PROPERTIES OF PHOTOACOUSTIC WAVES IN ONE-DIMENSION, 2-DIMENSION, AND 3-DIMENSION

The time dependence of photoacoustic waves generated by irradiation of fluid bodies with optical radiation can be found by solution of the wave equation for pressure. Consider the generation of ultrasonic waves where heat deposition is described by a spatial heating function times a delta function in time. Solution of the wave equation in one dimension, shows that the spatial deposition of heat is directly mapped into the time profile of the photoacoustic wave. In two dimensions, a cylindrically symmetric deposition of heat gives a photoacoustic wave described by an integral over a spatial source function. In three dimensions, a spherically symmetric deposition of heat gives the photoacoustic wave as a mapping of the product of the retarded time with the spatial heating function. For laser pulses long compared with the transit time of sound across the irradiated body, the photoacoustic wave-form is found to be proportional to the zero'th time derivative (the time profile) of the laser pulse in one dimension, the (1/2)'th time derivative of the laser pulse in two dimensions and the first time derivative of the laser pulse in three dimensions. Formulae for multipole radiation in one, two, and three dimensions are derived from the wave equation for sources having arbitrary spatial dependencies.