Formation of Optical Bullets in Laser-Driven Plasma Bubble Accelerators

Electron density bubbles—wake structures generated in plasma of density ${\overline{n}}_e\sim {10}^{19}{\mathrm{cm}}^{-3}$ by the light pressure of intense ultrashort laser pulses—are shown to reshape weak copropagating probe pulses into optical “bullets.” The bullets are reconstructed using frequency-domain interferometric techniques in order to visualize bubble formation. Bullets are confined in three dimensions to plasma-wavelength size, and exhibit higher intensity, broader spectrum and flatter temporal phase than surrounding probe light, evidence of their compression by the bubble. Bullets observed at $0.8\lesssim {\overline{n}}_e\lesssim 1.2\times {10}^{19}{\mathrm{cm}}^{-3}$ provide the first observation of bubble formation below the electron capture threshold. At higher ${\overline{n}}_e$, bullets appear with high shot-to-shot stability together with relativistic electrons that vary widely in spectrum, and help relate bubble formation to fast electron generation.

Figure 1

Left column: Spectral interferograms at various plasma densities showing Stokes shifted streaks near $r\approx 0$ in (c)–(h) (highlighted by brackets). Middle column: reconstructed exit probe amplitude profiles: (a) undistorted profile; for (c)–(h) optical bullets (see vertical arrows) near front edge. Right column: energy spectrum of electrons produced. Regime I: bullets appear without relativistic electrons; Regime II: bullets appear with relativistic electrons. Plasma density ${\overline{n}}_e$ [${10}^{19}{\mathrm{cm}}^{-3}$] in each row was (a) 0; (b) 0.4; (c) 1.0; (d) 1.2; (e) 2.6; (f) 2.6; (g) 2.6; (h) 3.2 in the doubly ionized He region.

Figure 2

WAKE simulations for ${\overline{n}}_e=0.8\times {10}^{19}{\mathrm{cm}}^{-3}$ showing formation of plasma wake (top row), with pump $e^{-2}$ isointensity contours outlined in red, and refraction of 400 nm probe (shortened to 100 fs centered on first wake bucket) to form optical bullet inside the bubble and fringe outlining ionization front (2nd row) as they propagate (left to right) from gas jet entrance (left column), to $z=0.5\mathrm{mm}$ (middle column), to near $z_{\mathrm{exit}}$ (right column). Bottom left: simulated FD hologram shows broadened streak at $r=0$ corresponding to bullet inside the bubble. Bottom right: probe intensity profile reconstructed from FD hologram using experimental reference bandwidth and imaging resolution. Arrows: bullet (thick); ionization front (thin, horizontal).

Figure 3

VLPL simulations for ${\overline{n}}_e=2.3\times {10}^{19}{\mathrm{cm}}^{-3}$. Panels (a)–(c): plots of electron density showing formation of bubble, injection of electrons [(b) and (c)] at $z=0.56\mathrm{mm}$ (left), 0.92 mm (2nd column) and 1.56 mm (3rd column); Panels (e)–(g): plots of $|E_{\mathrm{pr}}(r,\zeta ,z)|$ of the $y$-polarized probe at the same $z$ values, showing optical bullet formation. Panel (d): accelerated electron spectrum at $z=1.56\mathrm{mm}$, showing quasimonoenergetic feature at 90 MeV similar to Fig. 1g. Panel (h): Enlarged image of bullet from Fig. 1g.