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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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