# Research on the Processing Method of Acoustic Focusing Cavities Based on the Temperature Gradient
## 1 Introduction  
The acoustic focusing effect [1, 2, 3, 4] has broad application prospects in the fields of acoustic imaging, ultrasonic medical treatment [5, 6], and nondestructive testing [7, 8]. At present, the acoustic focusing effect is widely used, with ultrasonic therapy being the most common application. It usually involves focusing a beam to guide ultrasonic energy to a small area within a tissue area that needs treatment. In such applications, nonlinear acoustic effects and acoustic cavitation usually play an important role. The tissue temperature in the focal zone can reach 70 \({}^{\circ}\)C to 90 \({}^{\circ}\)C in a few seconds. With the rapid development of phononic crystals and acoustic metamaterials, a variety of different types of acoustic focusing lenses have been realized by using the negative refraction mechanism of the two structures. By gradually changing the lattice size of the phononic crystal [9], Young's modulus, element shape, and lattice constant [10], the acoustic refractive index of gradient distribution can be obtained, and a variety of gradient acoustic focusing lenses can be designed. The acoustic metasurface was first proposed in 2013. A large number of experimental studies have shown that the reflection angle and refraction angle of acoustic waves on the metasurfaces of different materials are non-zero [11, 12, 13]. Accordingly, there have been several designs of acoustic metasurfaces, and many abnormal physical phenomena have been realized, such as an abnormal Doppler effect [14, 15, 16], negative refraction of sound waves, acoustic holographic imaging, and acoustic absorption [17]. With the development of acoustic metasurface materials, the problems of extreme impedance mismatch and large thickness of acoustic lens were solved. In 2016, [PERSON]'s team realized the sound vortex phenomenon by using acoustic metasurfaces [18]. Acoustic metasurfaces have a small unit size and a large negative refractive index; hence, it is possible to design a small and ultrathin acoustic focusing lens. The basic units of the related metamaterials mainly include a Helmholtz resonator [19], cross-shaped structure [20], coiling-up space structure, and impedance matching multicomponent structure [2]. The acoustic refractive index of gradient distribution is obtained by arranging different sizes of unit structures, and then the acousticfocusing effect is realized [21; 22]. However, the acoustic focusing performance of the metasurfaces depends on the discontinuous distribution of different unit structures; moreover, the metasurface unit is composed of at least two kinds of media, which easily lead to an acoustic impedance mismatch and a narrow working frequency band, sometimes even a single frequency, thus limiting the practical application of the acoustic focusing device. Using a gradient temperature field can change the refractive index of medium distribution, which can effectively solve the problems of acoustic impedance matching and acoustic energy loss, realize the arbitrary control of the sound wave propagation path, and obtain a series of broadband acoustic anomalies, such as acoustic focusing [23; 24], acoustic stealth [25], acoustic absorption [18], and acoustic unidirectional transmission [26]. However, in the abovementioned thermoacoustic devices, in order to obtain the temperature field with a gradient distribution, it is necessary to distribute multiple heat sources in the space, according to certain rules, which leads to the disadvantages of a large space size, irregular shape, and difficult integration of thermoacoustic devices. Therefore, the design of broadband planar ultrathin thermoacoustic devices has become a key problem to be solved urgently in this field. For this paper, using the finite element numerical simulation method [27], acoustic waves were introduced vertically incident on the metasurfaces, and two metasurfaces of the same material were used to form a transmission unit.