Numerical Analysis of Type I Third-Harmonic Generation through Third-Order and Cascaded Second-Order Nonlinear Optical Processes

We report on the numerical analysis of type I third-harmonic generation of ultrashort pulse lasers through third-order and cascaded second-order nonlinear optical processes. We derive a set of wave equations which includes group-velocity mismatch, group-velocity dispersion, and depletion of the fundamental pulse, and carry out numerical calculations for a type I β-barium borate (BBO) crystal with an 800 nm fundamental wavelength and a 100 fs pulse duration. Numerical results show that the third-harmonic pulse is temporally broadened and changes shape from a Gaussian to a super-Gaussian profile due to the group-velocity mismatch, and the third-harmonic intensity is approximately proportional to the cube of the initial fundamental intensity.