Photoacoustic generation for a spherical absorber with impedance mismatch with the surrounding media

Pressure generation in a spherical absorber due to energy deposition from pulsed lasers is studied. For a variety of conditions, analytical solutions are derived that allow quick computation of exact results. For the special case of identical acoustic impedance, the pressure transient spreads to the surrounding medium by a single compressive pulse followed by a tensile pulse at the end of illumination. For the general case of impedance mismatch, the pressure transient is in the form of a series of dampened compressive and tensile pressure pulses. In this paper both the amplitude ratio and the sign of consecutive pressure pulses are determined analytically, and are shown to be dependent upon the impedance mismatch. For laser pulses of duration much less than the absorber’s characteristic oscillation time, a stress confinement limit is reached for most of the absorber, but a sharp tensile stress in the core region of the sphere is predicted. This region of high stress is defined by $r<~r_c,$ and we show that $r_c$ is proportional to the laser pulse duration ${\tau }_0.$ Upon further shortening of the laser pulse duration, the strength of this tensile stress continues to increase while its spatial distribution is sharpened. This observation has relevance to a number of experiments where laser-induced pressure transients cause the absorber to fracture.