Extreme case of Faraday effect: magnetic splitting of ultrashort laser pulses in plasmas

The Faraday effect, caused by a magnetic-field-induced change in the optical properties, takes place in a vast variety of systems from a single atomic layer of graphenes to huge galaxies. Currently, it plays a pivot role in many applications such as the manipulation of light and the probing of magnetic fields and material's properties. Basically, this effect causes a polarization rotation of light during its propagation along the magnetic field in a medium. Here, we report an extreme case of the Faraday effect where a linearly polarized ultrashort laser pulse splits in time into two circularly polarized pulses of opposite handedness during its propagation in a highly magnetized plasma. This offers a new degree of freedom for manipulating ultrashort and ultrahigh power laser pulses. Together with technologies of ultra-strong magnetic fields, it may pave the way for novel optical devices, such as magnetized plasma polarizers. In addition, it may offer a powerful means to measure strong magnetic fields in laser-produced plasmas.Comment: 18 pages, 5 figure

Extreme case of Faraday effect : magnetic splitting of ultrashort laser pulses in plasmas

The Faraday effect due to magnetic-field-induced change in the optical properties takes place in a vast variety of systems from a single atomic layer of graphenes to huge galaxies. To date, it plays a pivot role in many applications such as the manipulation of light, and the probing of magnetic fields and material's properties. Basically this effect causes a polarization rotation of light during its propagation along the magnetic field in a medium. Here, we report an extreme case of the Faraday effect that a linearly polarized ultrashort laser pulse splits in time into two circularly polarized pulses of opposite handedness during its propagation in a highly magnetized plasma. This offers a new degree of freedom to manipulate ultrashort and ultrahigh power laser pulses. Together with technologies of ultra-strong magnetic fields, it may pave the way for novel optical devices, such as magnetized plasma polarizers. Besides, it may offer a powerful means to measure strong magnetic fields in laser-produced plasmas

Solutions of a system of diffusion equations

We study existence and multiplicity of homoclinic type solutions to the following system of diffusion equations on R x Omega: {partial derivative(t)u - Delta(x)u + b(t, x) . del(x) u + V(x)u = H-v (t, x, u, v), {-partial derivative(t)v - Delta(x)v - b(t, x) . del(x) v + V(x)v = H-u (t, x, u, v), where Omega = R-N or Omega is a smooth bounded domain of R-N, z = (u, v) : R x Omega -> R-m x R-m, and b is an element of C-1 (R x (Omega) over bar, R-N), V is an element of C((Omega) over bar, R), H is an element of C-1 (R x (Omega) over bar x R-2m, R), all three depending periodically on t and x. We assume that H(t, x, 0) 0 and H is asymptotically quadratic or superquadratic as vertical bar z vertical bar -> infinity. The superquadratic condition is more general than the usual one. By establishing a proper variational setting based on some recent critical point theorems we obtain at least one nontrivial solution, and also infinitely many solutions provided H is moreover symmetric in z

Some nonlocal elliptic problem involving positive parameter

We consider the following superlinear Kirchhoff type nonlocal problem: \cases \displaystyle -\bigg(a+b\int_\Omega |\nabla u|^2dx\bigg)\Delta u =\lambda f(x,u) & \text{in } \Omega,\ a> 0, \ b> 0, \ \lambda > 0, \\ u=0 &\text{on } \partial\Omega. \endcases Here, $f(x,u)$ does not satisfy the usual superlinear condition, that is, for some $\theta > 0,$ $$0\leq F(x,u)\triangleq \int_0^u f(x,s)ds \leq \frac1{2+\theta}f(x,u)u, \quad \text{for all } (x,u)\in \Omega \times \mathbb{R}^+$$ or the following variant $$0\leq F(x,u)\triangleq \int_0^u f(x,s)ds \leq \frac1{4+\theta}f(x,u)u, \quad \text{for all } (x,u)\in \Omega \times \mathbb{R}^+$$ which is quiet important and natural. But this superlinear condition is very restrictive eliminating many nonlinearities. The aim of this paper is to discuss how to use the mountain pass theorem to show the existence of non-trivial solution to the present problem when we lose the above superlinear condition. To achieve the result, we first consider the existence of a solution for almost every positive parameter $\lambda$ by varying the parameter $\lambda$. Then, it is considered the continuation of the solutions

Generating a tunable narrow electron beam comb via laser-driven plasma grating

We propose a novel approach for generating a high-density, spatially periodic narrow electron beam comb (EBC) from a plasma grating induced by the interference of two intense laser pulses in subcritical-density plasma. We employ particle-in-cell (PIC) simulations to investigate the effects of cross-propagating laser pulses with specific angles overlapping in a subcritical plasma. This overlap results in the formation of a transverse standing wave, leading to a spatially periodic high-density modulation known as a plasma grating. The electron density peak within the grating can reach several times the background plasma density. The charge imbalance between electrons and ions in the electron density peaks causes mutual repulsion among the electrons, resulting in Coulomb expansion and acceleration of the electrons. As a result, some electrons expand into vacuum, forming a periodic narrow EBC with an individual beam width in the nanoscale range. To further explore the formation of the nanoscale EBC, we conduct additional PIC simulations to study the dependence on various laser parameters. Overall, our proposed method offers a promising and controlled approach to generate tunable narrow EBCs with high density

Control of transmission of right circularly polarized laser light in overdense plasma by applied magnetic field pulses

National Natural Science Foundation of China [11475147, 11374262, 11304331, 11174303]; National Basic Research Program of China [2013CBA01504, 2011CB808104]; State Key Laboratory of High Field Laser Physics at SIOM; Fundamental Research Funds for CentralThe effect of a transient magnetic field on right-hand circularly polarized (RHCP) laser light propagation in overcritical-density plasma is investigated. When the electron gyrofrequency is larger than the wave frequency, RHCP light can propagate along the external magnetic field in an overcritical density plasma without resonance or cutoff. However, when the magnetic field falls to below the cyclotron resonance point, the propagating laser pulse will be truncated and the local plasma electrons resonantly heated. Particle-in-cell simulation shows that when applied to a thin slab, the process can produce intense two-cycle light pulses as well as long-lasting self-magnetic fields