Numerical modelling of pump-wavelength dependence of high harmonic generation efficiency

Abstract

High harmonic generation (HHG) provides a table-top source of extreme ultraviolet (XUV) and soft x-ray radiation. HHG pump-wavelength dependence is of significant practical interest for laser system design as HHG efficiency scales with pump wavelength to the power of P. First experiments suggested P = -6.5 while theoretical models predict P = -4.7 to -6.0. These investigations exploited single-atom models; insight into efficiencies for full experimental setups will further guide HHG laser designs. We developed a model that simulates the HHG process in full for an argon-filled capillary including all Ti:sapphire pump pulse and XUV propagation effects. With this we compare HHG of two geometries: a thin slice of argon, and an argon-filled capillary. For the thin slice with pump wavelengths 820-1890nm we found P = -4.5 scaling when the harmonic energies were integrated between 16 and 45eV. However, further analysis revealed a dependence of P = -6.4 for longer pump wavelengths (1500-1890nm), but P = -4.0 for shorter wavelengths (820-1500nm). By contrast, HHG in a 7-cm long capillary was found to scale with P = -3.4 (800-1850nm). We attribute this to phase-matching effects over longer propagation distances and nonlinear pump propagation distorting the pulse. Different scaling is observed when the energy of a single harmonic is calculated. In the thin slice the energy in the first harmonic above 20eV yields P = -6.1 (820-1890nm), P = -5.7 (820-1500nm), and P = -7.8 (1500-1890nm). For the whole capillary the corresponding value is P = -4.1 (800-1850nm).High-energy harmonics also exhibit very different scaling with pump wavelength as they cross the classical harmonic cutoff energy. For example, for the first harmonic beyond 41eV no value of P provides a good fit to the simulated HHG efficiencies, neither for the thin slice nor the whole capillary. Our simulations highlight pump-wavelength dependence of HHG efficiency is complex, with many contributing factors such as exact experimental geometry, optical nonlinearity, phase matching, and classical cutoff.

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Identifiers

ORCID for Samuel, Martin Senior: orcid.org/0000-0002-3428-9215

ORCID for William Brocklesby: orcid.org/0000-0002-2123-6712

ORCID for Peter Horak: orcid.org/0000-0002-8710-8764

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