A geometric optics approximation to a model of phase-compensated whole-beam thermal blooming: 1, General theory and numerical verification

Technical Report · Fri Jan 01 04:00:00 EST 1988

OSTI ID:6643045

Gautesen, A K; Morris, J R

We develop a geometric optics series expansion approximation to a model of phase-compensated whole-beam thermal blooming of high-power 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 high-power intensity profile at the laser, and a collimated beam boundary condition at an exit plane that is many e-folding scale lengths from the laser. The series expansion parameter is directly proportional to Smith's geometric optics distortion parameter. Expansion formulae are derived for both the intensity and phase at all propagation distances. The exit plane intensity profiles obtained from these formulae qualitatively agree with numerical results obtained from the wave-optics 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 return-wave phase-compensation iteration provides an estimate that the rms error in the initial phase obtained from our series approximation truncated at third-order is approximately 0.5% over the range of values we investigated. 3 refs., 2 figs., 1 tab.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6643045
• Report Number(s): UCID-21501; ON: DE89004606
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300 -- Engineering-- Lasers-- (-1989)
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
BEAM OPTICS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC RADIATION
EQUATIONS
EXPANSION
LASER RADIATION
MATHEMATICAL MODELS
MAXWELL EQUATIONS
NONLINEAR OPTICS
OPTICAL PROPERTIES
OPTICS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
RADIATIONS
REFRACTIVITY
SERIES EXPANSION
THERMAL EXPANSION
WAVE PROPAGATION