Evaluation of two-photon nonlinearity by a semiclassical method

In order to discuss the two-photon nonlinearity theoretically, both photons and nonlinear materials should be treated quantum mechanically, which usually is a heavy theoretical task. Contrarily, nonlinear optics for classical light has been developed well and a detailed analysis is possible for realistic complex nonlinear systems. Here we show that the two-photon nonlinearity can be evaluated from the linear and third-order nonlinear output fields against a classical input pulse, which contains 2(-1/2) photons on average.