Spatial, Spectral and Temporal Response of High Intensity Laser Plasma Mirrors- Direct Observation of the Ponderomotive Push

TL;DR

This work presents a direct in situ 3D mapping of plasma-mirror surface evolution under relativistic femtosecond irradiation by analyzing the reflected wavefront, spectrum, and temporal profile. Using a combination of high-contrast laser experiments, structured targets, and extreme-contrast pulses, the authors reveal surface deformations on the order of hundreds of nanometers and substantial spatio-temporal modifications to the reflected pulse, consistent with 3D PIC simulations and a ponderomotive-force–based model. The results demonstrate how PM curvature, spectral broadening, and pulse reshaping arise from intensity-driven surface dynamics, with implications for high-harmonic generation, attosecond pulse control, and QED regimes at extreme intensities. The study validates PMs as robust, high-damage-threshold optical elements for future ultrafast and high-field applications, offering new input for laser-plasma coupling and surface dynamics theory.

Abstract

Plasma-based optics have emerged as a powerful platform for manipulating and amplifying ultra-intense laser pulses. However, the inherently nonlinear and dynamic nature of plasma leads to significant spatial, spectral, and temporal modulations when driven at relativistic intensities. These modifications can dramatically alter the structure of the reflected laser pulses, posing challenges for their use in applications such as vacuum ultraviolet (VUV) and X-ray generation, as well as relativistic particle acceleration. Comprehensive, multidimensional diagnostics are essential to accurately characterize these so-called `plasma mirrors' (PMs). We present a direct, \textit{in situ} measurement of the three-dimensional plasma surface evolution during femtosecond laser irradiation, achieved through simultaneous analysis of the wavefront, spectrum, and temporal profile of the reflected light. Our measurements reveal surface deformations on the order of a few hundred nanometers at relativistic intensities, in agreement with three-dimensional particle-in-cell (3D-PIC) simulations. Additionally, the PM induces substantial modifications to the pulse spectrum and temporal profile, introducing spatio-temporal couplings.

Figures (10)

• Figure 1: a) Schematic of the experimental setup for measuring laser effects on electrons with a QWLSI wavefront sensor as the detector. The figure illustrates the ponderomotive push caused by the intense laser and shows various forces acting on an electron. The PMF on an electron has three components along three directions, as illustrated. $F_{pol}$ is directed along the polarization direction, $F_{k}$ is in the laser propagation direction, and $F_{grad}$ is along the gradient of the average intensity of the field. b) Measured focal spot in vacuum. c) Laser contrast measured using a third-order nonlinear process. d) Diagram of a QWLSI wavefront sensor, which comprises a cross grating and a CCD. e) Example of a raw and zoomed-out portion of an interferogram as measured by the QWLSI wavefront sensor.
• Figure 2: a) Wavefront of the reflected laser at different intensities for Setup-A. These are real time 3D surface deformations measured. X and Y represents the spatial dimension and Z is the phase plotted in terms of OPD in vacuum. (Note: for better visualization, the plot has been flipped upside down along the Z-axis) b) Top left sketch represents two dimensional density profile at low intensity, just start of the pulse, as the intensity increases, the plasma surface gets deformed, piling up of electrons and ions happens, represented by the top right figure. The bottom figure shows the exponential density profile in the x direction. The pulse initially reflects from $n_c cos^2(\theta)$ where $\theta$ is the incidence angle with respect to the target normal. The cartoon also shows the density bump created by the laser pulse and the total surface deformation. c) Line outs taken at each intensities. Line curves represent the corresponding surface deformation obtained from the theoretical calculation. Shows the experimental data and the model is in good agreement.
• Figure 3: a) Wavefront of the reflected laser at different intensities from sub-$\lambda$ grating [Setup-B]. (Note: for better visualization, the plot has been flipped upside down along the Z-axis.) b) Left: Schematic of the laser incidence on the grating, Right: image of laser shots taken on the grating. c) The linecut of the wavefronts represented on a. Line curves represent the corresponding surface deformation obtained from the theoretical calculation.
• Figure 4: a. Experimentally measured focal spot from the beam homogenizer, b. The measured wavefront at highest reachable intensity $4\times 10^{17}$ W/cm$^2$.
• Figure 5: a) Measured wavefronts of the extreme contrast pulse. The headings indicate the peak intensities corresponding to each shot, in units of $W/\mathrm{cm}^2$. b) Measured focal spot of the 400 nm pulse at the target surface, showing elongation along the $y$-direction. c) Computed temporal contrast of the second harmonic (400 nm) pulse, derived from the measured contrast of the 800 nm fundamental pulse.