Three-dimensional. view of signal propagation in femtosecond four-wave mixing with application to the boxcars geometry

Maxwell's equations for the apparently complicated generation and propagation of femtosecond four-wave-mixing signals in optically thick samples can be solved by triple Fourier transformation into the three-dimensional (3D) frequency domain. Given the linear absorption and refractive-index spectra, the propagation problem can be solved in three dimensions under the assumption that nonlinear distortions of the excitation pulses can be neglected. A propagation function exactly incorporates the linear evolution of the excitation pulses, the nonlinear generation of the signal, and the linear propagation of the signal. A quantitative treatment of the directional filtering of the 3D susceptibility that arises from excitation with noncollinear pulses and selective interference detection of signal in one phase-matched direction is developed. This 3D treatment is used to examine the influence of phase-matching bandwidth, directional filtering, and sample absorption on femtosecond four-wave-mixing signals in the rectangular and square boxcars phase-matching geometries. (C) 2005 Optical Society of America.