Reduced harmonic representation for continuous wave, shock-producing focused beams

An extension to the frequency domain solution to Burgers´ equation (FDSBE) is presented in the context of a continuous wave, nonlinear beam propagation model. The extension adds a specified number of harmonics to each FDSBE nonlinear substep in the shock-bearing region. The extension harmonics have amplitudes given by a 1/n amplitude decay assumption. The corresponding phases are given by linear extrapolation. The extension scheme allows for stable and accurate, reduced harmonic focal beam modeling. An algorithm is also presented that allows this scheme to provide accurate heating rate and radiation force output.