Experimental Scaling of Diffraction Efficiency in Laser-Induced Plasma Gratings

Abstract

We demonstrate efficient diffraction of intense ultrashort laser pulses using optical field ionization plasma-neutral gratings formed by spatially patterned gas ionization in the interference field of two femtosecond pump pulses. The resulting transient refractive index modulation is shown to be persistent over tens of picoseconds at a 10 Hz repetition rate. An intense femtosecond signal pulse is diffracted by the plasma structure with an average single-order efficiency of up to 35$\%$ at intensities exceeding $ 10^{14}\text{ W/cm}^2$. The diffraction efficiency increases with pump energy, scales with grating aperture, and is optimized at a specific grating length in agreement with coupled-mode theory for periodic media. These results demonstrate the scalability and high damage threshold of photonic plasma structures crucial for controlling ultrashort intense laser beams, with potential applicability to multi-petawatt systems.

Figures (7)

• Figure 1: (a) Schematic of the plasma grating experimental setup. Key components: iris (IS), beamsplitter (BS), D-shaped pick-off mirror for a plasma diagnostic probe (D), automated beam shutter (AS), motorized delay stage (DS), neutral density filter (ND), periscope (PS1, PS2, PS3), lens (L), gas cell (GC), vacuum chamber (VC), linear polarizer (Pol), and Teflon scattering screen (TS). Camera P images the pump and signal beam scattering from the Teflon screen to measure the diffraction efficiency, camera S is used for plasma grating shadowgraphy, and camera G for interferometric measurements of the electron density. (b--g) Beam profiles at the gas cell: small-aperture grating -- (b) signal, (c) pump A, (d) pump B; large-aperture grating -- (e) signal, (f) pump A, and (g) pump B.
• Figure 2: (a) The beam geometry inside the gas cell is shown for the small-aperture grating with pump beams focused at the center of the gas cell at $z_{\text{f,pumps}}=0$ and the signal beam co-linear with pump A. The transverse interference pattern is shown to the left of the GC. The image of the Teflon scattering screen after the gas cell is shown after subtracting out the residual pump beams with the diffracted beam outlined by the black square. (b) The beam geometry for the large-aperture grating with pump beams focused at $z_{\text{f,pumps}} = 2$ cm after the center of the gas cell with the signal beam directly above pump A angled downwards onto the grating. The diffracted signal beam is outlined by the black square. The red arrows indicate the beams' propagation after the gas cell (optics after the gas cell are not depicted). The interference pattern of the pump beams is shown in both (a) and (b) at $z=0$. The top-down view of the pump beams crossing inside the gas cell is shown for the (c) small- and (d) large-aperture grating. Blue arrow denotes direction of gas flow from nozzle. Insets above (c) and (d) show corresponding shadowgraphs.
• Figure 3: Spatial distributions of electron density in the (a)small- and (b) large-aperture plasma grating retrieved by two-dimensional Fourier transform analysis of the plasma-induced phase shift in the interferogram obtained with the folded Mach–Zehnder interferometer. Lineouts of the electron density at $z = 0.09$ mm (small-aperture) and $z = 0.14$ mm (large-aperture) are shown in (c) and (d), respectively. The gray shaded regions indicate the grating apertures, $D = 23$$\upmu$m and $D = 98$$\upmu$m.
• Figure 4: Experimental (circles) and theoretical (lines) diffraction efficiency versus grating length for the (a) small- and (b) large-aperture gratings. Red circles show measured average efficiency with black error bars indicating the standard deviation (SD), and gray circles show single-shot efficiencies. The dotted black line is a best-fit obtained by numerical integration of Eq. (2), including Bragg condition mismatch from angular and spectral bandwidths, with the electron density as a free parameter. The fit yields average electron densities of $4.9\times10^{17} \text{cm}^{-3}$ and $3.9\times10^{17} \text{cm}^{-3}$ for the small- and large-aperture gratings, respectively.
• Figure 5: (a) Average diffraction efficiency (blue circles) and electron density (red triangles) as a function of pump intensity for grating length $L=$ 2.67 mm. Blue and red shaded regions indicate the standard deviation (SD) over 400 single shots (efficiency) and 100 single shots (electron density), respectively. Horizontal error bars show the standard deviation of the average intensity of the interference pattern formed by the two pump beams. (b) Average diffraction efficiency as a function of electron density, controlled by varying the pump energy. Red circles show the average experimental $\eta$ for $L=2.67$ mm with error bars corresponding to one standard deviation over 100 single shots. The red dotted line shows the theoretical prediction calculated using $\Delta\lambda=80$ nm and $\Delta\theta_1=\pm0.54^\circ$ in Eq. (2).