Plasma zone plate for high-power lasers driven by a Laguerre-Gaussian beam Lukai Wang1 Wei Liu1 Qing Jia1and Jian Zheng12

2025-05-02 0 0 5.03MB 12 页 10玖币

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Plasma zone plate for high-power lasers driven by a

Laguerre-Gaussian beam

Lukai Wang1, Wei Liu1, Qing Jia1,∗and Jian Zheng1,2,∗

1Department of Plasma Physics and Fusion Engineering and CAS Key Laboratory

of Geospace Environment, University of Science and Technology of China, Hefei,

Anhui 230026, Peoples Republic of China

2Collaborative Innovation Center of IFSA, Shanghai Jiao Tong University, Shanghai

200240, Peoples Republic of China

E-mail: qjia@ustc.edu.cn and jzheng@ustc.edu.cn

September 2022

Abstract. Plasma-based optics has emerged as an attractive alternative to

traditional solid-state optics for high-power laser manipulation due to its higher

damage threshold. In this work, we propose a plasma zone plate (PZP) driven by the

ponderomotive force of a Laguerre-Gaussian beam when it irradiates an underdense

plasma slice. We formulate the theory of the PZP and demonstrate its formation and

function of focusing high-power lasers using particle-in-cell simulations. The proposed

scheme may oﬀer a new method to focus and manipulate high-power lasers with plasma-

based optics.

Keywords: plasma zone plate, laser manipulation, plasma optics, nonlinear plasma

dynamics, laser-plasma interaction

1. Introduction

In the last few decades, the rapid development of revolutionary laser techniques, such

as chirped pulse ampliﬁcation [1] and optical parametric chirped pulse ampliﬁcation [2],

has signiﬁcantly improved the peak intensity of lasers and opened up new avenues

for fundamental research in ﬁelds such as strong ﬁeld quantum electrodynamics [3, 4],

high-energy-density physics [5] and relativistic optics [6]. The highest laser intensity

available at the moment is delivered by high-power petawatt (PW) lasers [7] and can

realize intensities up to ∼1023W/cm2after being focused [8]. With the increasing

peak intensity of lasers, manipulation of such high-power lasers has become increasingly

challenging because the size of the traditional solid-state optical components must be

enlarged to avoid laser-induced thermal damage [9], which can be extremely costly

and technically challenging for large-scale PW laser systems [10]. As a result, plasma-

based optical components composed of free electrons and ions, which are not limited by

optical damage as the traditional solid-state optical components, have become potential

arXiv:2210.02815v1 [physics.plasm-ph] 6 Oct 2022

Plasma zone plate for high-power lasers driven by a Laguerre-Gaussian beam 2

alternatives for high-power laser manipulation and have been extensively studied in

recent years [11–23]. A series of plasma-based optical components and applications have

been proposed, such as plasma gratings or photonic crystals with band structure [11–13],

plasma holograms for focusing and mode conversion [14], plasma mirrors for probing

strong ﬁeld quantum electrodynamics [15, 16], plasma lenses for laser shaping [17],

plasma waveplates for polarization manipulation [18–20] and plasma-based ellipsoidal

mirror [21] and compound parabolic concentrator [22] with an intensity toleration over

1012W/cm2for focusing lasers. Recently, Edwards et al demonstrated a highly-eﬃcient

plasma-based zone plate by two copropagating lasers which tolerates a maximum

intensity of 1017W/cm2[23]. The structure of the zone plate reminds us of the intensity

patterns of Laguerre-Gaussian lasers.

Laguerre-Gaussian (LG) beams, the eigensolution of the Helmholtz equation in a

cylindrical coordinate system under the paraxial condition, are characterized by the

azimuthal mode index land the radial mode index p, where ldenotes the number of

2πphase cycles around the circumference and (p+ 1) denotes the number of radial

nodes in the mode proﬁle [24]. Almost all previous works on the interaction between

LG lasers and plasma focus on optical angular momentum related properties, which are

characterized by the azimuthal mode index l[25–27]. The intensity pattern of an LG

beam with a nonzero lconsists of phalos separated from each other by dark rings and

a dark center.

In this work, we propose a plasma zone plate (PZP) driven by the ponderomotive

force generated by an LG beam with a nonzero p. The formation and functioning of

PZP are considered theoretically and veriﬁed by numerical and particle-in-cell (PIC)

simulations. The merit of using an LG beam is that as an eigenstate in vacuum,

the distance of stable propagation is longer and the engineering complexity is lower

compared with a non-eigenstate beam, which makes it more plausible for potential

experiments. This study extends the understanding of the plasma density evolution

driven by the ponderomotive force, which could be of great beneﬁt to both theoretical

and experimental works of related research.

The paper is organized as follows: Proof-of-principle demonstrations of our scheme

by 3D-PIC simulations are shown in section 2. The theoretical model of PZP formation

is presented in section 3. The formation process is divided into three main stages and a

detailed comparison between the theoretical and simulation results is demonstrated. The

functioning of the PZP is speciﬁed in section 4. On the one hand, the theoretical model

and typical examples for focusing infrared and terahertz (THz) lights are presented.

On the other hand, the more realistic scenario of an obliquely incident probe beam is

discussed. Conclusions are summarized in section 5.

2. Proof-of-principle PIC demonstrations

First of all, we present proof-of-principle demonstrations of our scheme using 3D-PIC

simulations by the code EPOCH [28] to illustrate the formation and focusing function

Plasma zone plate for high-power lasers driven by a Laguerre-Gaussian beam 3

(a)

(b) (c) (d)

Figure 1: (a) Schematic of a PZP. An LG beam (l= 2, p = 4) is launched into the

plasma and generates a PZP. At a delayed time, a probe beam is focused by the PZP.

(b) Intensity pattern for the pump beam. (c) Transverse density distribution of the

PZP. (d) The laser intensity of the probe beam before, during, and after the interaction

with PZP. The white dotted lines (z= 18.2/21.8µm) represent the position of the PZP.

of a typical PZP. The schematic is shown in ﬁgure 1(a).

A circularly polarized (CP) LG beam (λp= 1µm, l = 2, p = 4), the intensity of

which is shown in ﬁgure 1(b), is launched from the z boundary as the pump beam to

irradiate a thin plasma slab for demonstration. The beam radius is wp= 10µm and the

maximum intensity is 2.7×1016W/cm2. The plasma slab consists of a constant density

slab of length 2λpwith Gaussian density ramps of length 1λpat each side along the

z-direction while uniformly distributed on the x-y plane. The maximum density is set

to be ne0= 0.3nc(λp), where nc(λp)[cm−3] = 1.12 ×1021/λ2

p[µm] is the critical density

for the laser with wavelength λp. We assume a fully-ionized electron-ion plasma with the

ions set to be qi=eand mi= 100me(e: the elementary charge, me: the electron mass)

to reduce the simulation time. The plasma temperature is Te= 25eV ,Ti= 2.5eV . The

dimensions of the simulation box are Lx×Ly×Lz= 160µm ×160µm ×40µm and

the spatial resolutions are ∆x= ∆y= 0.25µm and ∆z= 0.1µm. The plasma slab is

placed at the center of the simulation box and padded on both sides with suﬃciently

long vacuum regions.

As the pump beam interacts with the plasma, an annular density modulation starts

to develop and reaches the maximum at around 4ps, which is shown in ﬁgure 1(c). Then

a CP probe beam (λb= 1µm) is launched into this modulated plasma slice. Figure

1(d) shows the intensity distribution of the probe beam through its propagation. The

modulated plasma functions as a plasma zone plate (PZP), which magniﬁes the intensity

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Plasmazoneplateforhigh-powerlasersdrivenbyaLaguerre-GaussianbeamLukaiWang1,WeiLiu1,QingJia1;andJianZheng1;2;1DepartmentofPlasmaPhysicsandFusionEngineeringandCASKeyLaboratoryofGeospaceEnvironment,UniversityofScienceandTechnologyofChina,Hefei,Anhui230026,PeoplesRepublicofChina2CollaborativeInnovatio...

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Plasma zone plate for high-power lasers driven by a Laguerre-Gaussian beam Lukai Wang1 Wei Liu1 Qing Jia1and Jian Zheng12

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