The birth of attosecond physics began with the observation of high harmonic generation in gases. Today, such sources provide pulses shorter than 100 attoseconds and repetition rates above 10 MHz, but the photon flux remains low: typical conversion efficiency is about 0.001% for argon at repetition rates below 1 kHz. This work belongs to the line of research on optimizing phase matching and absorption in macroscopic generation. The classic model by Constant (1999) assumed a perfectly flat density profile, but real gas targets always have transition regions at the edges. Recent theoretical work predicted that the steepness of these gradients could strongly affect the flux, but a detailed experimental verification was lacking.
Experiments were performed at the HR Gas facility of the ELI ALPS laser center. A laser with a wavelength of 1030 nm, pulse energy of 0.68 mJ, and duration of 34 fs was focused to a spot of 52 μm (intensity ~1.3×$10^{14}$ W/cm²). The target was a specially designed gas cell filled with argon, allowing the aperture diameter and wall thickness to be varied, which set the steepness of the density gradient. The density profile was modeled with hydrodynamic simulations and approximated by a trapezoid. For analysis, an extended one-dimensional generation model was used, accounting for the linear variation of density and phase mismatch. Measurements were performed with a microchannel plate spectrometer and a calibrated photodiode.
It was experimentally confirmed that the harmonic flux increases with the steepness of the density gradient (parameter Θ₂) over the entire studied range, which spans two orders of magnitude. For example, for the 25th harmonic (30 eV) at a pressure of 90 mbar, the pulse energy increased from about 20 to 150 fJ when Θ₂ varied from 0.1 to 10. The increase is observed for all harmonics from the 21st to the 41st and for all pressures from 65 to 140 mbar. Modeling showed that both phase mismatch and absorption in the gradient region contribute comparably to the losses. The practical conclusion: reducing the transition length from 1.5 mm to 0.1 mm (technically achievable with laser-drilled foil) can increase efficiency by nearly a factor of 10.
This work provides the first systematic experimental verification of the role of density gradients in high harmonic generation. Unlike neighboring studies that used free gas jets or cells with uncontrolled profiles, here the profile is controlled through aperture geometry and a direct comparison with theory is made. This allows reconsidering the design of gas targets for all high harmonic sources, especially those operating at high repetition rates, where losses due to plasma and thermal effects are particularly critical.
The next step is to build and test cells with laser-drilled apertures in thin foil, which will provide extremely sharp gradients. It is also possible to create periodic density profiles for quasi-phase matching, which could further increase the flux. Such approaches naturally combine with shaping the laser beam and focusing.
Increasing the flux of ultraviolet photons directly impacts applications of high harmonic sources in semiconductor lithography, nanoscopy of biological and industrial samples, and nonlinear optics in the extreme ultraviolet.
Develop and test gas cells with apertures made of thin foil drilled by laser at high average powers. Investigate the mechanical and optical limits of such cells, including beam pointing stability.
For high harmonic physics, the problem of scaling the flux at higher laser repetition rates remains unsolved due to the formation of stationary plasma. Controlling density gradients can partially compensate for these losses, but requires further study under high average power conditions.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This work experimentally and theoretically investigates how the steepness of the gas density gradient affects the high-harmonic flux. The authors used a gas cell with controlled orifice geometry, hydrodynamic modeling of the density profile, and an extended one-dimensional generation model. They show that the flux increases with the steepness of the gradient and propose a practical way to enhance efficiency by reducing the transition length.
Where its strength is
The strong point is the systematic control of the density profile and the direct comparison of experiment with model, which allows a quantitative assessment of the contributions of phase mismatch and absorption in the gradient region.
Where it could go next
Worth trying
Why this may matter
If the recipe for reducing the transition length is confirmed on other setups, it could become a standard technique for improving the efficiency of high-harmonic sources, especially for systems with high repetition rates.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.53, against a usual 0.64. It looks like few have drilled nearby.
The transition length of the gradient was determined by analogy with the rise time of a signal in electronics: between the 10% and 90% levels.