Generation and control of Doppler harmonics approaching $10^{22} extrm{W/cm}^2$ on plasma mirrors

In this letter, we report Doppler harmonic generation with a relativistic plasma mirror at unprecedented intensities $>10^{21} ~\textrm{W/cm}^2$ using a PetaWatt-class laser. We show that beyond a few $10^{21} ~\textrm{W/cm}^2$ a precise control of the laser contrast at the sub-picosecond time scale becomes essential to drive the efficient generation of high-order harmonics. Such control is paramount for deploying plasma mirrors in high-field applications at PetaWatt-class laser facilities, including, for instance, their use as intensity boosters in the pursuit of the strong-field regime of quantum electrodynamics.

💡 Research Summary

In this work the authors demonstrate Doppler harmonic generation from relativistic plasma mirrors at laser intensities far beyond the previously explored regime, reaching peak on‑target intensities of 6.6 × 10^21 W cm⁻² and approaching 10^22 W cm⁻². The experiments were performed on the BELLA petawatt laser (up to 30 J, 37 fs) using a double‑plasma‑mirror (DPM) system to improve the nanosecond contrast to ≈10⁻¹². After the DPM the beam was focused to a 2.8 µm spot on a polished SiO₂ target. A low‑energy pre‑pulse was used to control the plasma density gradient scale length L (short, intermediate ≈λ/11, and long >λ/5). X‑ray‑UV spectra were recorded for three main‑pulse intensities (1.3, 2.4, and 6.6 × 10^21 W cm⁻²) and for each gradient length. At the two lower intensities clear harmonics up to the 40th order were observed, with optimal conversion at L≈λ/10. At the highest intensity the harmonic signal collapsed, with only a faint 11th order detectable.

To understand this behavior the authors carried out extensive 2‑D particle‑in‑cell simulations with the WarpX code. Simulations with an ideal Gaussian pulse (no pedestal) show that harmonic efficiency rises with intensity and that the optimal scale length remains ≈λ/10 regardless of intensity. When the measured sub‑picosecond pedestal (contrast ≈10⁻³, duration ≈200 fs) is included, the pedestal reaches relativistic intensities several hundred femtoseconds before the main pulse, heating and expanding the plasma surface. The resulting surface roughness (~100 nm) strongly suppresses high‑order harmonic generation, especially for orders above the 30th. The simulations reproduce the experimentally observed shift of the optimal L toward longer values and the rapid efficiency drop at 6.6 × 10^21 W cm⁻².

From the combined experimental and simulation data the authors derive a contrast‑requirement roadmap: for a given pedestal duration the required contrast scales steeply with the target intensity; for example, a 200 fs pedestal demands a contrast better than 10⁻⁵ to sustain efficient harmonic generation at 10^22 W cm⁻². Existing DPM designs, optimized for nanosecond contrast, are insufficient for this regime. The authors propose a modified DPM layout in which the first plasma mirror is placed farther from the focusing parabola (≈30 cm instead of 17.5 cm) so that the incident pedestal fluence remains below 1–2 × 10^13 W cm⁻², while the second mirror operates at higher fluence (>2 × 10^16 W cm⁻²) to retain high reflectivity. This configuration would lower the overall transmission to ~62 % but would meet the stringent contrast requirements needed for >10^21 W cm⁻² operation.

In summary, the paper identifies sub‑picosecond laser contrast as the fundamental limiting factor for scaling plasma‑mirror Doppler harmonic generation into the 10^22 W cm⁻² regime. By quantifying the contrast‑intensity‑pedestal relationship and offering concrete DPM design improvements, the work paves the way for using plasma mirrors as intensity boosters in next‑generation petawatt facilities, potentially enabling access to the strong‑field quantum electrodynamics regime (intensities >10^25 W cm⁻²).