# Design of NO\({}_{2}\) Photoacoustic Detection System Based on Finite Element Simulation
## 1 Introduction  
An excessive concentration of NO\({}_{2}\) in the air leads to photochemical smog, greenhouse effects, and acid rain [1, 2], and NO\({}_{2}\) also participates in the formation of secondary organic aerosols, nitric acid, and O\({}_{3}\)[3, 4]. Therefore, the detection of NO\({}_{2}\) is very important. In recent years, due to the continuous development of lasers, optical technology, and acoustic sensors, photoacoustic spectroscopy technology has increasingly become an important means of trace gas detection [5]. As a carrier producing photoacoustic effects, the performance of a photoacoustic cell directly affects the sensitivity of the entire detection system, and the design of a photoacoustic cell is extremely critical. The most classic cylindrical photoacoustic cell has been widely used in research at home and abroad. In terms of the measurement of trace gases, some researchers have made very important contributions [6, 7]. For example, [PERSON] designed a tunable portable TDLAS sensor, whose weight and power consumption were only 5 kg and 10 W, respectively, and the detection limits of CO\({}_{2}\) and H\({}_{2}\)O reached 0.13 ppm and 3.7 ppm [8]. [PERSON] built a NO\({}_{2}\)-detection system using a cylindrical resonant photoacoustic cell and studied the relationship between pressure, the NO\({}_{2}\) volume fraction, and resonance frequency with a 444 nm blue laser as the excitation light source [9]. [PERSON] used quartz-enhanced photoacoustic spectroscopy (QEPAS) and a distributed feedback quantum cascade laser to achieve high-sensitivity detection ofCO and N\({}_{2}\)O [10]. [PERSON] designed a high-mirror photoacoustic sensing system to enhance the laser power by increasing the number of reflections, and compared with traditional photoacoustic systems, the cell constant increased from 300.24 (Pa*cm)/W to 1450.64 (Pa*cm)/W, and signal sensitivity increased from 0.016 \(\mu\)V/ppb to 0.2562 \(\mu\)V/ppb [11]. [PERSON] used the finite element method (FEM) to simulate photoacoustic signals in cylindrical resonators and loss effects near the cavity walls, and these effects appear in the boundary conditions of the non-uniform Helmholtz equation controlling sound pressure, confirming the feasibility of using finite elements and derived boundary conditions to simulate photoacoustic signals [12]. [PERSON] carried out numerical research on various characteristics of photoacoustic cells and extended the pressure field into acoustic-characteristic mode based on a finite element analysis and studied the effects of laser parameters, photoacoustic cell geometry, and gas concentrations on signal intensity [13]. [PERSON] designed a miniaturized photoacoustic cell for atmospheric NO\({}_{2}\) monitoring through 3D printing technology [14]. [PERSON] used quartz-enhanced photothermal spectroscopy (QEPTS) to achieve high-sensitivity detection of acetylene (C\({}_{2}\)H\({}_{2}\)), and the lowest detection limit reached 718 ppb [15]. [PERSON] took a 450 nm laser diode as the radiation source, and the laser was reflected several times in a diffuse reflector sphere, which increased the optical path and significantly improved the amplitude of the photoacoustic signal [16]. [PERSON] built a finite element model of a photoacoustic sensor and studied the relationship among environmental factors, the structure of the photoacoustic cell, and the intrinsic frequency [17]. [PERSON] built a simulation model of a photoacoustic cell by using the finite cloud analysis method and optimized the design of the photoacoustic cell on the basis of a simulation [18]. [PERSON] designed a H-type differential photoacoustic cell, which greatly increased the photoacoustic signal and quality factor, with NO\({}_{2}\) as the sample gas, and the lowest detection limit reached 124 \(\times\) 10\({}^{-12}\)[19]. [PERSON] used quartz-enhanced photoacoustic spectroscopy (QEPAS) to continuously measure atmospheric carbon dioxide (CO\({}_{2}\)) at 2008 nm, and the detection limit reached 12 parts per million within an integration time of 10s [20].