The dependence of broadband four-wave mixing signal intensity on the length of the interaction region

摘要

A theoretical investigation of broadband four-wave mixing (FWM) signal intensity dependence on the length of the interaction region, L, is undertaken, for the case of weak intensity input beams. The phase diffusing model, PDM, is used to describe the statistics of the field fluctuations. A general result is derived which is in agreement with the quadratic L dependence obtained in previous work by Cooper et al. 1989, Phys. Rev. A, 40, 5707, where only the particular case of coherent lengths, Lc, much greater than L was considered. We particularize our general result for the opposite case, Lc L, where retardation effects in the randomly fluctuating phases can no longer be neglected. In this case we find the FWM signal intensity to have a linear, rather than a quadratic, dependence on L. An intuitive and simple physical justification is provided for this new result in terms of the short length scale, coherent dipole, contributions to the FWM signal, along the interaction region.