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 μ m 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 μ m and a conical one with a decreasing diameter from 70 to 50 μ m. 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.