Applications of Fresnel-Kirchhoff diffraction integral in linear and nonlinear optics: a didactic introduction

摘要

In nonlinear optics, the Gaussian beam intensity profile, I(r) ∝ exp(-2r~2/w~2) generates a refractive index profile An(r), and consequently a phase profile. Depending on the magnitude of the phase profile, rings structures can be observed in the beam far field intensity profile, the so called Transverse Self Phase Modulation effect. In this work, we calculated these rings formation due to thermal and Kerr nonlinearities, using the Fresnel-Kirchhoff diffraction integral (FKDI). In the case of Kerr nonlinearity, the refractive index profile is also Gaussian since n(r) = n_0+ n_2I(r). However, due to the effect of heat diffusion, in the case of thermal nonlinearity the refractive index profile is broader than I(r).