Comparison of the Gaussian-decomposition and the Fresnel-Kirchhoff diffraction methods in circular and elliptic Gaussian beams

In this investigation, the Gaussian decomposition and the Fresnel-Kirchhoff diffraction methods are compared from different view points. The virtues and faults of each method and also the reliable region of each one are discussed. This work is based on a numerical method for both the circular and elliptic Gaussian beams and results are compared with experimental data. This study is useful for materials exhibit optical Kerr effect such as two photon absorption and thermo-optical nonlinearities.