Quality of a Laser Beam in a Nonlinear Turbulent Medium

Summary form only given. Applications of laser beams in many instances require a well-defined, tight focus, with high intensity. In other cases, especially in directed energy applications, it is necessary for the laser beam to propagate long distances. These two requirements are interrelated and are affected by the laser beam quality as measured by, for example, M-squared. For steady state propagation in the paraxial limit, equations for the axial variation of the laser spot size and M-squared are derived. The derivation allows for the possibility that the refractive index of the medium may be fluctuating in space (e.g., due to turbulence) or be a nonlinear function of the laser field (e.g., due to the optical Kerr effect). Full-scale simulations of laser beam propagation, employing the three-dimensional code HELCAP, are shown and compared with numerical solutions of the equations for the spot size and M-squared. The comparison illustrates the limited range of validity of employing the equations for the spot size and M-squared. HELCAP simulation results are presented to show that as beam quality is reduced (i.e., M-squared is increased) the onset of Kerr self-focusing occurs earlier but, for sufficiently large M-squared, self-focusing is entirely eliminated. The effect of turbulence in the medium is shown to be similar to reducing the beam quality