Optically Controlled Solid-Density Transient Plasma Gratings

A general approach for optically controlled spatial structuring of overdense plasmas generated at the surface of initially plain solid targets is presented. We demonstrate it experimentally by creating sinusoidal plasma gratings of adjustable spatial periodicity and depth, and study the interaction of these transient structures with an ultraintense laser pulse to establish their usability at relativistically high intensities. We then show how these gratings can be used as a “spatial ruler” to determine the source size of the high-order harmonic beams produced at the surface of an overdense plasma. These results open new directions both for the metrology of laser-plasma interactions and the emerging field of ultrahigh intensity plasmonics.

Figure 1

(a) Temporal evolution of the spatially resolved phase shift induced on the Fourier-domain interferometry probe pulse by the plasma expansion triggered by a prepulse. (b) Fluence dependence of plasma expansion velocity $C_s$ at the center of the prepulse beam, as deduced from the measured phase shifts. The inset plots $T_e$ (at the critical plasma density $n_c$) as a function of prepulse fluence obtained from esther simulations for a fused silica target under typical experimental conditions.

Figure 2

(a) Experimental scheme for the creation of optically controlled plasma gratings and their irradiation by an ultraintense pulse. (b) Resulting intensity distributions of the two interfering prepulse beams (gray scale) when they are perfectly synchronized (${\tau }^{\prime }=0$), and of the main beam (colored scale) at focus. Panels (c) and (d) present the reconstructed plasma grating density calculated from esther simulations at two different time delays $\tau$. The black lines show the isodensity contours at $n=n_c$.

Figure 3

Panels (a) and (b) present experimental CWE angularly resolved harmonic spectra, respectively, at ${\tau }^{\prime }=0$ (maximum fringe contrast) and ${\tau }^{\prime }>{\tau }_c$ (no grating) for short gradient ($\tau =0.35\mathrm{ps}$) and $I_{\max }=2\times {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$. Panels (c) and (d) present similar measurement for ROM harmonics, now for long gradient ($\tau =1.18\mathrm{ps}$) and $I_{\max }=1\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$. The blue lines in (i)–(iv), respectively, correspond to lineouts of the 12th harmonic in (a)– (d). The red dashed lines in (i) and (iii) present the best fits obtained from our model, and in (ii) and (iv), the Gaussian beams calculated in the far field in the absence of plasma grating, using the values of the parameters $w_n$ and ${\alpha }_n$ deduced from these fits in (i) and (iii). The insets show the spatial pattern of the prepulses measured at focus (gray scale) superimposed with the focal spot of the main pulse (colored scale).

Figure 4

Different regimes of diffraction from a grating. Panels (a)–(c)–(e) show different unperturbed source [$h_n(x)$] amplitude (shaded red) and phase (blue) profiles, all modulated by the same sinusoidal grating (shaded gray). Panels (b)– (d)– (f) show the multiple replicas of the unperturbed beam ${|H_n(k)|}^2$ induced by the grating (dashed red) in the far field, which combination produce the total diffraction pattern (blue). In (a)–(b), the spacing between these replicas is larger than the divergence of the unperturbed beam, so that they do not overlap. In contrast, in (c)–(d) and (e)–(f), the replicas overlap and interfere, producing a pattern that depends on the spatial phase of $H_n(k)$.