Method for realizing Smith-Purse radiation focusing based on phase gradient metasurface

Abstract

The invention discloses a method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface. The method comprises the following steps: S1, generating Smith-Purcell radiation in a preset polarization state by adjusting an azimuth angle of a periodic dielectric grating; s2, enabling the Smith-Purcell radiation to pass through a phase gradient metasurface, generating phase gradient distribution covering 0-2pi by regulating and controlling geometric parameters and rotation angles of metasurface units, and focusing radiation energy on a preset focus; and S3, coding multi-focus phase distribution by multiplexing the metasurface structure or adjusting the spatial arrangement of the units, and realizing dynamic adjustment of the number, the position and the focal length of the focuses. Traditional line focusing is improved into point focusing, the energy density is improved, polarization and wavefront of Smith-Purs radiation are shaped by rotating the periodic grating and the phase gradient metasurface, energy focusing of Smith-Purs radiation is achieved, and polarization of a focusing field can be flexibly controlled.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic technology, and particularly relates to a method for realizing the focusing of Smith-Purcell radiation based on a phase gradient metasurface. Background Art

[0002] Smith-Purcell radiation is a phenomenon in which electromagnetic waves are radiated when a free electron beam skims over the surface of a grating. Recently, the wavefront control of Smith-Purcell radiation has been widely studied, and it provides broad prospects for realizing broadband electron radiation sources and nanoscale light sources. However, most of the focusing of Smith-Purcell radiation focuses the energy on a line, and the light field does not carry any polarization information or only mentions simple linear polarization.

[0003] Metamaterials are composed of sub-wavelength structures, can exhibit characteristics that natural materials do not have, and have achieved many breakthrough technologies. As a two-dimensional metamaterial, a metasurface is easier to integrate than a three-dimensional structure and has lower transmission losses, and can manipulate the phase, amplitude, and polarization of incident light at the sub-wavelength scale. In the past decade, metasurfaces have been widely applied to the design and manufacture of systems such as planar optics, broadband absorption, and holography.

[0004] Metasurfaces have demonstrated extraordinary light manipulation capabilities in micro-nano scale structures, which provides unprecedented potential for the development of planar radiation sources and high-density radiation sources. The unit structures of this two-dimensional surface are carefully arranged and designed to achieve many functions that traditional optical materials do not have. For example, beam deflection, polarization control, hologram, focusing.

[0005] Smith-Purcell radiation describes the process of radiating electromagnetic waves when an electron beam skims over the surface of a grating. This radiation can occur in a wide spectral range and provides a promising platform for creating nanoscale radiation sources. In recent years, people have been committed to studying the wavefront shaping of Smith-Purcell radiation, which can meet the needs of realizing superlenses and optical devices. The general method is to expand simple periodic structures to aperiodic structures, such as using a chirped grating to achieve the focusing of Smith-Purcell radiation. However, the focusing of Smith-Purcell radiation carrying specific polarization information has not been revealed, and there is not enough electric field information to analyze the characteristics of the focused spot. Summary of the Invention

[0006] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide a method for realizing the focusing of Smith-Purcell radiation based on a phase gradient metasurface, which can achieve the focusing of the energy of Smith-Purcell radiation, and use the phase gradient metasurface to focus the energy of Smith-Purcell radiation with different polarization states. In addition, the focal length, the number of focal points, and the focal point position can be controlled by precisely adjusting the spatial positions of the unit structures.

[0007] To solve the above technical problems, the specific technical solution of the present invention is as follows:

[0008] In some embodiments of the present application, a method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface is provided.

[0009] In some embodiments of the present application, the method includes the following steps:

[0010] Step S1: Polarization state regulation. By adjusting the azimuth angle of the periodic dielectric grating, Smith-Purcell radiation with a preset polarization state is generated.

[0011] Step S2: Wavefront regulation and point focusing. The Smith-Purcell radiation is made to pass through the phase gradient metasurface. By regulating the geometric parameters and rotation angle of the metasurface unit, a phase gradient distribution covering 0-2π is generated, and the radiation energy is focused on a preset focus.

[0012] Step S3: Multi-focus control. By multiplexing the metasurface structure or adjusting the spatial arrangement of the units, a multi-focus phase distribution is encoded to achieve dynamic regulation of the number, position, and focal length of the foci.

[0013] In some embodiments of the present application, in step S1:

[0014] When the grating azimuth angle is 0°, linearly polarized Smith-Purcell radiation is generated.

[0015] When the grating azimuth angle is 45°, right-handed circularly polarized Smith-Purcell radiation is generated.

[0016] When the grating azimuth angle is -45°, left-handed circularly polarized Smith-Purcell radiation is generated.

[0017] In some embodiments of the present application, the phase regulation of the phase gradient metasurface in step S2 includes:

[0018] The propagation phase is controlled by changing the lengths of l1 and l2 of the silicon nanorod cross structure.

[0019] The Pancharatnam-Berry geometric phase is introduced by rotating the nanorod angle θ.

[0020] Combining the propagation phase and the PB phase, spin-independent 0-2π phase coverage is achieved.

[0021] In some embodiments of the present application, the values of l1 and l2 of the silicon nanorods range from 0.218 to 0.354 μm, the values of l1 and l2 range from 0.364 to 0.524 μm, and the rotation angle θ is 0-180°.

[0022] In some embodiments of the present application, the formula for the focusing phase distribution in step S2 is:

[0023]

[0024] Among them, (x L , y L ) and (x R , y R ) are the focal positions of left-handed circularly polarized and right-handed circularly polarized radiation respectively, and f L and f R are the corresponding focal lengths.

[0025] In some embodiments of the present application, the multi-focus control in step S3 includes: for linearly polarized radiation, encoding a four-focus phase distribution so that the foci are distributed in four quadrants, and the first and third quadrants are LCP, and the second and fourth quadrants are RCP;

[0026] For circularly polarized radiation, encoding a two-focus phase distribution so that the foci are symmetrically distributed at preset diagonal positions.

[0027] In some embodiments of the present application, the adjustment range of the focal length is 28 - 42 μm, and the positioning accuracy of the focal position is ±1 μm.

[0028] In some embodiments of the present application, the working wavelength is 1550 nm, the period of the silicon nanocolumns of the phase gradient metasurface is 800 nm, the height is 800 nm, and the refractive index is 3.46.

[0029] In some embodiments of the present application, the transmittance of the unit structure of the phase gradient metasurface is greater than 80%, and wavefront control at the sub-wavelength scale is achieved at a wavelength of 1550 nm.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows. The present invention upgrades the traditional line focus to a point focus, improves the energy density, and shapes the polarization and wavefront of Smith-Purcell radiation by virtue of a rotating periodic grating and a phase gradient metasurface, realizing the focusing of Smith-Purcell radiation with opposite chiral circular polarizations; in addition, the focal length and the number of foci of the entire focusing system are controlled by precisely adjusting the spatial positions of the unit structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Moreover, throughout the drawings, the same reference numerals are used to represent the same components. In the drawings:

[0032] Figure 1 is a schematic diagram of the focusing of Smith-Purcell radiation provided by an embodiment of the present invention;

[0033] Figure 2Schematic diagram of the working process of Smith-Purcell radiation focusing provided by an embodiment of the present invention;

[0034] Figure 3 Schematic diagram of the silicon nanocolumn structure of the cross structure of the metasurface provided by an embodiment of the present invention;

[0035] Figure 4 Schematic diagram of 8 units with different geometric parameters under x-polarized incidence provided by an embodiment of the present invention;

[0036] Figure 5 Schematic diagram of the phase response spectrum of the unit structure provided by an embodiment of the present invention;

[0037] Figure 6 Schematic diagram of the transmittance spectrum of the unit structure provided by an embodiment of the present invention;

[0038] Figure 7 Schematic diagram of the structure of right-handed circularly polarized Smith-Purcell radiation focusing provided by an embodiment of the present invention;

[0039] Figure 8 Schematic diagram of the distribution of Stokes parameter S3 without adding a metasurface provided by an embodiment of the present invention.

[0040] Figure 9 Schematic diagram of the electric field intensity distribution in the corresponding x-y plane 28 μm below the metasurface provided by an embodiment of the invention;

[0041] Figure 10 Schematic diagram of the normalized electric field intensity curve at the focal point provided by an embodiment of the invention;

[0042] Figure 11 Schematic diagram of the structure of left-handed circularly polarized Smith-Purcell radiation focusing provided by an embodiment of the present invention;

[0043] Figure 12 Schematic diagram of the distribution of Stokes parameter S3 without adding a metasurface provided by an embodiment of the present invention;

[0044] Figure 13 Schematic diagram of the electric field distribution 30 μm below the structure under the incidence of left-handed circularly polarized Smith-Purcell radiation provided by an embodiment of the invention;

[0045] Figure 14 Provided by an embodiment of the invention Figure 13 Schematic diagram of the normalized electric field intensity curves at two focal points in;

[0046] Figure 15 Schematic diagram of the electric field distribution 30 μm below the structure under the incidence of right-handed circularly polarized Smith-Purcell radiation provided by an embodiment of the invention;

[0047] Figure 16 Provided for the invention embodiment Figure 15 Schematic diagram of the normalized electric field intensity curve at two focal points;

[0048] Figure 17 Schematic diagram of the structure of Smith-Purcell radiation focusing with linear polarization in the x direction provided for the invention embodiment;

[0049] Figure 18 Schematic diagram of the distribution of Stokes parameter S1 without adding a metasurface provided for the invention embodiment;

[0050] Figure 19 Schematic diagram of the electric field distribution of Smith-Purcell radiation focused by a metasurface with linear polarization in the x direction provided for the invention embodiment;

[0051] Figure 20 Provided for the invention embodiment Figure 19 Schematic diagram of the normalized electric field intensity curve at four focal points. Specific implementation manners

[0052] The following combines the accompanying drawings and embodiments to further describe in detail the specific implementation manners of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0053] In order to better understand the purpose, structure and function of the present invention, the following combines the accompanying drawings to further describe the present invention in detail.

[0054] Embodiment 1:

[0055] Please refer to Figures 1 - 20 , A method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface, the method comprising the following steps:

[0056] S1: Set the vector vortex Smith-Purcell radiation into a structure of a dielectric grating, a silica dielectric plate 1, a phase gradient metasurface and a silica dielectric plate 2, and use the periodic dielectric grating to regulate the polarization state of free electron radiation;

[0057] Wherein: when the grating azimuth angle is 0°, linearly polarized Smith-Purcell radiation is obtained; when the grating azimuth angle is 45°, circularly polarized Smith-Purcell radiation is obtained; when the grating azimuth angle is -45°, left-handed circularly polarized Smith-Purcell radiation is obtained;

[0058] S2: Use the phase gradient metasurface to regulate the wavefront of the radiation light and focus the energy of the Smith-Purcell radiation on a point;

[0059] S3: When the radiation light passes through the metasurface with phase gradient, by adjusting the geometric shape and rotation angle of the cross structure of the metasurface with phase gradient, geometric phase and transmission phase control within the range of 0 - 2π can be achieved near the resonant frequency.

[0060] For the metasurface with phase gradient in step S1 under the incidence of circularly polarized light, the phase modulation of the metasurface on light can be written as:

[0061]

[0062] where the propagation phase and the PB rotation angle θ can be written as:

[0063]

[0064] By changing the height of the metasurface nanocolumns, the transmission amplitude and phase shift of x - polarization and y - polarization can be controlled. Through the Jones matrix, and can be represented by and as:

[0065]

[0066] The phase distribution during metasurface focusing can be expressed as:

[0067]

[0068] where (x L , y L ) and (x R , y R ) are the focal positions when the Smith - Purcell radiation with polarization states of LCP and RCP is incident respectively. f L and f R are the focal lengths of two circular polarizations with opposite chiralities. Combining equations (4) and (5) can encode the focused Smith - Purcell radiation with arbitrary foci and focal lengths.

[0069] It also includes a dielectric grating, a first silica dielectric plate, a metasurface with phase gradient, and a second silica dielectric plate, which are distributed in sequence from top to bottom;

[0070] The polarization state of free - electron radiation is regulated by using a periodic dielectric grating;

[0071] The phase of the radiation light is regulated by using a metasurface with phase gradient.

[0072] Design three grating structures to change the polarization state of the obtained Smith-Purcell radiation, and control the focal length, number of foci, and focal position by precisely adjusting the spatial positions of the unit structures of the phase gradient metasurface.

[0073] Figure 1 The schematic diagram of the focusing of Smith-Purcell radiation is shown. Figure 2 Schematically illustrate the working process of the focusing of Smith-Purcell radiation. Electrons pass by parallel to the grating along the x direction, generating electron radiation with polarization information. The designed working wavelength is 1550 nm, and the energy passes through the phase gradient metasurface below the grating and is converged into a point.

[0074] The dielectric grating material is silicon with a refractive index of 3.46.

[0075] By manipulating the orientation angle of the dielectric grating structure, it is used to regulate linearly polarized or left- and right-handed circularly polarized electron radiation.

[0076] The thickness of silicon dioxide in the first silicon dioxide dielectric plate is 1000 nm, and its refractive index is 1.45.

[0077] The phase gradient metasurface is based on the Huygens principle and the Pancharatnam-Berry principle, and is used for the propagation phase and geometric phase with 2π phase coverage.

[0078] When the radiation light passes through the phase gradient metasurface, by adjusting the geometric shape and rotation angle of the cross structure of the phase gradient metasurface, 0-2π geometric phase and transmission phase control can be performed near the resonant frequency. Figure 3 The schematic diagram of the silicon nanocolumn of the cross structure of the metasurface. l1 and l2 respectively represent the two lengths in the orthogonal directions of the silicon nanocolumn in Table 1. Figure 4 The unit sizes of 8 with different geometric parameters under x-polarized incidence. Figure 5 Describes the phase response spectrum of the cross polarization of different unit structures of the phase gradient metasurface. Figure 6 Describes the transmittance spectrum of the cross polarization of different unit structures of the phase gradient metasurface. The horizontal axis and the vertical axis respectively represent l1 and l2. Through Figure 4 The eight basic unit structures in achieve a phase change covering 0 to 2π. Table 1 shows the detailed parameters of the eight unit structures, which respectively show the geometric dimensions of the unit structures.

[0079] Table 1 Geometric parameters of eight basic unit structures

[0080]

[0081] The present invention consists of a grating and a metasurface, demonstrating a method for designing multi-dimensional and multi-focus Smith-Purcell radiation focusing, providing a new mechanism for multi-functional and high-efficiency free electron radiation devices.

[0082] Further, to achieve right-handed circularly polarized (RCP) Smith-Purcell radiation focusing, the azimuth angle of the grating is adjusted to 0°, where the azimuth angle of the grating is the angle between the grating bar and the x-axis. Figures 7 - 10 The structure for realizing RCP Smith-Purcell radiation focusing. Figure 7 The subfigure in it describes the parameters of the grating. The grating period p1 is 570 nm, and the cross-sectional dimensions of the grating bar are a1 = 220 nm and b1 = 320 nm. Figure 8 The normalized Stokes parameter S3 in the x-y plane below the grating is provided. S3 = +1 indicates that the polarization state is RCP, and S3 = -1 indicates that the polarization state is left-handed circularly polarized (LCP). Obviously, the calculated results of S3 are all approximately 1, which means that the polarization states of the radiation fields are all RCP. Here, the metasurface is arranged by 36×36 unit cells. During the design, in this application, x l = x R = y l = y R = 0 μm, f L = 42 μm, f R = 28 μm. Figure 9 It is the electric field intensity distribution in the corresponding x-y plane 28 μm below the metasurface. When the Smith-Purcell radiation is RCP, the focal position of the focal plane is (0 μm, 0 μm). In addition, due to the characteristics of the PB phase, the polarization state of the RCP-polarized Smith-Purcell radiation after focusing is LCP. The normalized electric field intensity at the focus is as Figure 10 shown, and the full width at half maximum is about 1.86 μm.

[0083] Figure 11 It is the excitation structure for LCP Smith-Purcell radiation. The angle between the grating and the electron beam propagation direction is adjusted to -45°, and the other parameters are the same as those discussed for RCP. Figure 12 It is the distribution of the Stokes parameter S3 when no metasurface is added, indicating that the polarization state of the Smith-Purcell radiation is modulated to LCP by the grating. Figure 13 It is the electric field distribution 30 μm below the structure. When the Smith-Purcell radiation with a polarization state of LCP is incident, two bright spots appear at the positions of the second and fourth quadrants of the focal plane, and the polarization of the spots is opposite to the incident polarization. Their positions are approximately at (-12 μm, 12 μm) and (12 μm, -12 μm), which is consistent with the preset focal positions. For the incident RCP-polarized Smith-Purcell radiation, the electric field distribution is from Figure 15Given. The normalized electric field intensity distributions at the foci of the two implementation cases are shown respectively as Figure 14 and Figure 16 shown, where Q1 - Q4 respectively represent the high - light spots located in quadrants one to four.

[0084] Figures 17 - 20 This is the result of the present invention achieving the focusing of multi - focal linearly polarized vortex Smith - Purcell radiation. A linearly polarized light beam can be regarded as the superposition of two circularly polarized lights with equal amplitudes and opposite chiralities. Theoretically, when the Smith - Purcell radiation with a polarization state of LP is incident on the metasurface, four foci will simultaneously appear on the focal plane. To achieve linearly polarized Smith - Purcell radiation, the angle between the grating period direction and the electron beam propagation direction is adjusted to 0°, as shown in the structural diagram in Figure 17 . Here, the grating period p2 = 800 nm, a2 = 291.2 nm, and b2 = 400 nm. Figure 18 Illustrates the polarization state of the electron radiation generated by the interaction between the electron beam and the grating. In this application, the Stokes parameter S1 is used to describe the polarization at the x - y plane on the lower surface of the grating. When S1 is equal to +1 and -1, it represents polarizations of x - LP and y - LP respectively. In Figure 18 , S1 is approximately +1 on average, which means that the polarization of the Smith - Purcell radiation is x - LP. The electric field distribution of the x - LP Smith - Purcell radiation after being focused by the metasurface is shown in Figure 19 , and the normalized electric field intensity curve is shown in Figure 20 , where Q1 - Q4 respectively represent the high - light spots located in quadrants one to four. Four foci with equal focal lengths simultaneously appear in four regions of the x - y plane. The polarizations in the first and third quadrants are LCP, and the polarizations in the second and fourth quadrants are RCP. The focal positions are the same as those when the LCP or RCP Smith - Purcell radiation is incident alone. This design provides a spin - independent Smith - Purcell radiation focusing scheme, offering a promising method for realizing multi - dimensional and multi - functional free - electron radiation devices.

[0085] In the description of this application, it should be understood that the orientation or positional relationships indicated by the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the drawings. They are only for the convenience of describing this application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to this application.

[0086] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of this application, unless otherwise specified, the meaning of "a plurality" is two or more.

[0087] In the description of this application, it should be noted that unless otherwise clearly specified and defined, the terms "installed", "connected" and "coupled" shall be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0088] In this specification, the various embodiments are described in a progressive manner. The focus of each embodiment is on the differences from other embodiments. For the identical or similar parts among the embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description of the method part.

[0089] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface, characterized in that It includes the following steps: Step S1: Polarization state control. By adjusting the azimuth angle of the periodic dielectric grating, Smith-Purcell radiation with a preset polarization state is generated. Step S2: Wavefront control and point focusing. The Smith-Purcell radiation is made to pass through the metasurface with a phase gradient. By controlling the geometric parameters and rotation angle of the metasurface unit, a phase gradient distribution covering 0 - 2π is generated, and the radiation energy is focused on a preset focal point. Step S3: Multi-focus control. By multiplexing the metasurface structure or adjusting the spatial arrangement of the units, a multi-focus phase distribution is encoded to achieve dynamic adjustment of the number, position, and focal length of the focal points.

2. The method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface according to claim 1, wherein In the said Step S1: When the grating azimuth angle is 0°, linearly polarized Smith-Purcell radiation is generated. When the grating azimuth angle is 45°, right-handed circularly polarized Smith-Purcell radiation is generated. When the grating azimuth angle is -45°, left-handed circularly polarized Smith-Purcell radiation is generated.

3. The method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface according to claim 1, characterized in that The phase control of the metasurface with a phase gradient in the said Step S2 includes: The propagation phase is controlled by changing the lengths of l1 and l2 of the silicon nanocolumn cross structure. The Pancharatnam-Berry geometric phase is introduced by rotating the angle θ of the nanocolumn. Combining the propagation phase and the PB phase, a spin-independent 0 - 2π phase coverage is achieved.

4. The method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface according to claim 3, wherein The values of l1 and l2 of the silicon nanocolumn range from 0.218 - 0.354 μm, the values of l1 and l2 range from 0.364 - 0.524 μm, and the rotation angle θ is 0 - 180°.

5. The method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface according to claim 1, wherein The formula for the focusing phase distribution in the said Step S2 is: Among them, (x L , y L ) and (x R , y R ) are the focal positions of left-handed circularly polarized and right-handed circularly polarized radiation respectively, f L and f R are the corresponding focal lengths.

6. The method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface according to claim 1, wherein The multi-focus control in the said Step S3 includes: For linearly polarized radiation, a four-focus phase distribution is encoded, so that the focal points are distributed in four quadrants, and the first and third quadrants are LCP, and the second and fourth quadrants are RCP. For circularly polarized radiation, a two-focus phase distribution is encoded, so that the focal points are symmetrically distributed at the preset diagonal positions.

7. The method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface according to claim 1, wherein The adjustable range of the focal length is 28 - 42 μm, and the positioning accuracy of the focal point position is ±1 μm.

8. The method for realizing Smith-Purcell radiation focusing based on a phase gradient metasurface according to claim 1, characterized in that The working wavelength is 1550 nm, the period of the silicon nanocolumn of the metasurface with a phase gradient is 800 nm, the height is 800 nm, and the refractive index is 3.

46.

9. The method for realizing Smith-Purcell radiation focusing based on a phase-gradient metasurface according to claim 1, wherein The transmittance of the unit structure of the metasurface with a phase gradient is greater than 80%, and wavefront control at the sub-wavelength scale is achieved at a wavelength of 1550 nm.

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