Abstract

The quantum statistical equations for the field produced in the process of second-harmonic generation (SHG) are expressed, based on a method proposed for four-wave mixing.¹ We start from the following assumptions: 1) the field absorption in the nonlinear medium may be neglected; 2) the amplitude of the fundamental field is much greater than that of the SH field; 3) the Wigner function associated with the density operator of the field depends significantly only on the variables of the SH field. The coefficients of the Fokker–Planck equation thus obtained depend on the Laplace transforms of the correlation functions of the atomic polarization operator. The moments of the Wigner function² are related to the moments of the SH field photon number; consequently, we impose the condition for sub-Poissonian photon-statistics and derive the corresponding relationships satisfied by the atomic correlation functions. A numerical interpretation is given.

© 1992 Optical Society of America