Phase-matching successive high-order harmonic generation in a hollow fiber

High-order harmonic generation in hollow fibers through step processes invo lving lower order intermediate nonlinear processes is considered. Analysis of equations derived for the amplitudes of high-order harmonics produced th rough direct and step processes with allowance for the dispersion of wavegu ide modes of a hollow fiber shows that, with an appropriate choice of the s ort and the pressure of the gas filling the fiber, parameters of the fiber, the wavelength of pump radiation, and the waveguide modes, phase-matching conditions can be simultaneously satisfied for both steps of a successive h igh-order harmonic-generation process involving third-harmonic generation a t the first step. Phase-matching conditions of this type are determined for ninth-harmonic generation in a hollow fiber filled with helium.