The difference analysis of nonlinear absorption coefficient β in the beam sections of plain and Gaussian distribution

The differences of nonlinear absorption coefficient β are theoretically and numerically studied under both of the beam sections of plain and Gaussian distribution. The formula of energy transmission is derived on the base of temporal profile of Gaussian pulse beam. According to the formula, the absolute and relative differences of β are also estimated in compare with plain beam and the pulse beam that is rectangular in time but Gaussian in space. The relative differences turn out theoretically to be about 183% and 41.4% respectively. The further numerical simulation shows that these values are only the least differences. The existed differences mean that, according to the temporal influence of pulse, one should get a lager value of β in past performed routine experiments of nonlinear energy transmission. Our result suggests that, by taking temporal profile of a pulse beam into account, one can obtain more exact value of two-photon absorption cross section of the molecule experimentally.