Temperature modes for nonlinear Gaussian beams

In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions.