A novel method to measure relative second harmonic optical susceptibilities of crystals by use of Rayleigh scattering and numerical studies on the spatial and temporal profiles of the second harmonic pulse with consideration of both thermal absorption and intensity dependent refractive index for various thermal relaxation times are described. As for the second harmonic optical susceptibility measurements we use two crystals in a fixed alignment : one is a phase-matched crystal with varying degrees of phase matching, which serves as a reference point of the phase relation-ship and a source for the second harmonic beam to be incident at the sample crystal, and the other is a sample crystal for measurement. The second harmonic signals generated each from the two crystals are superposed in the sample crystal to give a rise to Rayleigh scattering at the second harmonic frequency, the analysis of which can determine the relative values of the second harmonic optical susceptibilities of the sample crystals. We have applied this method to obtain $d_{14}(KDP) \simeq 1.8 d_{36}(KDP),\; d_{36}(ADP) \simeq 1.1 d_{36}(KDP),\; d_{31}(KTP) \simeq 15 d_{36}(KDP),\; d_{32}(KTP) \simeq 13 d_{36}(KDP)$ where $d_{36}$ of KDP crystal was taken as a reference. The two effects, thermal absorption and intensity dependent refractive index deteriorate the SHG efficiency and also make beam profiles much different from that of fundamental wave. If the signs of the refractive index gradient are opposite between the two contributions of different origins, they may counterbalance each other to help reduce deterioration of the SHG efficiency.
