacoustic spectroscopy (PAS) is a technique based on the generation of an acoustic signal after the absorption of light by molecules [1]. It has been widely applied in numerous fields ranging from evaluation of materials [2, 3], agriculture [4, 5], medical/biological applications [6, 7, 8] and environmental analysis [9, 10, 11]. PAS offers high detection sensitivity as low as the parts per billion (ppb) level [12] and is suitable for the measurement of optically opaque samples where traditional absorption spectroscopic methods fail. Often, acoustic resonators are employed to significantly amplify the photoacoustic signal. In a conventional experimental setup the sample is located inside a sealed resonator. However, in specific applications a closed resonator is not suitable, and an open resonator configuration is required. Photoacoustic (PA) measurements of blood glucose levels are performed using open T-shaped resonators [13, 14]. One of the resonator ends is left unsealed to prevent an increase of humidity within the resonator that is caused by skin transpiration [13]. This is because PA glucose measurements are performed using mid-infrared radiation (MIR) and water has strong absorption in the MIR region. Humidity leads to increased absorption of MIR that interferes with PA glucose measurements. Furthermore, the opening helps to improve the stability of the measurement by minimizing temperature fluctuations [13]. However, the opening deteriorates the photoacoustic (PA) signal. As a consequence, the detection sensitivity is not quite sufficient for an industrial implementation of a diagnostic sensor. Improving the sensitivity is therefore crucial for a continuation of the concept and real-life blood glucose monitoring based on that. The strength of the PA signal is strongly dependent on the resonance amplification. Numerous studies have reported optimization strategies for PA resonators. [PERSON] et al. [15] used the transmission line model to optimize the geometry of a closed cylindrical resonator with buffer volumes for maximum ratio of the PA signal to the background signal fromwindow absorption. They established that large buffer volume radii suppress the background signal thus improving the sensitivity of the measurements. Using finite element modeling, [PERSON] et al. (2016) optimized the strength of the PA signal of an H-shaped resonator using the amplitude mode expansion (AME) method. They split the resonator into axially symmetric cones of equal length and optimized the shape of each individual cone. The optimized resonator had an hourglass shape and was experimentally confirmed to have a signal improvement of around 13% compared to the original resonator ([PERSON] et al., 2016). [PERSON] et al. (2018) optimized the geometry of a closed cylindrical resonator capped with buffer volumes for improved signal-to-background ratio (SBR). For their studies, they simulated the photoacoustic signal using the viscothermal (VT) method and verified the results with experimental measurements. They demonstrated that the signal-to-background ratio (SBR) is maximized using buffer volumes with large radii and a length that is half the length of the resonator. Later, they extended their studies to the optimization of a two-resonator PA cell used in aerosol applications. Their study concluded that the general rule of setting the buffer length to half the resonator length is not universal and varies depending on the resonator ([PERSON] et al., 2016). [PERSON] et al. (2017) worked on the improvement of the sensitivity of PA glucose measurements. They optimized the resonator geometry by calculating its acoustic eigenmodes and matched one of the resonances of the resonator with that of their microphone. The synergetic resonance amplification increased the signal-to-noise ratio of their measurement system 3.5 times. In contrast to the above, in this paper we present a numerical optimization of an open PA resonator using the finite element method.