Maximum cross sections for excited state and two-photon absorption

摘要

There is a maximum value for any nonlinear process, which can be found on the basis of fundamental quantum mechanics. With regard to single photon processes, there is a maximum absorption cross section, sigma_a, which any molecule may reach. The maximum is 1.13 x 10~17 lambdaQ/n cm~2, where lambda is the wavelength of the light, n is the refractive index of the host medium, and Q is the quality factor ascribed to the absorption line width. Thus large cross sections can only be obtained at the expense of a narrow operating range. The maximum is set by fundamental physics. Since nonlinear phenomena are highly resonant, the maxima of higher-order processes are also a strong function of the width of the resonance and the peak wavelength. In the case of two-photon absorption the peak value of the maximum cross section, signa_2N or delta, is roughly 3.5 x 10~-32 lambda ~4nQ cm~4/GW, or about 7 x 10~-57lambda~3nQ cm~4/photon. No value for a nonlinear coefficient is meaningful in the absence of the width of the measurement.