Ultrarelativistic nanoplasmonics as a route towards extreme-intensity attosecond pulses

The generation of ultrastrong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum electrodynamical tests and matter probing at extremely short scales. Here we demonstrate that a laser irradiated plasma surface can act as an efficient converter from the femto- to the attosecond range, giving a dramatic rise in pulse intensity. Although seemingly similar schemes have been described in the literature, the present setup differs significantly from the previous attempts. We present a model describing the nonlinear process of relativistic laser-plasma interaction. This model, which is applicable to a multitude of phenomena, is shown to be in excellent agreement with particle-in-cell simulations. The model makes it possible to determine a parameter region where the energy conversion from the femto- to the attosecond regime is maximal. Based on the study we propose a concept of laser pulse interaction with a target having a groove-shaped surface, which opens up the potential to exceed an intensity level of ${10}^{26}$ W/cm${}^2$ and observe effects due to nonlinear quantum electrodynamics with upcoming laser sources.

Figure 1

The dynamically accumulated by plasma energy $\delta$ obtained from one-dimensional PIC simulations of a plasma with density $N_e$ at oblique irradiation ($\theta ={60}^{\circ }$, $p$ polarization) by a wave with constant intensity $I$ and $1\mu \mathrm{m}$ wavelength during one optical cycle. $S$ is the ultrarelativistic similarity parameter, defined as the quotient between dimensionless density and the dimensionless amplitude [see Eq. (3)].

Figure 2

Transformation to a moving reference frame. Here the plasma density $n$, wave amplitude $a$, and frequency $\omega$ have subscript 0 denoting the moving frame.

Figure 3

(a) Space-time distribution of electrons density $N$ (green) and amplitudes of incident $a_{\mathrm{in}}$ (red) and backradiated $a_g$ (blue) electromagnetic fluxes obtained from 1D PIC simulation of plasma with density $4\times {10}^{23}$ cm${}^{-3}$ at oblique irradiation ($\theta =11.{25}^{\circ }$) by a wave with constant intensity $5\times {10}^{22}$ W/cm${}^2$ and 1 $\mu$m wavelength during three optical cycles. The dashed red curve shows position of the thin layer obtained using the RES model. Time and coordinate are in dimensionless units [see Eq. (3)]. (b) Backradiated signal obtained by PIC simulation (blue curve) and using the RES model (dashed red curve). (c) Electron density distribution $N\left(x\right)$ at the instant of maximum displacement ($t=3.19$).

Figure 4

(a) Regions on the plane of parameters $S,\theta$ corresponding to qualitatively different forms of solution of Eq. (12). (b)–(f) Form of solution on the plane $\{\eta ,u\}$ (red), its limit cycle (black), lines of phase portrait for the “$+$” sign (blue) and the “$-$” sign (green) in Eq. (12), and the corresponding form of electromagnetic backradiation from the plasma.

Figure 5

Giant pulse generation moment ${\xi }_g$, pulse amplitude $a_g/a_0$, and its duration ${\tau }_g$ obtained from the RES model with $\gamma =10$ and $\chi =56$ (d), (e), (f) and from 1D PIC simulations (a), (b), (c) of semi-infinite plasma obliquely irradiated by one optical cycle pulse with 1 $\mu$m wavelength and amplitude $a=191.1$, which corresponds to 5$\times {10}^{22}$ W/cm${}^2$ intensity. For the PIC simulations, the pulse duration was assessed as a distance between maximum and minimum electric field points, and the region of unipolar pulse generation is given in white.

Figure 6

The amplitude increase factor $a_g/a_0$ obtained from 1D PIC simulations with the same parameters as in Fig. 1.

Figure 7

(a) Schematic representation of the concept of groove-shaped target. (b) Intensity distribution at focusing instant obtained from 2D PIC simulation: a linearly polarized wave with intensity $5\times {10}^{22}$ W/cm${}^2$ and wavelength 1 $\mu$m obliquely incident at an optimal angle ${\theta }_g={62}^{\circ }$ on a parabolic groove-shaped target with density $0.85\times {10}^{23}$ cm${}^{-3}$, which corresponds to $S=0.4$. PIC simulation in the moving frame implies that the transverse size of the laser pulse is fairly large compared to the wavelength, which is a rather weak restriction. Fully relativistic parallel fast Fourier transform (FFT) based PIC code elmis [29] is used; an $8\times 8$-$\mu$m region is represented by $8192\times 8192$ cells; plasma ions are taken to be Au${}^{6+}$; each target cell contains approximately 100 virtual particles of each type; the time step is 3 as; the laser pulse front has a sine-squared profile with two wave periods duration.