Method for generating high-order mode relativistic vortex laser based on axial focusing pinhole plate

Abstract

The application relates to a method for generating high-order mode relativistic vortex laser based on an axial focusing pinhole plate, which comprises the following steps: preparing an axial focusing spiral pinhole plate, wherein the axial focusing spiral pinhole plate is provided with multiple pinhole groups arranged along the circumferential direction of the plate body in a regular manner, and each pinhole group comprises multiple pinholes arranged in a spiral manner; a Gaussian laser with relativistic intensity is irradiated onto the axial focusing spiral pinhole plate, and different optical paths of the laser transmitted by different pinholes to the optical axis are caused based on the pinholes on the axial focusing spiral pinhole plate, an angular phase difference is introduced into the transmitted Gaussian laser, and vortex laser is formed in a focusing area. The axial focusing spiral pinhole plate can effectively generate vortex laser, and the arrangement mode of the pinholes on the axial focusing spiral pinhole plate is adjusted to adjust the optical path difference of the transmitted laser, so that the corresponding vortex laser is generated in the focusing area, and the method is more flexible and has lower cost.

Description

Technical Field

[0001] This invention relates to the field of laser and plasma technology, and in particular to a method for generating high-order mode relativistic vortex lasers based on an axially focused pinhole plate. Background Technology

[0002] Due to their unique properties, such as carrying orbital angular momentum, having phase singularities, and hollow intensity distributions, vortex lasers have attracted widespread attention. These remarkable properties have led to extensive research and applications of vortex lasers in multiple fields, from optical tweezers, quantum entanglement, and communications to optical fabrication and imaging. Over the past decade, research on relativistic vortex lasers and their interactions with plasmas has rapidly progressed due to their outstanding prospects. Thanks to their ultra-high intensity and helical electromagnetic fields, relativistic vortex lasers are considered excellent tools for manipulating relativistic charged particle beams, emitting photon beams with orbital angular momentum, and exploring particle and electromagnetic field angular momentum transfer under high-energy, momentum, and angular momentum density conditions. Despite a wealth of theoretical and numerical studies, experimental research on the interaction of relativistic vortex lasers with plasmas has lagged behind. This is mainly due to the limited damage threshold of solid-state optical materials, making the generation of high-quality relativistic vortex lasers experimentally a challenging task.

[0003] To overcome this obstacle, researchers have made significant efforts in theoretical, numerical, and experimental studies. Numerous theoretical and numerical studies have proposed various plasma-based schemes for generating relativistic vortex lasers. However, it is noteworthy that the vast majority of these schemes primarily focus on generating low-order modes of vortex lasers. However, research on the generation of higher-order mode relativistic vortex lasers remains relatively limited. Using off-axis spiral phase mirrors, researchers have been able to generate lasers with an intensity of approximately [insert value here] in the laboratory. The main mode is Vortex lasers. However, the generation of higher-order mode relativistic vortex lasers remains an area to be explored. Therefore, exploring a feasible scheme to generate high-quality higher-order mode relativistic vortex lasers is of great value for the research on generating high-angular-momentum relativistic particle beams or ultra-strong magnetic fields and extending the interaction between relativistic vortex lasers and plasma. Summary of the Invention

[0004] The purpose of this invention is to provide a method for generating high-order mode relativistic vortex lasers based on an axially focused pinhole plate.

[0005] To achieve the above-mentioned objective, this invention provides a method for generating high-order mode relativistic vortex lasers based on an axially focusing pinhole plate, comprising the following steps:

[0006] S1. Prepare an axially focusing spiral pinhole plate, wherein the axially focusing spiral pinhole plate is provided with multiple rows of pinhole groups regularly arranged along the circumference of its plate body, and each pinhole group includes multiple pinholes arranged in a spiral.

[0007] S2. A Gaussian laser beam of relativistic intensity is irradiated onto the axially focusing spiral pinhole plate, and based on the pinholes on the axially focusing spiral pinhole plate, the optical path of the laser transmitted through different pinholes to the optical axis is different, introducing an angular phase difference to the transmitted Gaussian laser, so as to form a vortex laser in the focusing region.

[0008] According to one aspect of the present invention, in step S1, the step of preparing the axially focusing spiral pinhole plate, the angular and radial positions of each pinhole on the axially focusing spiral pinhole plate are represented as follows:

[0009]

[0010] in, For the first The angular position of each pinhole For the first The radial position of each pinhole For the first The focal length of a pinhole is expressed as: Furthermore, the focal length range of the pinhole is the minimum focal length. to maximum focal length , focus is ; Number of pinholes; It is the distance from the first pinhole in each pinhole group to the center of the axial focusing spiral pinhole plate. Let be the topological charge of the axially focused spiral pinhole plate, and let its value be a positive integer. It is the wavelength of the incident laser.

[0011] According to one aspect of the invention, the minimum focal length of the pinhole on the axial focusing spiral pinhole plate is... Represented as:

[0012] ;

[0013] The maximum focal length of the pinholes on the axial focusing spiral pinhole plate Represented as:

[0014] .

[0015] According to one aspect of the present invention, in the axial focusing spiral pinhole plate, each column of pinholes is arranged in a right-hand spiral configuration;

[0016] The first pinhole in each pinhole group is the pinhole closest to the center of the axial focusing spiral pinhole plate, and the distance from the first pinhole to the center of the axial focusing spiral pinhole plate is in the range of:

[0017] .

[0018] According to an aspect of the present application, the radius of the pinholes on the axial focusing spiral pinhole plate satisfies:

[0019] .

[0020] According to an aspect of the present application, the axial focusing spiral pinhole plate is made of fully ionized carbon ions and hydrogen ions, and the density ratio of carbon ions to hydrogen ions is 1:4.

[0021] According to an aspect of the present application, the thickness of the axial focusing spiral pinhole plate satisfies:

[0022] .

[0023] According to an aspect of the present application, in step S2, a beam of relativistic intensity Gaussian laser with a Gaussian intensity distribution is used, and the peak intensity is located at the optical axis.

[0024] According to an aspect of the present application, in step S2, the intensity of a beam of relativistic intensity Gaussian laser is .

[0025] According to an aspect of the present application, the axial focusing spiral pinhole plate is made by electron beam etching.

[0026] According to a scheme of the present application, the axial focusing spiral pinhole plate can effectively generate vortex laser, and by adjusting the arrangement of pinholes on the axial focusing spiral pinhole plate to adjust the optical path difference of the transmitted laser and generate corresponding vortex laser in the focusing area, the scheme is more flexible and has lower cost.

[0027] According to a scheme of the present application, by adjusting the arrangement of pinholes on the axial focusing spiral pinhole plate, vortex laser with a main mode can be generated, the intensity is greater than and the proportion of the main mode is maintained at more than 60%. In addition, the axial focusing spiral pinhole plate can adjust the topological charge of the vortex laser and amplify the intensity of the output vortex laser by more than four times. This shows that the axial focusing spiral pinhole plate has significant potential in generating high-order mode vortex laser and manipulating the angular momentum of relativistic laser.

[0028] According to one scheme of the present application, the axial focusing spiral pinhole plate is used to generate super-strong high-order mode vortex laser, which can expand the research range of the interaction between the relativistic vortex laser and the plasma, and is of great significance to promote the research in this field. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a schematic block diagram showing the steps of a method for generating high-order mode relativistic vortex laser based on an axial focusing pinhole plate according to one embodiment of the present application;

[0030] Figure 2 is a schematic diagram showing the principle of a method for generating high-order mode relativistic vortex laser based on an axial focusing pinhole plate according to one embodiment of the present application;

[0031] Figure 3 is a structural diagram of an axial focusing spiral pinhole plate according to one embodiment of the present application;

[0032] Figure 4 is a simulation result diagram of a simulation box in Example 1;

[0033] Figure 5 is a simulation result diagram of a simulation box in Example 1; and of the simulation result diagram of the simulation box in Example 1; show the simulation result diagrams of the transverse electric field and the phase thereof, wherein (a) shows the simulation result of the transverse electric field at x=0, (b) shows the simulation result of the transverse electric field at x=0.5, (c) shows the phase simulation result at x=0, and (d) shows the phase simulation result at x=0.5;

[0034] Figure 6 is a simulation result diagram of a simulation box in Example 1; and of the simulation result diagram of the simulation box in Example 1; show the theoretical result diagrams of the transverse electric field and the phase thereof, wherein (a) shows the theoretical result of the transverse electric field at x=0, (b) shows the theoretical result of the transverse electric field at x=0.5, (c) shows the phase theoretical result at x=0, and (d) shows the phase theoretical result at x=0.5;

[0035] Figure 7 ​​​​​​​​This is a schematic diagram showing the intensity, mode spectrum, angular momentum, energy conversion efficiency, and average photon angular momentum of the output vortex laser in Example 1, where (a) represents The intensity of the output vortex laser is at The distribution in the yz plane, (b) represents Output vortex laser at time The mode spectrum distribution diagram in the yz plane, (c) represents the evolution of the angular momentum of the output vortex laser and the energy conversion efficiency from the incident laser to the output vortex laser, and (d) represents the evolution of the average angular momentum of the photons of the output vortex laser.

[0036] Figure 8 This schematically represents the topological load of the axially focused spiral pinhole plate in Embodiment 1. The simulation results in the simulation box when set to 5 are shown in the figure. (a) shows the structure of the axially focused spiral pinhole plate, and (b) shows the electric field of the output vortex laser. exist Place The distribution diagram at time, (c) represents the electric field of the output vortex laser. phase in Place The distribution diagram at time, (d) represents the electric field of the output vortex laser. exist Place The distribution of the mode spectrum at that time;

[0037] Figure 9 This schematically represents the topological load of the axially focused spiral pinhole plate in Embodiment 1. The simulation results in the simulation box when set to 6 are shown in the figure. (a) shows the structure of the axially focused spiral pinhole plate, and (b) shows the electric field of the output vortex laser. exist Place The distribution diagram at time, (c) represents the electric field of the output vortex laser. phase in Place The distribution diagram at time, (d) represents the electric field of the output vortex laser. exist Place The distribution of the mode spectrum at that time;

[0038] Figure 10 This schematically represents the topological load of the axially focused spiral pinhole plate in Embodiment 1. When set to 4, the incident laser mode is The simulation results in the simulation box are shown in the figure. (a) shows the structure of the axially focused spiral pinhole plate, and (b) shows the electric field of the output vortex laser. exist Figure 3 shows the distribution of the phase of the electric field of the output vortex laser at the time t = 0; Figure 4 shows the distribution of the phase of the electric field of the output vortex laser at the time t = T / 4; Figure 5 shows the distribution of the phase of the electric field of the output vortex laser at the time t = T / 2; Figure 6 shows the distribution of the phase of the electric field of the output vortex laser at the time t = 3T / 4; Figure 7 shows the distribution of the phase of the electric field of the output vortex laser at the time t = T; Figure 8 shows the mode spectrum distribution of the output vortex laser at the time t = 0; Figure 9 shows the mode spectrum distribution of the output vortex laser at the time t = T / 4; Figure 10 shows the mode spectrum distribution of the output vortex laser at the time t = T / 2; Figure 11 shows the mode spectrum distribution of the output vortex laser at the time t = 3T / 4;

[0039] Figure 12 shows the mode spectrum distribution of the output vortex laser at the time t = T. Figure 11 Figure 13 shows a three-dimensional isosurface distribution of the electric field of the output vortex laser in the simulation box of the axial focusing spiral pinhole plate in Figure 1. Figure 10 Figure 14 shows a three-dimensional isosurface distribution of the electric field of the output vortex laser in the simulation box of the axial focusing spiral pinhole plate in Figure 2. Figure 15 shows a three-dimensional isosurface distribution of the electric field of the output vortex laser in the simulation box of the axial focusing spiral pinhole plate in Figure 3. DETAILED DESCRIPTION

[0040] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments, and the embodiments cannot be exhaustively described here, but the embodiments of the present application are not limited to the following embodiments.

[0041] According to an embodiment of the present application, as shown in Figures 1 to 15, a method for generating a high-order mode relativistic vortex laser based on an axial focusing pinhole plate according to the present application comprises the following steps: Figure 1 S1. preparing an axial focusing spiral pinhole plate, wherein the axial focusing spiral pinhole plate is provided with a plurality of pinhole groups arranged regularly along the circumferential direction of the plate body, and each pinhole group comprises a plurality of pinholes arranged in a spiral; Figure 2 S2. irradiating a beam of relativistic intensity Gaussian laser onto the axial focusing spiral pinhole plate, and introducing an angular phase difference into the transmitted Gaussian laser based on the pinholes on the axial focusing spiral pinhole plate so as to form a vortex laser in the focusing region. Figure 3 As shown in Figure 1, in step S1 of preparing an axial focusing spiral pinhole plate, in the step of preparing an axial focusing spiral pinhole plate, a plurality of pinhole groups are arranged at equal intervals along the circumferential direction of the plate body on the axial focusing spiral pinhole plate to achieve regular arrangement of the pinhole groups. In this embodiment, each pinhole group comprises a plurality of pinholes arranged in a spiral, and the rotational direction of the pinholes arranged in a spiral in each pinhole group is consistent, so that the pinholes on the axial focusing spiral pinhole plate exhibit a spiral radiation arrangement form from the center to the periphery. In this embodiment, the pinholes penetrate the body of the axial focusing spiral pinhole plate along the axial direction of the axial focusing spiral pinhole plate.

[0042] As shown in Figure 2, in step S1 of preparing an axial focusing spiral pinhole plate, in the step of preparing an axial focusing spiral pinhole plate, a plurality of pinhole groups are arranged at equal intervals along the circumferential direction of the plate body on the axial focusing spiral pinhole plate to achieve regular arrangement of the pinhole groups. In this embodiment, each pinhole group comprises a plurality of pinholes arranged in a spiral, and the rotational direction of the pinholes arranged in a spiral in each pinhole group is consistent, so that the pinholes on the axial focusing spiral pinhole plate exhibit a spiral radiation arrangement form from the center to the periphery. In this embodiment, the pinholes penetrate the body of the axial focusing spiral pinhole plate along the axial direction of the axial focusing spiral pinhole plate.

[0043] As shown in Figure 3, in step S1 of preparing an axial focusing spiral pinhole plate, in the step of preparing an axial focusing spiral pinhole plate, a plurality of pinhole groups are arranged at equal intervals along the circumferential direction of the plate body on the axial focusing spiral pinhole plate to achieve regular arrangement of the pinhole groups. In this embodiment, each pinhole group comprises a plurality of pinholes arranged in a spiral, and the rotational direction of the pinholes arranged in a spiral in each pinhole group is consistent, so that the pinholes on the axial focusing spiral pinhole plate exhibit a spiral radiation arrangement form from the center to the periphery. In this embodiment, the pinholes penetrate the body of the axial focusing spiral pinhole plate along the axial direction of the axial focusing spiral pinhole plate.

[0044] Figure 2 As shown in Figure 4, in step S1 of preparing an axial focusing spiral pinhole plate, in the step of preparing an axial focusing spiral pinhole plate, a plurality of pinhole groups are arranged at equal intervals along the circumferential direction of the plate body on the axial focusing spiral pinhole plate to achieve regular arrangement of the pinhole groups. In this embodiment, each pinhole group comprises a plurality of pinholes arranged in a spiral, and the rotational direction of the pinholes arranged in a spiral in each pinhole group is consistent, so that the pinholes on the axial focusing spiral pinhole plate exhibit a spiral radiation arrangement form from the center to the periphery. In this embodiment, the pinholes penetrate the body of the axial focusing spiral pinhole plate along the axial direction of the axial focusing spiral pinhole plate.

[0045] In this embodiment, the axially focusing spiral pinhole plate can be made of a regular plate, such as a square plate or a circular plate.

[0046] With the above configuration, the present invention sets spirally arranged pinholes on the axial focusing spiral pinhole plate, so that when a Gaussian laser beam of relativistic intensity is irradiated on the axial focusing spiral pinhole plate, the optical path of the laser transmitted through different pinholes to the optical axis is different, thereby introducing an angular phase difference to the transmitted laser, thus forming a vortex laser in the focusing area, that is, realizing the modulation of the seed laser into a vortex laser in the focusing volume.

[0047] like Figure 2 As shown, according to one embodiment of the present invention, in step S1, the angular and radial positions of each pinhole on the axially focusing spiral pinhole plate are represented as follows:

[0048]

[0049] in, For the first The angular position of each pinhole For the first The radial position of each pinhole For the first The focal length of a pinhole is expressed as: Furthermore, the focal length range of the pinhole is the minimum focal length. to maximum focal length , focus is ; Number of pinholes; It is the distance from the first pin in each spiral arrangement of pins to the center of the axially focusing spiral pin plate. Let be the topological charge of the axially focused spiral pinhole plate, and let its value be a positive integer. It is the wavelength of the incident laser.

[0050] According to one embodiment of the present invention, the minimum focal length of the pinhole on the axial focusing spiral pinhole plate Represented as:

[0051] ;

[0052] Furthermore, the maximum focal length of the pinhole on the axially focusing spiral pinhole plate. Represented as:

[0053] .

[0054] The above settings effectively ensure that the vortex laser generated by this invention has a wide focusing range, making it more widely applicable and further guaranteeing its ease of use.

[0055] According to an embodiment of the present application, the axial focusing spiral pinhole plate is arranged in a right-handed spiral manner.

[0056] The first pinhole in each pinhole group is closest to the center of the axial focusing spiral pinhole plate, and the distance between the first pinhole and the center of the axial focusing spiral pinhole plate is .

[0057] .

[0058] Through the above arrangement, the first pinhole in each pinhole group is arranged to have a spacing from the center of the axial focusing spiral pinhole plate, which can more advantageously generate high-order mode vortex laser in the corresponding focusing area, making the generated vortex laser more stable.

[0059] According to an embodiment of the present application, the radius of the pinholes on the axial focusing spiral pinhole plate satisfies:

[0060] .

[0061] Through the above arrangement, the radius of the pinholes is set within the above range, which can make the arranged pinholes more matched with the input Gaussian laser, more advantageously generate high-order mode vortex laser in the corresponding focusing area, and make the generated vortex laser more stable and accurate.

[0062] According to an embodiment of the present application, the axial focusing spiral pinhole plate is made of fully ionized carbon ions and hydrogen ions target material, and the density ratio of carbon ions and hydrogen ions is 1:4.

[0063] Through the above arrangement, the axial focusing spiral pinhole plate made of fully ionized carbon ions and hydrogen ions target material with a density ratio of 1:4 can enhance the interaction between laser and plasma, optimize the laser acceleration process, promote the generation of high-order mode vortex laser, and improve the propagation characteristics of the laser beam. The axial focusing spiral pinhole plate arranged in the above manner can form a more matched Gaussian laser input, which can significantly enhance the nonlinear effect of the laser. Moreover, the density ratio arranged can significantly improve the focusing ability.

[0064] According to an embodiment of the present application, the thickness of the axial focusing spiral pinhole plate satisfies:

[0065] .

[0066] Through the above arrangement, the scheme is more advantageous to generate high-order mode vortex laser in the corresponding focusing area by setting the thickness of the axial focusing spiral pinhole plate in the above range, so that the generated vortex laser is more stable and effective.

[0067] According to an embodiment of the present application, in step S2, the adopted one beam of Gaussian laser with relativistic intensity has a Gaussian type intensity distribution, and the peak intensity is located at the optical axis.

[0068] Through the above arrangement of Gaussian laser, it is more matched with the corresponding pinhole arrangement mode, so that the generation of high-order mode vortex laser is more reliable and beneficial.

[0069] According to an embodiment of the present application, in step S2, the intensity of the adopted one beam of Gaussian laser with relativistic intensity is .

[0070] Through the above arrangement, the present application can more effectively adapt to the input of high intensity laser, and also provides more advantageous conditions for realizing high intensity vortex laser.

[0071] According to an embodiment of the present application, the axial focusing spiral pinhole plate is made by electron beam etching.

[0072] In order to further illustrate the present scheme, the present scheme is further exemplified.

[0073] Embodiment 1

[0074] Specifically, it is proved by 3D-PIC simulation using the relativistic electromagnetic code EPOCH. In the present embodiment, the grid size of the simulation box is , and thus the grid is set to 2000x800x800, and there are 9 macro particles in each grid.

[0075] Further, the dimensionless laser electric field amplitude of the linearly polarized Gaussian laser pulse is , which is incident from the left side of the simulation box; wherein, and are the peak amplitude of the laser electric field and the laser focusing spot size, respectively; is the laser wavelength, wherein is the laser period, is the laser frequency; , and are the unit charge, electron mass and light speed in vacuum, respectively, is the y-direction basis vector of the electric field of the electromagnetic field, is the radial coordinate of the cylindrical coordinate system.

[0076] Further, the initial position of the axial focusing spiral pinhole plate is in the position of the simulation box , and the thickness of the axial focusing spiral pinhole plate is ; wherein the focal length range of the pinholes on the axial focusing spiral pinhole plate can be set between and , and further, the initial position of the pinholes in the simulation box based on the initial position set by the axial focusing spiral pinhole plate makes the focal length range start from to end at .

[0077] In the embodiment, the distance from the first pinhole in each pinhole group on the axial focusing spiral pinhole plate to the center of the axial focusing spiral pinhole plate is , the radius of each pinhole is , the number of pinholes is , and the topological charge of the axial focusing spiral pinhole plate is .

[0078] Further, the pinholes in each pinhole group on the axial focusing spiral pinhole plate are arranged in a right-handed spiral manner.

[0079] Further, the axial focusing spiral pinhole plate is made of fully ionized carbon ions and hydrogen ions, and its composition is composed of fully ionized carbon ions and hydrogen ions at a density ratio of 1:4; wherein the corresponding densities of electrons, protons and carbon ions are , and .

[0080] Further, the axial focusing spiral pinhole plate is made by electron beam etching.

[0081] With the axial focusing spiral pinhole plate set as above, when the incident seed laser (i.e. a beam of relativistic intensity Gaussian laser) irradiates the axial focusing spiral pinhole plate, only a part of the laser can pass through the pinhole area. Because the optical path difference of the laser passing through different position pinholes is different when it reaches the focusing volume, the axial focusing spiral pinhole plate can modulate the seed laser into vortex laser in the focusing volume.

[0082] As shown in Figure 4 , Figure 5 and Figure 6 , it shows the three-dimensional isosurface of the transverse electric field of the output laser at , showing a significant spiral spatial distribution. To further understand the characteristics of the transverse electric field of the output laser, the and of the simulation box are The transverse electric field is shown on the plane and its phase distribution. It is noted that, similar to most particle codes, the EPOCH code adopts real number representation for the electromagnetic field data in order to improve the performance and reduce the memory footprint of the simulation process. However, the electromagnetic field information from the numerical simulation output can be reconstructed through the complex spectral coefficient form. To this end, the phase of the laser electromagnetic field can be expressed as:

[0083]

[0084] where, and denote the Fourier transform and inverse Fourier transform, respectively, denotes taking the imaginary part, denotes taking the real part, denotes the frequency of the laser, denotes the wave vector component of the laser, denotes the modulus of the wave vector of the laser, denotes the component of the wave vector of the laser, denotes the component of the wave vector of the laser, denotes the component of the magnetic field of the laser, denotes the component of the magnetic field of the laser.

[0085] As shown in Figure 5 (a) and Figure 5 (b), the emitted laser electric field exhibits a petal-like periodic distribution around the optical axis. The phase distribution shows that the transverse electric field of the laser undergoes four periods around the optical axis ( ). This indicates that the dominant mode of the output laser has a topological charge of , which is consistent with the topological charge setting of the axially focusing spiral pinhole plate.

[0086] Further, to evaluate the performance of the axially focusing spiral pinhole plate, we use the Fresnel-Kirchhoff diffraction formula to calculate the electric field and phase distribution of the output laser, which is expressed as follows:

[0087]

[0088] where, denotes the imaginary number; denotes the electric field of the incident Gaussian laser; denotes the transmittance of the axially focusing spiral pinhole plate; denotes the tilt factor, and is expressed as: ; denotes the representative point to point The radius and Point normal The included angle; Point Time Spatial distance.

[0089] Based on this, the theoretical calculations and simulations show excellent consistency in the electric field and phase distribution of the output laser. Furthermore, the focal spot size of the output vortex laser is significantly larger than that of the incident laser. Reduced to approximately This is due to the focusing capability of the axially focused spiral pinhole plate. However, because the radial intensity of the Gaussian laser decreases along the optical axis, the enhancement of the focused intensity of the output laser is not significant, remaining almost identical to the incident laser. In the region corresponding to the pinhole area of ​​the axially focused spiral pinhole plate target, the intensity has already dropped below its maximum value.

[0090] Based on the above simulation process, output is selected from the simulation box. Place Transverse electric field The slices are plotted, and their mode spectra are calculated. It is well known that any laser field can be decomposed into a weighted superposition of Laguerre-Gaussian (LG) modes, the weights of which are defined as:

[0091]

[0092] in, A slice of the electric field representing the output laser; yes Electric field slicing of patterned lasers; These represent the three coordinates in the cylindrical coordinate system.

[0093] Pattern in cylindrical coordinate system The definition in Chinese is:

[0094] ,

[0095] in, Represents a constant. Indicates having a radial index and azimuth index The generalized Laguerre polynomial, in computation, Set to 0, Considered a variable, Represents the wave vector of a laser beam.

[0096] Figure 7 (b) shows that the dominant mode of the output vortex laser is With a weight of 64.54%, and Figure 4 ,Figure 5 and Figure 6 The simulation results in FIGS. 13(a) and 13(b) are consistent with the results in FIGS. 12(a) and 12(b). In addition, the total angular momentum of the output vortex laser, the energy conversion efficiency from the incident laser to the output laser, and the average angular momentum of the output laser photons in the focusing volume (Vf) are further calculated. The angular momentum and energy of the laser pulse (i.e., the Gaussian laser output by the light source) can be represented as and and wherein represents the vacuum permeability, represents the vacuum permittivity, represents the radial distance of the space, represents the electric field of the laser, represents the magnetic field of the laser, represents the volume element in the integral, represent the component, component, component of the angular momentum of the laser pulse, respectively. The average angular momentum of the laser photons can be written as wherein and represent the spin and orbital angular momentum of the photon, represents the reduced Planck constant. Given that the direction of the angular momentum carried by the laser is mainly along its propagation axis, the angular momentum mainly corresponds to . As shown in FIG. 13(c), as the laser gradually enters the focusing volume, it is converted into a vortex laser, and the angular momentum increases to a maximum value Figure 7 in . As the laser gradually leaves the focusing volume, its vortex phase gradually loses, and the angular momentum begins to decrease. The evolution of the energy conversion efficiency of the output vortex laser is consistent with the angular momentum, reaching a maximum value of 5.4%. (d) shows the evolution of the average angular momentum of the output laser photons. As the laser enters the focusing region, the average angular momentum carried by the photons rapidly increases, reaching a maximum value Figure 7 at . While the output laser is still in the focusing region, its average angular momentum of the photons can be maintained for more than . This indicates that the vortex phase of the output laser in the focusing region can be well maintained. Further, when the topological charge of the axially focusing spiral pinhole plate or the incident laser is changed, the scheme can also adjust the dominant mode of the output laser. First, the topological charge of the axially focusing spiral pinhole plate is changed to 5 and 6, respectively. Combined with FIGS. 14(a) and 14(b), FIGS. 15(a) and 15(b) show the cross-sectional structure of the axially focusing spiral pinhole plate, the transverse distribution of the electric field, the phase distribution, and the

[0097] Figure 8 Figure 9 ​​​​Mode spectrum. As shown in FIG. 4, when the topological charge Figure 8 changes, the number of the spiral arms (i.e., pinhole groups) formed by the pinhole arrangement also changes accordingly. Correspondingly, the electric field phase of the output laser also changes, experiencing 5 and 6 periods around the optical axis. The dominant mode of the output laser changes to Figure 9 and , with the mode weight being 61.03% and 62.45%, respectively. In addition, besides the topological charge of the pinholes, the topological charge of the incident laser can also change the dominant mode of the output laser. In the simulation, the case where the incident laser is

[0098] is considered, while keeping other parameters unchanged. Although , the dominant mode of the output laser changes to , with the weight being 72.52%. This shows that the topological charge of the dominant mode of the output laser is determined by the axial focusing spiral pinhole plate and the incident laser together, which can be expressed as In addition, the annular intensity distribution of the input laser leads to its peak intensity being located in the pinhole region of the axial focusing spiral pinhole plate. This makes the focusing effect of the output laser better, with the maximum intensity reaching Although the existing scheme has been able to generate a relativistic vortex laser with the dominant mode being and the intensity being as high as in the laboratory by using an off-axis spiral phase mirror. However, based on the current theoretical calculation, it shows that the use of an off-axis spiral phase mirror faces challenges in generating high-order mode vortex lasers due to the relatively low weight of the dominant mode. This shows that the present scheme can generate high-order vortex lasers with higher intensity and high mode purity, which may expand the scope of the research on the interaction between relativistic vortex lasers and plasmas. The above merely illustrates the specific scheme of the present application, and for the devices and structures not described in detail, it should be understood that the general devices and methods in the art are adopted to implement them.

[0099] The above merely illustrates the specific scheme of the present application, and for the devices and structures not described in detail, it should be understood that the general devices and methods in the art are adopted to implement them.

[0100] The above merely illustrates the specific scheme of the present application, and for the devices and structures not described in detail, it should be understood that the general devices and methods in the art are adopted to implement them.​

Claims

1. A method for generating high-order mode relativistic vortex laser based on an axially focused pinhole plate, characterized in that, The method comprises the following steps: S1. Preparing an axial focusing spiral pinhole plate, wherein the axial focusing spiral pinhole plate is provided with a plurality of pinhole groups arranged regularly along the circumferential direction of the plate body, and each pinhole group comprises a plurality of pinholes arranged in a spiral manner, so that the pinholes present a spiral radiation arrangement form from the center to the periphery; wherein the angular position and the radial position of each pinhole on the axial focusing spiral pinhole plate are represented as: wherein α n is the angular position of the nth pinhole, r n is the radial position of the nth pinhole, f n is the focal length of the nth pinhole, and is expressed as: f n = f min + nδf / N, and the focal length range of the pinhole is from the minimum focal length f min to the maximum focal length f max , the depth of focus is δf = f max - f min ; N is the number of pinholes; r0 is the distance from the first pinhole in each column of pinhole groups to the center of the axial focusing spiral pinhole plate, l ALPP is the topological charge of the axial focusing spiral pinhole plate, and its value is a positive integer, and λ0 is the wavelength of the incident laser. S2. A beam of relativistic intensity Gaussian laser is irradiated onto the axial focusing spiral pinhole plate, and based on the pinholes on the axial focusing spiral pinhole plate, the optical path of the laser transmitted by different pinholes to the optical axis is different, an angular phase difference is introduced for the transmitted Gaussian laser, so as to form vortex laser in the focusing area.

2. The method of claim 1, wherein, The minimum focal length f of the axial focusing helical pinhole plate pinhole min is represented as: f min >10λ0; The axial focusing spiral pinhole plate has a maximum focal length f of the pinhole max is represented as: f max >f min .

3. The method of claim 2, wherein, On the axial focusing spiral pinhole plate, each column of pinhole groups is arranged in a right-handed spiral manner; The pinhole closest to the center of the axial focusing spiral pinhole plate in each column of pinhole groups is a first pinhole, and the distance r0 of the first pinhole to the center of the axial focusing spiral pinhole plate is in the range of: 0<r0。 4. The method of claim 3, wherein, The radius r of the pinholes on the axially focusing pinhole plate pinhole satisfies: 0 < r pinhole <λ0。 5. The method of claim 4, wherein, The axial focusing spiral pinhole plate is made of fully ionized carbon ions and hydrogen ions, and the density ratio of carbon ions to hydrogen ions is 1:

4.

6. The method of claim 5, wherein, The thickness d0 of the axial focusing spiral pinhole plate satisfies: d0=0.3λ0.

7. The method of claim 6, wherein, In step S2, the beam of relativistic intensity Gaussian laser has a Gaussian intensity distribution, and the peak intensity is located at the optical axis.

8. The method of claim 7, wherein, In step S2, the intensity of the one beam of a relativistic intensity Gaussian laser used is 10 18 W / cm 2 ~ 10 22 W / cm 2 .

9. The method of claim 8, wherein, The axial focusing spiral pinhole plate is made by electron beam etching.

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