Modal effects on pump-pulse propagation in an Ar-filled capillary

Abstract

Accurate three-dimensional modelling of nonlinear pulse propagation within a gas-filled capillary is essential for understanding and improving the XUV yield in high harmonic generation. We introduce both a new model based on a multimode generalized nonlinear Schrödinger equation and a novel spatio-spectral measurement technique to which the model can be compared. The theory shows excellent agreement with the measured output spectrum and the spatio-spectral measurement reveals that the model correctly predicts higher order mode contributions to spectral broadening of the pulse. Fluorescence from the excited argon is used to verify the predicted ion distribution along the capillary.

Multimode Nonlinear Fibre Optics: Theory and Applications

“…9(c) the partial Ar + pressures of (a) and (b) are averaged over the transverse cross section of the capillary. The distribution shown in this figure can be easily verified experimentally as it is proportional to the intensity of the Ar + ion fluorescence observed at 488nm (Chapman et al, 2010;Froud et al, 2009). Finally, in Fig.…”

“…It is interesting to note that these short wavelength parts of the spectrum are more pronounced in the higher order modes LP 02 and LP 03 of the capillary, in fact they contain more power than the fundamental mode at these wavelengths for launched pulse energies above 0.6mJ. This finding has again been confirmed by experiments, where a strong position-dependence of the spectrum was observed in the far field beyond the capillary (Chapman et al, 2010). These selected results demonstrate clearly that mode interference and mode coupling, i.e., transverse spatial effects, play a significant role in the propagation of high-intensity laser pulses in regimes where ionisation becomes important.…”

“…The full MM-NLSE in the presence of gas ionisation by tunneling in the strong-field limit thus becomes (Chapman et al, 2010)…”

Spatiotemporal phase-matching in capillary high-harmonic generation

“…This short buildup length also allows us to ignore the effect of propagation on the driving pulse during generation, as the pulse can be assumed not to change significantly over the generation length. As the pulse propagates through the capillary it will broaden and blue-shift, as well as lose energy to ionization and coupling losses [34][35][36][37]. Here, although efforts are made to remain in a region where nonlinear effects are relatively weak, we use the experimentally measured values at the exit of the capillary to account for any change in pulse properties.…”

Spectral broadening and temporal compression of ∼100 fs pulses in air-filled hollow core capillary fibers

“…These simulations are based on a multimode generalized nonlinear Schrödinger equation [17] that accounts for mode dispersion, nonlinear Kerr and Raman effects, self-steepening, ionization, plasma refractive index, and nonlinear mode coupling, which has been tested previously for high-power pulse propagation in short capillaries [18,19]. The lowest 15 transverse modes with rotational symmetry were included in the simulations (for details of mode calculations and sample dispersion curves see Sec.…”