Parametric Phase Conjugation for the Second Harmonic of a Nonlinear Ultrasonic Beam

摘要

The effect of phase conjugation for the second harmonic of a focused ultrasonic beam was investigated experimentally and by numerical simulation. An ultrasonic pulse with the carrier frequency f = 3 MHz was emitted into water and focused at a point between the source and the phase conjugating system. The phase conjugation for the second harmonic of the incident wave (2f = 6 MHz) was performed in a magnetostrictive ceramic as a result of the parametric interaction of the incident wave with the pumping magnetic field (the pumping frequency was f_p = 4f = 12 MHz). The axial and focal distributions of sound pressure in the incident and conjugated beams were measured using a broadband PVDF membrane hydrophone. The corresponding calculations were performed by solving numerically the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation allowing for the nonlinearity, diffraction, and thermoviscous absorption. The results of measurements agreed well with the calculations and showed that the field of a conjugate wave adequately reproduces the field of the second harmonic of the incident wave. A certain advantage of focusing with the phase conjugation for the second harmonic was demonstrated in comparison with the operation at the doubled frequency of the incident wave. The results of this study can serve as a basis for the utilization of the phase conjugation of harmonics in ultrasonic tomography and nondestructive testing.