Abstract
The accurate control of the relative phase of multiple distinct sources of radiation produced by high harmonic generation is of central importance in the continued development of coherent extreme UV (XUV) and attosecond sources. Here, we present a novel approach which allows extremely accurate phase control between multiple sources of high harmonic radiation generated within the Rayleigh range of a single-femtosecond laser pulse using a dual-gas, multi-jet array. Fully ionized hydrogen acts as a purely passive medium and allows highly accurate control of the relative phase between each harmonic source. Consequently, this method allows quantum path selection and rapid signal growth via the full coherent superposition of multiple HHG sources (the so-called quasi-phase-matching). Numerical simulations elucidate the complex interplay between the distinct quantum paths observed in our proof-of-principle experiments.
Highlights
Another approach is to exploit the distinct intensity dependence of the return phase of the two quantum paths in combination with the phase-matching conditions in the generating medium
The accurate control of the relative phase of multiple distinct sources of radiation produced by high harmonic generation is of central importance in the continued development of coherent extreme UV (XUV) and attosecond sources
Coherent build-up of the harmonic signal throughout requires that the nonlinear medium is shorter than one coherence length Lc = π/ k, i.e. that the radiation generated at the beginning of the medium should be less than half a wave out of phase with radiation generated at the end of the medium
Summary
QPM can be achieved by any means that allows one to modulate the strength of the source term: for example, by varying the driving laser intensity with modulated capillary diameters [16, 21] or multi-mode beating in a capillary [22, 23], by using counterpropagating pulses [24] and by polarization gating [25]. To achieve ideal performance the phase introduced by each matching half-period would have to be varied freely from one hydrogen zone to the This is important because it is very difficult to achieve perfectly uniform conditions over long lengths along a high-power laser focus and especially for very high orders (e.g. sub-10 nm wavelengths) the laser field will experience sub-cycle modifications due to non-adiabatic effects in the generation medium [32]. This implies that Lc is not a constant along the propagation path and the dual-gas QPM scheme should allow for fine-tuneability to ensure that the total phase added by each QPM period corresponds to 2π. If this condition is fulfilled, the QPM effect will lead to effective control of the quantum path contributions
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