Beam divergence effects on nonlinear frequency mixing

Abstract

The effects of the beam divergence of the input pump laser beams on the nonlinear frequency mixing process in a dielectric medium is discussed. The divergent laser beams have finite angular spreads so that all of the interactions between the two input beams can never satisfy the phase-matching condition exactly. A numerical model is developed to investigate the effects of input beam divergence on conversion efficiency. The angular spread of each of the input beams is represented by a set of plane waves having a distribution of propagation directions. Each of the plane-wave components from one input beam is allowed to interact with all the plane-wave components of the second input beam. This model is applicable to processes such as sum frequency generation, difference frequency generation, and optical parametric amplification. Second-harmonic generations as a special case of sum frequency generation is used as an example in the numerical studies. Results indicate that the conversion efficiency is dependent on the amount of beam divergence, the input intensity, and the length of the nonlinear medium. These parameters must be optimized with respect to one another to maximize the conversion. The optimization is especially critical in high-power systems where high conversion efficiency is sought.