# A Feasibility Study for a Nonlinear Guided Wave Mixing Technique
## 1 Introduction  
Ultrasonic waves and radiation are normally used for non-destructive testing. In the case of ultrasonic testing, the velocity, time, and distance of ultrasonic waves help the user to find defects. However, these simple parameters do not satisfy all evidence for evaluating micro-damage in a material, such as damage from corrosion, plastic deformation, or microstructure variation. The estimation ability of nonlinear information in the frequency domain also needs to be improved. In ultrasonic nonlinear techniques, it is important to measure the second harmonic component. The ratio between the primary and secondary harmonic wave amplitudes becomes the nonlinear parameter called nonlinearity. Based on the nonlinearity derived from the second harmonic component, many research results have been widely studied for micro-damage assessments [1, 2, 3]. Even though nonlinearity indicates good micro-damage assessment sensitivity, it usually shows relative results. One of the main reasons that it shows relative results is that the nonlinearity is affected by the experimental setup. A certain portion of nonlinearity comes from the system, which includes the equipment, sensors, and cables. As such, nonlinearity influenced by the system acts as an error. This means that reducing system nonlinearity could increase the accuracy of the results. One of the few techniques that can reduce system nonlinearity is the wave mixing technique [4]. Currently, many researchers are researching a nonlinear method to measure the third harmonic ratio, but the third harmonic has a very small relative ratio, so many variablesexist, and as such it is difficult to apply in practical applications, and theoretical and experimental verification is being performed [5; 6]. There are two reasons why the mixing technique could minimize the system nonlinearity. The first reason is that the key point of the wave mixing technique is that one mixing wave is generated from two primary waves. In contrast to conventional ultrasonic nonlinear techniques, the received signal does not come directly from the equipment, which thus does not influence the mixing signal much. In the words, the mixing technique has less system nonlinearity [7]. The second reason is that mixing techniques are classified into two types depending on the frequency, or the sum or difference of the primary wave frequencies. Theoretically, each primary wave signal produces the same or similar system nonlinearity. If the mixing signal were to have the difference of the primary wave frequencies, the system nonlinearity would theoretically be canceled out [7; 8]. Mixing technique theory has been studied for a long time, but there are not as many experimental studies as theoretical studies. [PERSON] et al. [8] and [PERSON] et al. [9] developed a theoretical mixing basement. Based on basic equations, wave mixing terms and information are derived. The major features of its study consider equations to contain linear and nonlinear information. The main factors include the interaction angle and mixing signal propagation. [PERSON], [PERSON] et al. [10] numerically analyzed the one-way mixing of S0 and A0 modes using simulation, and [PERSON], [PERSON] et al. [11] detected micro-defects with nonlinear mixing experiments and simulations in S0 single mode. [PERSON] et al. [7] measured the material nonlinearity using a non-collinear mixing technique, conducting experiments on large and thick specimens. Moreover, [PERSON] et al. [4] theoretically and experimentally studied a collinear mixing technique. Recently, research to study nonlinearity by constructing four-wave mixing (FWM) using highly nonlinear fiber (Bi-HNLF) and laser has also been actively conducted [12; 13]. All researchers mentioned in this paper have tried to reduce the system influence on the results. However, these studies were limited to bulk waves, and guided wave mixing has not been studied as much, because guided waves have a dispersive characteristic [14; 15; 16; 17; 18].