Metasurface capable of realizing any three-dimensional space curve focusing track

Abstract

The invention provides a metasurface capable of realizing any three-dimensional space curve focusing track, which is characterized in that the metasurface consists of a plurality of non-isotropic units and is integrated on a substrate; when incident polarized light vertically enters the substrate and is modulated by the metasurface, a gradient-adjustable focusing track along any curve can be generated in a three-dimensional space. A metasurface phase distribution formula is composed of an intensity focusing item and a phase gradient item, two functions about space coordinate variables introduced into the intensity focusing item jointly determine a focusing track in a three-dimensional space, and the function about the space coordinate variables in the phase gradient item provides an adjustable phase gradient for a focusing area. Through the combined action of the two aspects, a three-dimensional space curve focusing track with an adjustable track and adjustable phase distribution in a focusing area can be realized. The metasurface capable of achieving any three-dimensional space curve focusing track can accurately control focusing of light beams, has wide application potential and can be applied to the fields of light field modulation, light manipulation and the like.

Description

TECHNICAL FIELD

[0001] The application relates to a super surface capable of realizing an arbitrary three-dimensional space curve focusing track, which can be used in the fields of optical imaging, light manipulation, particle transportation and the like. BACKGROUND

[0002] With the progress of micro-nano manufacturing technology, the demand for high-performance and low-cost micro optical systems is increasing, and the size of optical systems is continuously reduced, developing towards miniaturization, light weight and integration. Traditional optical elements are limited by modulation mechanism and the characteristics of natural materials, and it is difficult to meet the requirements in terms of ultra-light and ultra-thin, wavelength and polarization control and other multi-functional integration, which leads to the fact that the control of electromagnetic waves at the nanoscale has become an important trend in the development of modern optics and nanophotonics. Optical super surface introduces a sudden phase by designing nano unit structure in the sub-wavelength scale, realizes flexible manipulation of light wave front, including amplitude, phase and polarization and other parameters, thereby effectively adjusting the transmission characteristics of light. In recent years, the optical super surface technology has developed rapidly, and has shown great application potential in the research field of three-dimensional holographic display, high-resolution imaging, sensors, super lens and other new optical devices, and has promoted the further development of optical system integration.

[0003] The precise focusing of light beams using the regulation of electromagnetic waves by metasurfaces is an important branch of metasurface research. In particular, the realization and regulation of optical line focusing, which is a high aspect ratio focusing light field, has become a hot topic in metasurface research. In 2020, Shen et al. proposed a method for driving metal nanoparticles in a focal field based on a phase gradient metasurface (IEEE Photonics Journal, 2020, 12, 4600810). This method is achieved by focusing a transverse optical needle with a phase gradient, successfully driving and separating Ag nanoparticles with a radius of 50-200 nm. In 2022, Shanei et al. reported a full-dielectric phase gradient metasurface, also used to construct an optical needle and drive particle transport (Optics Letters, 47(24), 6428). This work uses a phase step with a period of 6 μm to form a series of optical potential wells, achieving stable capture and transport of 2 μm polystyrene microspheres. In 2024, Li et al. successfully generated a super-long transverse optical needle with a length of 40 μm (about 80 times the wavelength) by designing a superlens based on a single layer of MoS2 (Adv. Optical Mater. 2024, 13, 2402024). The superlens designed in this study can achieve sub-diffraction-limited transverse focal points and has a wide working wavelength range. These studies show that the regulation of optical line focusing using metasurface technology has important research prospects and can achieve sub-diffraction-limited precise focusing and efficient optical manipulation without relying on traditional large-sized optical elements, showing great application potential in the fields of biological imaging and particle capture.

[0004] In order to expand the scale range and applications of metasurface regulation of optical line focusing, the present invention proposes a metasurface that can realize arbitrary three-dimensional spatial curve focusing trajectories. Unlike traditional lenses that modulate point focusing or one-dimensional line focusing of light beams, this method can generate focusing trajectories along arbitrary curves in three-dimensional space, and the modulation of the phase gradient term in the phase distribution formula of the metasurface can provide different phase gradients for the focusing region. SUMMARY

[0005] The present invention aims to provide a metasurface that can realize arbitrary three-dimensional spatial curve focusing trajectories.

[0006] The purpose of the present invention is achieved as follows:

[0007] The application provides an ultrathin surface device capable of realizing arbitrary three-dimensional spatial curve focusing track in the field of light field modulation and light manipulation, wherein the ultrathin surface (1) is composed of a plurality of non-isotropic units (101) and is integrated on a substrate (2); when incident polarized light (3) is vertically incident to the substrate (2) and is modulated by the ultrathin surface (1), a gradient-adjustable focusing track (4) along an arbitrary curve can be generated in three-dimensional space. The phase distribution formula of the ultrathin surface is composed of an intensity focusing term and a phase gradient term , and can be expressed as . In the three-dimensional coordinate space defined by , the focusing track (4) converging in the direction of is controlled by two functions about spatial coordinate variables and introduced in the intensity focusing term ; and the phase gradient in the focusing area can be controlled by the function about spatial coordinate variables in the phase gradient term .

[0008] The straight line distance between the incident position of light on the ultrathin surface and the central point position is r, in order to focus the light at different incident positions to the same position, the ultrathin surface needs to provide a sudden phase at the position r, which can be described by the following formula:

[0009] wherein, is the wavelength of light, is the focal length.

[0010] In order to enhance the flexibility of the focusing track, taking the convergence in the direction of as an example, the application introduces functions about spatial coordinate variables , and in the phase distribution formula to realize an arbitrary three-dimensional curve focusing track converging in the direction of . The phase distribution formula can be expressed as:

[0011] wherein, and are three-dimensional spatial coordinate variables. In the formula, the first term

[0012] is the intensity focusing term, and The curve shape and position of the focusing trajectory in three-dimensional space are jointly determined, which are respectively represented as the dynamic focal length of the focusing trajectory and the offset in the converging direction (x direction) The second term is a phase gradient term, which determines the phase distribution within the focusing trajectory.

[0013] In the following, the design and working principle of the metasurface that can realize arbitrary three-dimensional spatial curve focusing trajectory will be described in detail, taking Cartesian coordinate system and cylindrical coordinate system as examples respectively.

[0014] In Cartesian coordinate system, the converging direction is the x direction, and are linear functions, and the phase gradient modulation term is a power function, that is

[0015] Take the focusing trajectory of a curve in the x-y plane as an example. Corresponding to the offset along the x axis, it can be represented as , Corresponding to the dynamic focal length in the y direction, it can be represented as , that is , , In the phase gradient modulation term, d is the distance between the centers of the unit structures, that is, the period of the metasurface unit array, and a and b are phase gradient parameters, which respectively determine the size of the phase gradient and the mapping relationship of the phase gradient with respect to the independent variable y.

[0016] The focusing trajectory of an arbitrary curve in the x-y plane can be realized by introducing modulation, and the phase distribution formula of the metasurface is as follows:

[0017] When the offset is a linear function, it can be defined as:

[0018] wherein is the maximum value of the offset, representing the maximum distance that the focusing trajectory can be offset in the x direction. The ratio part in the formula maps the value of the independent variable y to the range of , and multiplying the maximum offset can realize the linear change of the offset with the value of y, so as to realize the inclined focusing trajectory in the x-y plane.

[0019] When realizing the focusing trajectory of an arbitrary curve in the y-z plane, the phase distribution of the metasurface can be described by the following formula:

[0020] Take the linear function as an example, the introduced dynamic focal length Similarly, based on The change of coordinates, which is realized by proportional mapping, can be defined as:

[0021] wherein, and respectively represent the minimum and maximum values of the focal length. and defined The value range of the coordinates, with the change of y value, the focal length will be linearly adjusted according to the formula, so as to realize the focusing trajectory in the y-z plane.

[0022] When the dynamic focal length and the offset control the focusing trajectory at the same time, the focusing trajectory along any curve in three-dimensional space can be realized, and at this time, the super surface phase distribution formula is:

[0023] The meanings of the parameters are the same as above.

[0024] In addition, by changing the function form of the phase gradient term with respect to the coordinate variable y and the parameters, different phase distributions can be provided in the focusing area to realize specific optical effects and the application of focusing trajectory in the fields of light field control, particle manipulation, biological imaging, etc.

[0025] In the cylindrical coordinate system, the phase formula of the traditional super lens focusing can be expressed as:

[0026] wherein, is the radial distance.

[0027] Corresponding to the focusing along the x direction in the Cartesian coordinate system, when focusing along the radial distance direction in the cylindrical coordinate system, the focal length, offset, and phase gradient can be a function of the azimuth angle , and the offset and focal length are constant, and the phase gradient is a linear function of Take the linear function as an example, the incident polarized light can be focused into a circular ring focal line in the focal plane after being modulated by the super surface, and a phase gradient linearly changing along the azimuth angle is provided in the focusing area. At this time, the phase distribution of the super surface can be expressed as:

[0028] wherein, is the offset along the converging direction (x) direction), i.e. the radial distance of the focal position, here is a constant, representing the radius of the circular focal line; is the phase gradient parameter, the phase change along the focal line for one rotation is .

[0029] The super surface designed to realize the arbitrary three-dimensional spatial curve focusing trajectory significantly enhances the flexibility of the super surface in optical line focusing regulation. By introducing a function about the spatial coordinate variable, the focusing position and trajectory of the light field are accurately controlled, which can provide more flexible light field manipulation ability compared with traditional optical line focusing technology; in addition, by changing the mapping relationship of the phase gradient term about the spatial coordinate variable, different phase distributions can be provided in the focusing trajectory, thereby improving the accuracy of light focusing and energy transfer efficiency to adapt to different application requirements. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a working principle diagram of the super surface that can realize the arbitrary three-dimensional spatial curve focusing trajectory.

[0031] Figure 2 (a) is a phase distribution diagram of the super surface when the super surface realizes the inclined focusing trajectory in the x-y plane and provides a linear phase gradient; Figure 2 (b) is a phase distribution diagram of the super surface when the super surface realizes the inclined focusing trajectory in the y-z plane and provides a linear phase gradient; Figure 2 (c) is a phase distribution diagram of the super surface when the super surface realizes the three-dimensional focusing trajectory and provides a linear phase gradient.

[0032] Figure 3 is a simulation result diagram of the inclined focusing trajectory in the x-y plane and the y-z plane: (a) the focusing light field distribution of the focal plane when the inclined focusing trajectory in the x-y plane is realized; (b) the transmission light field distribution in the x-z section corresponding to y=0 when the inclined focusing trajectory in the x-y plane is realized; (c) the focusing light field distribution of the y-z section corresponding to x=0 when the inclined focusing trajectory in the y-z plane is realized; (d) the transmission light field distribution in the x-z section corresponding to y=0 when the inclined focusing trajectory in the y-z plane is realized.

[0033] Figure 4 (a) is a phase distribution diagram of the focal plane where the inclined focusing trajectory in the x-y plane is located; Figure 4 (b) is a phase distribution diagram of the inclined section where the inclined focusing trajectory in the y-z plane is located.

[0034] Figure 5is a simulation result schematic diagram of realizing three-dimensional focusing trajectory: (a) focusing area intensity distribution; (b) focusing area phase distribution.

[0035] Figure 6 is a phase distribution diagram of the metasurface when the metasurface realizes circular ring focusing in the focal plane and provides a phase gradient that varies linearly along the azimuthal angle.

[0036] Figure 7 is a simulation result schematic diagram of realizing circular ring focusing trajectory in the focal plane: (a) focusing light field distribution; (b) phase distribution.

[0037] Figure 8 is a preparation schematic diagram of a metasurface device capable of realizing arbitrary three-dimensional spatial curve focusing trajectory.

[0038] Figure 9 is an optical system schematic diagram for observing device output light field. DETAILED DESCRIPTION

[0039] The present application will be further described below in conjunction with specific examples.

[0040] In conjunction with Figure 1 , the embodiment of the present application mainly provides a metasurface device capable of realizing arbitrary three-dimensional spatial curve focusing trajectory, characterized in that: the metasurface (1) is composed of a plurality of anisotropic units (101) and is integrated on a substrate (2); when incident polarized light (3) is normally incident to the substrate (2) and is modulated by the metasurface (1), a gradient-adjustable focusing trajectory (4) along an arbitrary curve can be generated in three-dimensional space, and the focusing trajectory (4) is regulated by two functions about spatial coordinate variables introduced in a focusing term. The phase gradient in the focusing area is regulated by a function about spatial coordinate variables in a phase gradient term.

[0041] When a large-mode-area optical fiber (5) is used as the substrate (2), taking the metasurface device capable of realizing arbitrary three-dimensional spatial curve focusing trajectory integrated on the end of the large-mode-area optical fiber (5) as an example, in conjunction with Figure 8 , the preparation of the device can be divided into the following eight steps:

[0042] Step 1: uniformly apply photoresist (6) on the silica substrate (2), as shown in Figure 8 (a).

[0043] Step 2: use the method of electron beam lithography to selectively expose the photoresist (6), scan the pattern onto the photoresist (6), so that it forms an exposed area (6.1) corresponding to the position of each subwavelength structure unit (101) constituting the metasurface (1), as shown in Figure 8 (b).

[0044] Step 3: After the excess photoresist (6) is removed and cleaned and dried, the desired geometric pattern is completely retained on the photoresist (6), as shown in Figure 8 (c).

[0045] Step 4: A full dielectric film (7) is deposited on the photoresist (6) by a thermal evaporation method, as shown in Figure 8 (d).

[0046] Step 5: After the photoresist (6) in the unexposed area in Step 2 is peeled off, the metasurface (1) is obtained, as shown in Figure 8 (e).

[0047] Step 6: The thermosetting epoxy resin (9) is applied on the glass slide (8), and the fiber end of the large-mode-area fiber (5) is brought into contact with the epoxy resin (9) by dispensing, so as to form an epoxy resin (9) adhesion layer on the fiber end, as shown in Figure 8 (f).

[0048] Step 7: The center of the metasurface (1) is aligned with the core of the large-mode-area fiber (5) using an optical microscope, and then the metasurface (1) is cured at room temperature, as shown in Figure 8 (g).

[0049] Step 8: The silica substrate (2) is separated from the fiber end of the large-mode-area fiber (5), and since the adhesion effect of the metasurface (1) to the epoxy resin (9) is better than that to the silica substrate (2), the metasurface (1) is retained on the end face of the large-mode-area fiber (5), as shown in Figure 9 (h).

[0050] According to the above steps, the large-mode-area fiber (5) is prepared as a substrate (2) of a metasurface device capable of realizing an arbitrary three-dimensional spatial curve focusing trajectory.

[0051] In combination with Figure 9 , the light signal input of the above-mentioned metasurface device capable of realizing an arbitrary three-dimensional spatial curve focusing trajectory is realized in the following manner: the light signal output by the broadband light source laser (10) is coupled into the core of the large-mode-area fiber (5) through an optical system, and a dispersion-flattened guided mode (501) is maintained for transmission.

[0052] The observation of the device output light field adopts ​The optical system is shown to achieve: the system selects a broadband light source laser (10), the light signal output by the laser (10) is transmitted to the lens (13) after passing through the polarization and power control module (11) and then through the mirror (12), the incident light (3) is coupled into the core of the large mode area fiber (5) by the objective lens (14), the guided mode (501) with flat dispersion is excited, the guided mode (501) is transmitted to the super surface (1) at the fiber end, the output is modulated by the super surface (1), the focusing track of arbitrary curve is formed above the fiber end, and the sample (16) can be moved to the focal plane of the CCD digital camera (17) by controlling the electrically controlled displacement table (15) to observe the output light field distribution of the sample (16).

Claims

1. The present invention provides a metasurface capable of realizing any three-dimensional spatial curved focusing trajectory, characterized in that: The metasurface (1) is composed of a plurality of non-isotropic units (101) integrated on a substrate (2); when the incident polarized light (3) is perpendicularly incident on the substrate (2) and modulated by the metasurface (1), a focusing trajectory (4) along an arbitrary curve can be realized in three-dimensional space; the phase distribution formula of the metasurface is composed of the intensity focusing term and the phase gradient term Composition, which can be expressed as , in In the three-dimensional coordinate space defined by Function and , can be along Directional convergence of the focusing trajectory of any three-dimensional space curve (4) is achieved by introducing the spatial coordinate variable in the phase gradient term. Function , which can provide an adjustable phase gradient within the focusing track, thereby realizing a focusing track with adjustable gradient along any three-dimensional spatial curve.

2. The metasurface capable of realizing arbitrary three-dimensional spatial curved focusing trajectories according to claim 1, characterized in that: The substrate 2 is a transparent or semi-transparent material.

3. The metasurface capable of realizing arbitrary three-dimensional spatial curved focusing trajectories according to claim 1, wherein: In Taking directional convergence as an example, the metasurface phase distribution formula is: in, is the wavelength of the incident polarized light, and is the three-dimensional space coordinate variable, the first term in the formula is the intensity focus term, and Together they determine the shape and position of the focusing trajectory in three-dimensional space, which are respectively expressed as the dynamic focal length of the focusing trajectory and the direction of convergence ( direction); the second term in the formula is the phase gradient term, which determines the phase distribution within the focusing track.

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