Four-wave mixing of picosecond pulses in hollow fibers: Phase matching and the influence of high-order waveguide modes

The processes of third-harmonic and difference-frequency generation through the four-wave mixing of picosecond pulses in gas-filled hollow fibers are experimentally studied. Due to the improvement of phase-matching conditions with an appropriate choice of the gas pressure and optimal parameters of the hollow fiber, we were able to use hollow fibers with a large length (up to 30 cm) for difference-frequency generation, which resulted in a considerable increase in the power of the difference-frequency signal at the output of the fiber. Our experimental data reveal a considerable influence of high-order waveguide modes on four-wave mixing processes in a hollow fiber. It is shown that the waveguide regime of nonlinear optical interactions implemented in hollow fibers removes the limitations on the efficiency of third-harmonic and sum-frequency generation, which are characteristic of the tight-focusing regime in media with normal dispersion and which are due to the geometric phase shift arising in tightly focused light beams.