A geometric optics approximation to a model of phasecompensated wholebeam thermal blooming. 1: General theory and numerical verification
Abstract
We develop a geometric optics series expansion approximation to a model of phasecompensated wholebeam thermal blooming of highpower laser beams. The model consists of a nonlinear medium whose thermal blooming coupling coefficient decreases exponentially with the propagation distance from the laser and whose motion relative to the laser beam is taken to be unidirectional, a Gaussian highpower intensity profile at the laser, and a collimated beam boundary condition at an exit plane that is many efolding scale lengths from the laser. The series expansion parameter is directly proportional to Smith's geometric optics distortion parameter. Expansion formulas are derived for both the intensity and phase at all propagation distances. The exit plane intensity profiles obtained from these formulas qualitatively agree with numerical results obtained from the waveoptics thermal blooming code FOURD, except when the FOURD results indicate that caustics are forming; quantitative agreement is also excellent, except for small differences in fine structure near the downwind edge of the beam. FOURD's returnwave phasecompensation iteration provides an estimate that the rms error in the initial phase obtained from our series approximation truncated at thirdorder is approximately 0.5 percent over the range of values we investigated.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1988
 Bibcode:
 1988STIN...8916162G
 Keywords:

 Approximation;
 Beams (Radiation);
 Geometrical Optics;
 Models;
 Thermal Blooming;
 High Power Lasers;
 Mathematical Models;
 Thermal Expansion;
 Wave Propagation;
 Lasers and Masers