阅读说明：本技术 基于无阈值切伦科夫辐射的自由电子源设计方法 (Free electron source design method based on non-threshold Cerenkov radiation ) 是由 肖龙 郭龙颖 陈俊峰 陈亮 张崎 谭辉 刘其凤 于 2019-11-12 设计创作，主要内容包括：本发明公开了一种基于无阈值切伦科夫辐射的自由电子源设计方法,双曲超材料由于其双曲线型色散曲线可以将电子周围消逝场转化为传播场,借助双曲超材料来突破产生CR电子速度限制,为实现太赫兹自由电子源提供了可能。本发明针对低能电子束在双曲超材料中CR的产生、传输和耦合的特性,探明CR在双曲超材料中波矢压缩、能流密度的规律,本发明实现太赫兹自由电子光源设计,能够在生物医学、成像和通讯领域产生广泛的应用。(The invention discloses a free electron source design method based on non-threshold Cerenkov radiation.A hyperbolic metamaterial can convert an evanescent field around electrons into a propagation field due to a hyperbolic dispersion curve, and breaks through the speed limit of CR electrons by means of the hyperbolic metamaterial, so that the possibility is provided for realizing a terahertz free electron source. Aiming at the characteristics of generation, transmission and coupling of CR of low-energy electron beams in the hyperbolic metamaterial, the rule of wave vector compression and energy flux density of CR in the hyperbolic metamaterial is proved, the terahertz free electron source design is realized, and the terahertz free electron source can be widely applied to the fields of biomedicine, imaging and communication.)

1. A free electron source design method based on non-threshold Cerenkov radiation is characterized in that a constant speed u is positioned above a hyperbolic metamaterial at a position d between 100nm and 500nm ₀Moving at least one electron beam, the hyperbolic metamaterial being composed of alternating layers of silicon and graphene.

2. The method for designing a free electron source based on non-threshold cerenkov radiation as claimed in claim 1, wherein the dispersion relation of the hyperbolic metamaterial is as follows:

k _z ²/ε _x+k _x ²/ε _z＝k ₀ ²， (1)

wherein k is _x,k _zIs wave vector, ε _x,ε _zIs the effective dielectric constant in the x, z directions.

3. Method for designing a free electron source based on non-threshold cerenkov radiation according to claim 1 or 2, characterized in that the thickness h of the silicon _mIs 50-200nm, and the thickness h of graphene _dIs 1 nm.

4. The method for designing the free electron source based on the non-threshold Cerenkov radiation as claimed in claim 3, wherein the method comprises 20-60 pairs of alternating layers of silicon and graphene.

5. The method of designing a free electron source based on non-threshold cerenkov radiation of claim 4, wherein the radiation spectrum is between 2THz and 20 THz.

6. The method for designing a free electron source based on Cerenkov radiation as claimed in claim 1 or 2, wherein the velocity of the electron beam can be smaller than the phase velocity of the electromagnetic wave in the hyperbolic metamaterial.

Technical Field

The invention belongs to the technical field of high-power microwave device design, and particularly relates to a free electron source design method based on non-threshold Cerenkov radiation.

Background

When charged particles pass through a dielectric medium at a certain threshold of speed, the electromagnetic radiation emitted by the driving medium is called cerenkov radiation, which was first observed in the early twentieth century. The cerenkov radiation is characterized in that the velocity of charged particles exceeds the phase velocity of a medium, in a common medium material, the phase velocity of light is usually in the order of C × 10^ -1, for example, the refractive index of quartz is 2, if the cerenkov radiation is generated by electrons flying on the surface of the quartz, the velocity of the electrons is accelerated to 0.5C, and at the moment, the energy of the electrons is 100KeV, so that the voltage of 100KeV is required for acceleration, and the radiation source in the case of the cerenkov radiation cannot meet the practical application condition from the aspects of safety, cost and stability. The discovery of Cerenkov radiation greatly promotes scientific development, is widely applied to particle detectors and counters, and particularly can be taken as an important path for miniaturization of free electron laser because a periodic magnetic field is not needed as a wobbler in realizing the free electron laser, and the volume of the free electron laser can be reduced to a certain extent.

The terahertz radiation has a very wide frequency range, covers the rotation and oscillation frequencies of macromolecules including proteins, and many macromolecules show strong absorption and resonance characteristics in a terahertz wave band, so that a corresponding terahertz characteristic frequency spectrum is formed, and substances and biological information can be obtained by measuring and analyzing terahertz signals in the macromolecules, wherein the information is significant for researching the structure of the substances.

Disclosure of Invention

The invention aims to solve the technical problem of providing a free electron source design method based on non-threshold Cerenkov radiation, which can realize Cerenkov radiation of a terahertz wave band by the design of a hyperbolic metamaterial structure process and the selection of material components and the selection of a radiation source for extracting low-energy electron Cerenkov radiation on a chip.

The technical scheme adopted by the invention for solving the technical problems is as follows: providing a free electron source design method based on non-threshold Cerenkov radiation, and using d-100 nm-500 nm above the hyperbolic metamaterial to obtain a constant speed u ₀Moving at least one electron beam, the hyperbolic metamaterial being composed of alternating layers of silicon and graphene.

According to the technical scheme, the dispersion relation of the hyperbolic metamaterial is as follows:

k _z ²/ε _x+k _x ²/ε _z＝k ₀ ²， (1)

wherein k is _x,k _zIs wave vector, ε _x,ε _zIs the effective dielectric constant in the x, z directions.

According to the above technical scheme, the thickness h of the silicon _mIs 50-200nm, and the thickness h of graphene _dIs 1 nm.

According to the technical scheme, the silicon/graphene composite material is composed of 20-60 pairs of alternating layers of silicon and graphene.

According to the technical scheme, the radiation spectrum is between 2THz and 20 THz.

According to the technical scheme, the speed of the electron beam can be smaller than the phase speed of the electromagnetic wave in the hyperbolic metamaterial.

The invention has the following beneficial effects: firstly, the coupling and the propagation of evanescent fields around free electrons in a terahertz frequency band can be realized, and the output energy is higher by one order of magnitude than that of the existing report.

Secondly, the electromagnetic wave has a large wave vector along the material transmission direction through a special structural design, namely the speed of free electrons is reduced by several orders of magnitude in the formation of Cerenkov radiation.

Thirdly, a micro-processing technology is used, the scatterer is processed on the chip, and the method can be applied to the fields of biomedicine, imaging, communication and the like.

Drawings

The invention will be further described with reference to the accompanying drawings and examples, in which:

FIG. 1 is a schematic view of a multilayer structure in an embodiment of the present invention;

FIG. 2 is a schematic dispersion relation of an HMM and an electromagnetic wave in a surrounding electron beam in an embodiment of the present invention;

FIG. 3 is a graph showing the relationship between the frequencies of Cerenkov radiation at different electron velocities according to an embodiment of the present invention;

FIG. 4 is a theoretical result of the variation of the wave vector direction and the poynting vector with frequency in the embodiment of the present invention, the frequency dotted lines are 5THz,10THz and 20 THz;

fig. 5 shows an electric field Ez when the electron beam moves over a HMM distance d of 100nm in the embodiment of the present invention, and the simulation result is 5 THz;

fig. 6 shows an electric field Ez when the electron beam moves over a distance d of 100nm from the HMM in the embodiment of the present invention, and the simulation result is 10 THz;

fig. 7 shows an electric field Ez when the electron beam moves over a HMM distance d of 100nm in the embodiment of the present invention, and the simulation result is 20 THz;

fig. 8 is an electric field Ez when the electron beam moves over a HMM distance d of 100nm in the embodiment of the present invention, and the simulation result is 27 THz;

FIG. 9 is an integral of upper surface power flow density at different frequencies in an embodiment of the present invention;

FIG. 10 is a Fourier transform of an Ez field in an embodiment of the present invention;

FIG. 11 is a graph illustrating the calculation of local density of states for different frequencies according to an efficient model in an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

As shown in fig. 1, in the method of the present embodiment, a constant speed is applied along the z-direction at a position d of 100nm at the top of a hyperbolical Meta-material (HMM)u ₀(constant energy) moves an electron beam. In the embodiment of the present invention, the thickness h is selected _mIs 69nm of silicon and a thickness h _dIs composed of 1nm graphene alternating layers. Unlike natural materials, the wave vector of the electromagnetic wave in the HMM may be selected to be larger than the vacuum wave vector, and may convert the evanescent field of the surrounding electron beam into a propagating electromagnetic field and generate cerenkov radiation in the HMM. And qualitatively analyzing the Cerenkov radiation in the hyperbolic metamaterial and the characteristics of the frequency range, wave vector and hill-print pavilion vector thereof by using an effective medium method. Meanwhile, a time domain finite difference method (PIC-FDTD) is adopted to obtain a quantitative result, and the quantitative result is compared with a qualitative result. The power of cerenkov radiation in HMM was simulated using PIC-FDTD method. According to the effective medium theory, the multilayer structure shown in fig. 1 can be regarded as an effective HMM, and its dispersion relation is:

k _z ²/ε _x+k _x ²/ε _z＝k ₀ ²， (1)

wherein k is _x,k _zIs wave vector, ε _x,ε _zIs the effective dielectric constant in the x, z directions. Formula (1) describes ε _x·ε _zTo study cerenkov radiation in HMM, the evanescent field around the electron beam is considered as the incident wave on the HMM plate, while the effective refractive index of the electromagnetic wave in HMM is n or β.

Where n is the effective refractive index of the HMM, c is the velocity of the light in vacuum and ρ is the ratio of the electron beam velocity to c. For type II HMM (. epsilon.) _z＜0,ε _x> 0), the imaginary part of n is smaller than the real part due to the frequency of the electromagnetic wave away from the intrinsic resonance of the metal. The imaginary part of the equation is ignored. Equation (2) can be simplified to (c/u) ₀) ²＞ε _x. The second class of HMM generates Cerenkov radiation with the condition that

Indicating that cerenkov radiation can be obtained even with very low electron beam velocities.

Fig. 2 depicts a schematic dispersion relationship of an HMM and an electromagnetic wave in a surrounding electron beam. Here, let ε be _x,ε _zThe hyperbola described by equation (1) is an open hyperboloid, which is not varied with frequency, and is represented by plane β ═ ω/u ₀An evanescent electromagnetic field of the electron beam is described. Under the condition of inequality (3), the intersection between two curved surfaces in fig. 2 represents the dispersion relation of cerenkov radiation in the HMM. In the diagram it is shown that the frequencies of cerenkov radiations in the HMM cover the whole spectrum. However, the requirement ε can only be satisfied in view of the frequency-dependent change in the dielectric constants of metals and media _z< 0, i.e., the multilayer structure is a type II HMM, the frequency range of which is limited. The width of the radiation spectrum is limited by the dispersion of the material. Nevertheless, the frequency range of cerenkov radiation in HMMs may be much larger than the grating.

Wherein k is _z＝ω′/u ₀，

Is that At an angle of the HMM in the z-direction, and

is that

The angle in the z direction at the HMM.

In the invention, a Cerenkov radiation-based method is realized by selecting proper materials and designing a structureThe broadband high-strength terahertz source is shown in fig. 1, a multilayer structure provided by the embodiment of the invention is shown, and an HMM is composed of 60 pairs of alternating layers and is used for rapidly growing single-layer graphene (h) through processes of sputtering, evaporation, electron beam evaporation and the like _m1nm) and a silicon layer (h) _d69 nm). FIG. 3 is a theoretical calculation based on equation (2) with a radiation spectrum of between about 2THz and 20THz, followed by analysis of wave vector and hill-print vector features.

According to the equations (4) and (5), as shown in fig. 4, the results indicate that, when the frequency is changed from 2THz to 20THz, continuously varying from-90 deg. to 0 deg. Continuously varying from 0 deg. to 90 deg.. When ε is measured as shown in FIG. 4 _z< 0 a And

the direction is almost always vertical. Fig. 4 shows the corresponding relationship of the resonant frequencies when the emitted electron beam velocities are 0.0373C, 0.2C and 0.4C, respectively. The electromagnetic field distributions of 5THz,10THz and 20THz are shown in fig. 5-8. Quantitative results were obtained by the finite difference time domain method (PIC-FDTD), and we obtained 5THz,10THz, 20THz and 27THz based on the FDTD method

At an intersection with a broken line

The theoretical results are consistent, as shown in fig. 4. Because of e _z＜0，

Compared with the traditional ChelunkThe Fourier radiation contrast is inversely related. In addition, HMM at 27THz becomes a general anisotropic material. Beyond the calculation range of the mode (2), Cerenkov radiation cannot be generated. The arrows in fig. 5 indicate the electron beam position.

To quantitatively describe the radiation caused by the mobile electrons, we calculate the spectral density of the radiation energy. By integrating the power flow density over a certain time, the spectral density of the radiation as shown in fig. 9 can be obtained. This indicates that cerenkov radiation is from 2THz to 25THz and there is a peak at 23.5 THz. Surface radiation field E _zAnd its fourier spectrum is shown in figure 10 for validation. To quantitatively evaluate the radiant energy, we considered an electron beam with p 100pC/cm, and predicted a total radiant energy density of 14.4kW/cm ²(u ₀0.0373c), one order of magnitude greater than the most recently reported. Furthermore, in response to the bandwidth from 2THz to 25THz, we analyze a model in which the dipole is located above the HMM by a distance d of 100nm, such as the local density of states of the HMM shown in fig. 11, which indicates that high intensity broadband output power may be caused by high LDOS, and that external voltage on the graphene can adjust the fermi level, further affecting the bandwidth and output power, so we can adjust the characteristics of the terahertz source accordingly.

It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.