Pushing the Frontiers of Light: Magnetized Plasma Lenses and Chirp Tailoring for Extreme Intensities

TL;DR

The paper proposes a magnetized-plasma-lens (MPL) scheme to reach extreme laser intensities by using a curved MPL immersed in a structured magnetic field to raise the refractive index for RCP light ($n_R>1$) and enable transverse focusing, complemented by a nonlinear chirp that temporally compresses the pulse. The approach is validated with 3D PIC simulations (OSIRIS-4.0), demonstrating up to ~$10^{2}$-fold peak-intensity enhancement (e.g., from $I_{init}\approx1.36\times10^{16}$ W/cm$^2$ to $I_{fin}\approx1.58\times10^{18}$ W/cm$^2$) when the focal point lies near or outside the MPL, along with self-focusing and self-compression. Key findings include the importance of the magnetic field gradient (tunable via $B_0$) and chirp profile for optimizing compression and minimizing detrimental resonant heating ($\omega_{ce}\approx\omega_l$); shifting the focus outside the lens can preserve pulse quality while maintaining amplification. The work suggests a viable pathway to exawatt-scale intelligible light using modest initial pulses, leveraging advances in high-field magnets, shaped plasma targets, and programmable chirped pulses, with implications for high-field physics and laboratory astrophysics.

Abstract

In this work, an innovative scheme is proposed that exploits the response of magnetized plasmas to realize a refractive index exceeding unity for right circularly polarized (RCP) waves. Using two- and three-dimensional Particle-in-Cell (PIC) simulations with the OSIRIS 4.0 framework, it is shown that a shaped magnetized plasma lens (MPL) can act as a glass/solid-state-based convex lens, amplifying laser intensity via transverse focusing. Moreover, by integrating three key ingredients, a tailored plasma lens geometry, a spatially structured strong magnetic field, and a suitably chirped laser pulse, simultaneous focusing and compression of the pulse has been achieved. The simulations reveal up to a 100-fold increase in laser intensity, enabled by the combined action of the MPL and the chirped pulse profile. With recent advances in high-field magnet technology, shaped plasma targets, and controlled chirped laser systems, this approach offers a promising pathway toward experimentally reaching extreme intensities.

Figures (6)

• Figure 1: The figure demonstrates the schematic representation (not to scale) of the geometry chosen for 3D simulation. Subplot (a) shows the negatively chirped right circularly polarized laser pulse incident onto a magnetized plasma lens (MPL) immersed in an inhomogeneous magnetic field $\vec{B}_{ext}(x,y,z)$. Here $w_i,w_f$ represent incident and final spot sizes, and $f_{\text{init}},f_{\text{fin}}$ denote the location of the incident and final focus points of the field. Subplot (b) demonstrates simultaneous chirp pulse compression due to inhomogeneous $\vec{B}_{ext}$ in MPL. Here $\tau_i, \tau_f$ represent the pulse duration of the incident chirped pulse and the final compressed pulse after passing through the MPL.
• Figure 2: The peak of EMF energy density with simultaneous transverse spot-size (FWHM) evolution for a linear chirp laser has been shown in figure a) for a convex lens immersed in the magnetic field for $\vec{B}_{N,ext}(2.2,0.005)$ described in equation (\ref{['eq:mag_field']}). Figure (b) depicts the longitudinal profile of the laser at different times, and peak amplitude is achieved at $t=330\omega_{pe}^{-1}$. Figures (c,d) are similarly plotted for the same plasma lens and $\vec{B}_{N,ext}(2.2,0.005)$ but with the nonlinear chirp laser. Figure (e,f) is plotted for the same plasma lens and a little higher $\vec{B}_{N,ext}(2.4,0.005)$ but with a linear chirp profile.
• Figure 3: The figure $(a)$ demonstrates the time evolution of an incoming laser pulse launched with a peak amplitude of $0.014 m_e^2c^2\omega_{pe}^2e^{-2}$ ($\times 117$ zoom) at $t=0 \omega_{pe}^{-1}$ and a maximum compressed and focused pulse achieved at a location $f_{\text{fin}}=249c/\omega_{pe}$ at time $t=330 \omega_{pe}^{-1}$ with a peak amplitude reaching a $1.63 m_e^2c^2\omega_{pe}^2e^{-2}$ ($\sim 117$ fold increase); afterwards it again diverges. The figure $(b,c)$ shows surface projection in the $x-y$ plane at the center $z=110c/\omega_{pe}$ of EMF energy density for the initial and final max compressed and focused pulse. Figure $(d)$ presents a 1-D snapshot of the longitudinal pulse profile at various times. This clearly shows that the chirp pulse is compressed by $1/3$ times from MPL.
• Figure 4: Figure (a) demonstrates the ratio of final and initial intensity as a function of initial intensity. (b) The kinetic energy absorbed by the electrons in plasma with time has been plotted here. The black dashed line represents the laser exiting time from the plasma lens.
• Figure S1: Normalized EMF energy density evolution in time for cases I and II under interaction with MPL, shown in figures $(a)$ and $(b)$ respectively. At each time t, $(\times M)$ magnified field has been plotted.