5A5 - The second harmonic generation of light by focused laser beams

An experimental and theoretical study is reported on second-harmonic generation (SHG) by focused laser beams in nonlinear crystals which are large compared to the extent of the focus. The gas laser beam is in the lowest order (Gaussian) mode and very close to index-matching conditions in the crystal. The intensity pattern of the SHG observed photographically has roughly the shape of a half moon with a very sharp edge. Fine structure has been observed consisting of a series of fringes extending from the edge into the bright region. The power has also been measured as a function of crystal orientation, and the position of the edge has been determined for the orientation giving maximum power. The theoretical treatment of the problem is based upon an exact formula for the second-harmonic field for the case in which the laser beam is in a Gaussian mode. A detailed analysis of the experimental data is presented which shows the theory to be in quantitative as well as qualitative agreement with experiment.