Nonlinear frequency-mixing photoacoustic imaging of a crack: Theory

Abstract

One-dimensional theory of the nonlinear frequency-mixing photoacoustic crack imaging is developed. This imaging can be realized through the excitation of the crack by two laser beams independently modulated in intensity at two very different frequencies ωH⪢ωL and the detection of the components of photoacoustic spectrum at frequencies ωH±nωL with an integer n. It is predicted that the high contrast of this imaging can be caused by strong dependence of the efficiency of photoacoustic conversion on the mechanical state of the crack, i.e., on whether the crack is open or is at least partially closed due to the contacts between the crack faces. The theory relates earlier experimental observation of the large number of the side-lobes ωH±nωL to strong bimodular nonlinearity of the crack. In response to sinusoidal modulation of pump laser intensity at low frequency ωL the rigidity of the crack varies in a strongly nonsinusoidal manner through abrupt jumps between its value corresponding to an open soft state of the crack and its value corresponding to a much more rigid closed state of the crack. Parametric interaction of the acoustic waves generated by probe laser radiation harmonically modulated in intensity at high frequency ωH with this strongly nonsinusoidal motion excites multiple side-lobes around ωH. The theory indicates that information on the crack rigidity could be obtained from the measurements of photoacoustic conversion efficiency and that the information on the parameters of force/width relation of the crack can be obtained from the measurements of the dependence of the side-lobes spectrum on the pump laser intensity.