Optimization of the shape of Gaussian beams

The applicability and accuracy of the Gaussian beam method depend on the proper choice of the shape of beams. Gaussian beams become inaccurate solutions of the elastodynamic equation if the velocity field changes considerably within the beam width. We present a procedure of determining the optimum initial shape of Gaussian beams based on minimizing the average squared widths of Gaussian beams and smoothing the distribution of the optimum parameters of Gaussian beams on the Hamiltonian hypersurface in the phase-space. The original method of smoothing represents an essential part of the algorithm, which is designed particularly for the optimization of the shape of Gaussian beams for Gaussian beam or packet migrations.