Effects of higher-order nonlinear processes on harmonic-generation phase matching

We experimentally and theoretically reinvestigate the significant third-harmonic enhancement via plasma generation using time-resolved methods with two-color, copropagating femtosecond laser pulses. By measuring plasma densities with digital in-line holography and using carrier-resolved unidirectional pulse propagation equations to model the experiment, we show that a fifth-order nonlinearity contributes to third-harmonic generation mainly via phase matching. In particular, our study confirms that self- and cross-phase modulation including higher-order nonlinear processes can play a crucial role in harmonic-generation phase matching, which has recently been proposed by Weerawarne et al. [Phys. Rev. Lett. 114, 093901 (2015)] and should be potentially applicable to high-order harmonic generation.