Modeling generation of harmonics in the water window region in hollow core waveguides by mid-infrared femtosecond pulses

We numerically investigate generation of harmonics in the water window region (down to 2.8 nm) by 2 μm femtosecond pulses propagating in hollow core waveguides filled with high pressure He. Numerical calculations are based on a three dimensional macroscopic model, which solves the pulse propagation by a split-step method, uses the strong field approximation to evaluate the single atom response, and integrates it coherently to obtain the harmonic field. Two configurations for the waveguides are considered: the standard one with a constant diameter of 70 μm and a conical one with a decreasing diameter from 70 to 50 μm. We demonstrate that harmonic field enhancement can be obtained in spectral domains of great practical interest, from 2.8 to 20 nm, and identify quasi-phase matching induced by multimode beating as the mechanism responsible for this enhancement.