[Paper Review] Phase-matching mechanism for high-harmonic generation in the overdriven regime driven by few-cycle laser pulses

Johannes Schötz, Benjamin Förg+12 more|Figshare|Dec 17, 2019

Laser-Matter Interactions and Applications4 citations

TL;DR

This paper identifies ionization-induced transient phase-matching as the mechanism enabling isolated attosecond pulse (IAP) generation in argon at 80 eV using few-cycle laser pulses in the overdriven regime. The mechanism arises from plasma-induced pulse reshaping—blue-shifting and intensity decay—enabling phase-matching near the XUV cutoff despite high plasma densities, validated through experiments and simulations across gases and wavelengths.

ABSTRACT

Isolated attosecond pulses (IAPs) produced through laser-driven high-harmonic generation (HHG) hold promise for unprecedented insight into biological processes via attosecond x-ray diffraction with tabletop sources. However, efficient scaling of HHG towards x-ray energies has been hampered by ionization-induced plasma generation impeding the coherent buildup of high-harmonic radiation. Recently, it has been shown that these limitations can be overcome in the so-called 'overdriven regime' where ionization loss and plasma dispersion strongly modify the driving laser pulse over small distances, albeit without demonstrating IAPs. Here, we report on experiments comparing the generation of IAPs in argon and neon at 80 eV via attosecond streaking measurements. Contrasting our experimental results with numerical simulations, we conclude that IAPs in argon are generated through ionization-induced transient phase-matching gating effective over distances on the order of 100 $μ$m. We show that the decay of the intensity and blue-shift due to plasma defocussing are crucial for allowing phase-matching close to the XUV cutoff at high plasma densities. We perform simulations for different gases and wavelengths and show that the mechanism is important for the phase-matching of long-wavelength, tightly-focused laser beams in high-pressure gas targets, which are currently being employed for scaling isolated attosecond pulse generation to x-ray photon energies.

Motivation & Objective

• To understand the phase-matching mechanism enabling isolated attosecond pulse (IAP) generation in the overdriven regime with few-cycle laser pulses.
• To resolve the challenge of plasma-induced pulse distortion and ionization losses that hinder efficient high-harmonic generation (HHG) at high photon energies.
• To identify how plasma defocusing and intensity decay enable phase-matching near the XUV cutoff under high-pressure, tightly focused conditions.
• To demonstrate that transient phase-matching is critical for scaling HHG to x-ray photon energies using long-wavelength, high-intensity lasers.
• To provide a simulation framework that models pulse propagation, plasma dynamics, and XUV source term generation for accurate prediction of HHG efficiency.

Proposed method

• Simulations model the HHG process using the paraxial approximation of the Helmholtz equation, incorporating nonlinear polarization as the source term.
• The XUV source term is calculated via the inverse Fourier transform of a Gaussian-modulated spectrum centered at 80 eV with FWHM of 6.4 eV.
• Laser pulse propagation through gas targets is simulated using a beamline model with defined distances and optical components (iris, filters, mirrors).
• Gas targets are modeled with Lorentzian pressure profiles to simulate realistic density gradients in high-pressure, short-duration gas cells.
• The system is solved in the co-moving frame of reference, accounting for group velocity, wavevector, and refractive index dispersion.
• Phase-matching is analyzed by tracking intensity decay, spectral blue-shifting, and beam convergence, particularly in front of the focus.

Experimental results

Research questions

• RQ1 How does plasma-induced pulse reshaping enable phase-matching in the overdriven regime despite high ionization and plasma density?
• RQ2 What role do intensity decay and spectral blue-shifting play in sustaining phase-matching near the XUV cutoff in high-pressure gases?
• RQ3 Why is placing the gas target in front of the focus advantageous for maximizing XUV flux under strong focusing and high pressure?
• RQ4 How does transient phase-matching differ from conventional phase-matching in few-cycle HHG, especially for long-wavelength drivers?
• RQ5 To what extent can the phase-matching mechanism be generalized across different gases and laser wavelengths in high-harmonic generation?

Key findings

• Ionization-induced transient phase-matching enables isolated attosecond pulse generation in argon at 80 eV, with the mechanism effective over distances of ~100 µm.
• Plasma defocusing and intensity decay are critical for maintaining phase-matching at high plasma densities near the XUV cutoff.
• Placing the gas target in front of the focus balances beam convergence and plasma defocusing, leading to significantly higher XUV flux.
• Simulations show that the phase-matching mechanism is robust for long-wavelength, tightly focused laser beams in high-pressure gas targets.
• The mechanism is essential for scaling isolated attosecond pulse generation to x-ray photon energies, particularly in the water-window region.
• The peak intensity in argon reaches 4.8 × 10¹⁴ W/cm², with phase-matching sustained despite strong plasma-induced pulse distortions.