Computation of Kerr lensing effect in laser amplifiers

The Kerr lensing effect influences the amplification of ultra short pulses with high repetition rate. Numerical simulations can estimate this effect and support the optimal design an ultra short laser amplifier. We compare two approaches to simulate laser amplifiers with respect to Kerr lensing effect modeling. These are a Gaussian beam amplification method and the angular spectrum method. In both cases, by Fourier transformation, the beam is considered as a continuous wave beam with a certain spectrum. Then, the Gaussian beam amplification method allows to take into account this spectrum of the beam. This means that the wavelength dependency of stimulated emission cross section and reabsorption cross section can be taken into account. However, a Gaussian beam amplification method does not simulate diffraction effects, which arise from the non-parabolic index of refraction obtained by the Kerr effect. This is an advantage of the angular spectrum method of plane waves. It can model diffraction effects obtained by the Kerr effect. But taking into account the spectrum of the beam is more computational intensive. A parameter which indicates the strength of the Kerr lensing effect is the B-integral. Numerical simulations compare this parameter computed by the Gaussian beam amplification method and the angular spectrum method.