Investigation of Material Nonlinearity Measurements Using the Third-Harmonic Generation.

With respect to harmonic generation measurements in isotropic materials, the amplitude of the third-harmonic wave generally depends on both $\beta ^{2}$ (the square of the second-order nonlinear parameter $\beta $) and $\gamma $ (the third-order nonlinear parameter). Therefore, some care should be taken when measuring these parameters using the third-harmonic amplitude. The purpose of this paper is to investigate detailed theoretical and measurement techniques for the accurate determination of $\beta ^{2}$ which dominates the third-harmonic amplitude in most biological fluids and crystalline solids. The theory deals with harmonic generation in materials with cubic nonlinearity and defines the formula for measuring $\beta ^{2}$ with corrections for diffraction and attenuation. These corrections are derived from the Westervelt equation and play an important role in the measurement of nonlinear parameters. The third-harmonic amplitude that varies with the distance in water is obtained for the measurement of $\beta ^{2}$. $\beta $ is also measured from the second-harmonic amplitude for comparison. We also confirm the required input voltage to stably generate the third harmonic and discuss the effects of diffraction and attenuation correction on the $\beta ^{2}$ determination. The measured $\beta ^{2}$ in the propagation range of 0.05–0.2 m agrees well with the square of the measured $\beta $ , revealing that the third-harmonic amplitude is closely related to $\beta ^{2}$ , not $\gamma $. This paper covers comprehensive theories, experimentation, and analysis related to the measurement of third-harmonic generation in isotropic media and can be immediately applied to crystalline solids. [ABSTRACT FROM AUTHOR]