The three-dimensional (3-D) pulse propagation code, pulsed ultrashort laser simulation emulator (PULSE), has been used to model the interaction of thermal blooming, diffraction, and nonlinear self-focusing in the atmosphere. PULSE is a derivative of the free-electron laser (FEL) simulation code, free-electron laser experiment (FELEX) [Nucl. Instrum. Methods Phys. Res. A 250, 449 (1986)] that was used for many years to model the 3-D interaction of optical pulses with electron beams. This code has now been modified to model nonlinear material interactions. In its current configuration, an electromagnetic pulse is modeled on a Cartesian grid, thereby allowing for arbitrary amplitude and phase modulations in the transverse and longitudinal (z) directions. The code includes models for thermal blooming (in a laminar transverse wind field), diffraction, Kerr self-focusing and self-phase modulation, plasma defocusing and absorption, and multiphoton and avalanche ionization. Simulation of picosecond length pulses indicate that the defocusing effects of thermal blooming and diffraction can be effectively eliminated by Kerr self-focusing. Simulation results show that the beam arrives at the target with a spot size comparable to (or less than) its initial spot size. For propagation distances of many kilometers, this can result in order-of-magnitude increases of the on-target intensity at range, which can significantly reduce the average power requirement of the laser required to provide a given irradiance level.
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