Effect of redistributed radiation on degenerate four-wave mixing

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Abstract
A model is formulated to investigate quantitatively how near-resonant degenerate four-wave mixing (DFWM) in a vapor of homogeneously broadened two-state atoms is affected by radiation scattered from the pump beams. The spectral intensity distribution of the scattered radiation in the interaction volume is obtained by solving the equation of radiative transfer and a detailed treatment of the modification this fluctuating field causes on the optical dipole induced by the coherent laser fields is presented. For a broad parameter regime, this modification can be expressed via a single quantity that incorporates the energy of the fluctuating field together with bandwidths and frequency offsets from the atomic resonance. Numerical solutions are given which show that the scattered field causes the DFWM reflectivity to be depressed by a signficant amount, depending most strongly on a characteristic transverse length of the interaction volume. Approximate analytic expressions for the reflectivity are also given which assist in physically understanding the underlying mechanisms.