A metasurface-based near-field surface wave in-plane wavefront modulation device

Abstract

The application belongs to the technical field of electromagnetic metasurface, and particularly relates to a near-field surface wave in-plane wave front regulating device based on a metasurface. The regulating device is composed of a geometric phase metasurface and a surface wave eigen region. The metasurface region is composed of artificial super-structure units with double rotational symmetry, and the radiation phase distribution of the theoretical design is realized by designing the geometric size and the rotational azimuth angle of the units. The eigen region is a double-layer structure composed of a dielectric film and a metal film. The device has a central working frequency of 12 GHz and a wide frequency working characteristic, and can be extended to other frequency bands. When the surface wave is transmitted from the eigen region to the metasurface region, the artificial microstructures at different positions serve as secondary wave sources to reconstruct the surface wave with an arbitrary complex wave front distribution in the near-field plane, thereby solving the problems of large volume, non-subwavelength, multiple modes and low efficiency in the transmission and regulation of traditional devices in the near-field plane.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic metasurface technology, specifically relating to a metasurface device for achieving near-field surface wavefront modulation of propagation. Background Technology

[0002] Surface waves (SWs) are localized modes of electromagnetic waves existing at the interface between two media (such as a medium and a metal). They include surface plasmon polaritons (SPPs) in the optical frequency band and spoof surface plasmon polaritons (SSPPs) in the low-frequency band. Surface waves possess subwavelength resolution and local field enhancement properties, and are used in various on-chip photonics applications, such as super-resolution imaging, sensing, integrated photonic circuits, and nonlinear enhancement. The ability to freely manipulate in-plane surface waves is essential for realizing these applications and is a key objective in many cutting-edge research areas.

[0003] Currently, there are two main types of surface wave modulation methods: the first involves designing traditional coupler structures to couple far-field transmitted waves into near-field surface waves on a chip, simultaneously achieving wavefront modulation of the surface waves' in-plane propagation; the second involves designing diffraction structures to directly modulate the surface waves transmitted by the on-chip device. However, the first type of modulation requires external transmitted wave illumination to excite the surface waves, which cannot meet the needs of certain applications requiring direct surface wave modulation. In the second type of modulation, traditional methods involve designing micro / nano structures with special geometries or periods to utilize the optical path difference of the surface waves or periodic diffraction effects to achieve wavefront modulation. These devices suffer from drawbacks such as multi-mode operation, low efficiency, and limited degrees of freedom in modulation.

[0004] Metasurfaces are planar artificial electromagnetic structures composed of a series of meticulously designed subwavelength microstructures arranged in a certain manner, and are currently widely used in various electromagnetic wave manipulation scenarios. This invention aims to utilize electromagnetic metasurfaces to achieve direct in-plane propagation wavefront manipulation of near-field surface waves. Compared to previous surface wave manipulation devices, the solution proposed in this invention offers advantages such as subwavelength manipulation, single-mode operation, high efficiency, and high integration. Summary of the Invention

[0005] The purpose of this invention is to design a near-field surface wavefront modulation device based on metasurfaces, so as to overcome the defects of traditional surface wave modulation photonic devices in the process of modulating near-field surface waves, such as large volume, non-subwavelength, multi-mode, low efficiency, and low integration.

[0006] This invention relates to a near-field surface wavefront manipulation device based on a metasurface, abbreviated as SW in-plane wavefront manipulation device. This device can reconstruct surface waves incident on a metasurface into surface waves with a pre-designed target wavefront distribution. By designing the phase distribution of the metasurface, this invention achieves the construction of various complex surface wavefront distributions, such as unidirectional deflection, focusing, Bessel beams, and Airy beams. Based on the physical principle of in-plane wave vector conservation, this invention constructs a Pancharatnam-Berry phase (PB phase, also known as geometric phase) gradient metasurface with special functions through the geometric design of artificial meta-atoms. This metasurface can reconstruct the wavefront of near-field surface waves (including surface plasmons and artificial surface plasmons) propagating in-plane and convert it into a pre-designed wavefront distribution. Its structural principle is described in [link to relevant documentation]. Figure 15 As shown.

[0007] First, in order to achieve arbitrary in-plane wavefront distribution in a surface wave excited system, this invention provides a phase distribution Φ MS (x,y) Generalized design. To realize the in-plane wavefront modulation device, a suitable physical system needs to be designed and verified through numerical simulation and experiments. The physical system, namely the near-field in-plane wavefront modulation device based on a metasurface, is composed of an electromagnetic geometric phase metasurface region and a surface wave eigenregion; the electromagnetic geometric phase metasurface region is composed of a series of metasurface units (also called artificial metastructures) according to the calculated phase distribution Φ. MS The surface wave intrinsic region is a two-dimensional array region formed by rotating (x, y) units; the surface wave intrinsic region is a two-dimensional array region formed by periodically extending intrinsic units in the X and Y directions; wherein, the metasurface unit cell is a three-layer structure of metal microstructure-dielectric thin film-metal thin film; the intrinsic unit cell is the structure after removing the upper metal microstructure from the metasurface unit cell, that is, a two-layer structure composed of dielectric thin film and metal thin film; the intrinsic region is used to support lossless transmission of surface waves; the metasurface unit cell and the intrinsic unit cell have the same size, both being square;

[0008] The metasurface unit cell has a double rotationally symmetric geometry (i.e., it coincides with the original shape after rotating 180 degrees), and the metasurface unit cell is distributed according to the phase Φ. MS The (x,y) rotational arrangement, where the rotation angle refers to the angle between the left and right symmetry axes of the metal microstructure with double rotational symmetry geometry and the y direction; the surface wave propagates along the x-axis and is incident from the intrinsic region of the surface wave into the electromagnetic geometric phase metasurface region.

[0009] In this invention, the near-field surface wave includes: surface plasmons and artificial surface plasmons.

[0010] Specifically, the upper metal microstructure geometry of the metasurface unit cell (artificial meta-unit) designed in this invention is required to satisfy double symmetry. A typical structure is an I-shaped structure (i.e., symmetrical arcs at the upper and lower ends), see [link to relevant documentation]. Figure 1 As shown. Its geometric parameters are: unit period is p, inner diameter of the arc ring is r1, outer diameter of the arc ring is r2, line width is w (=r2-r1), central angle (angle of expansion) between the upper and lower arc rings is β, medium thickness is d, and metal thickness is h.

[0011] In the metasurface unit cell, the metal microstructure is metallic copper, the dielectric film is an isotropic homogeneous medium, and the metal thin layer is a complete metal layer.

[0012] In this invention, the size of the metasurface region is M×N, where M and N are the number of metasurface units; the value of M / N is preferably between 3 and 4. The size of the intrinsic region is M×Q, where M and Q are the number of intrinsic units. It can be seen that the width of the intrinsic region is the same as the width of the metasurface region (the width in the x-axis direction is the same), that is, they are mutually matched and connected.

[0013] Surface waves propagate along the x-axis and are incident from the intrinsic region of surface waves onto the electromagnetic geometric phase metasurface region.

[0014] In this invention, the surface waves in the TM mode include: surface plasmons and artificial surface plasmons; in this invention, different phase distributions Φ are pre-designed. MS (x, y) can, in principle, achieve arbitrary wavefront reconstruction in the in-plane near field. To verify the generalization of the design scheme, this invention designs two different wavefront distributions: deflection wavefronts and focusing wavefronts. The deflection and focusing wavefronts are verified through numerical simulation and experimental testing.

[0015] In this invention, firstly, the physical properties of the metasurface unit cell (artificial meta-unit) and intrinsic structure are characterized by numerical simulation and microwave experiments, including: (1) the reflection phase of the artificial meta-unit; (2) the surface wave dispersion curve of the intrinsic structure; then, metasurface-1 and metasurface-2 are constructed based on the artificial meta-unit and the surface wave intrinsic unit cell.

[0016] Next, we performed a numerical simulation of the near-field propagation behavior of surface waves after they are incident on the metasurface to obtain its electric field distribution. To verify the accuracy of the numerical simulation, we fabricated a sample and conducted experimental verification. The theoretical prediction, numerical simulation, and experimental results are in good agreement.

[0017] The near-field surface wavefront modulation device based on metasurface designed in this invention has the following characteristics:

[0018] (1) The generality of phase design enables arbitrary wave reconstruction of surface waves in TM mode within the plane;

[0019] (2) The generalization of the design of artificial meta-units, that is, the structure only needs to satisfy double rotational symmetry;

[0020] (3) The central operating frequency of this invention is 12GHz, and it can be extended to any other operating frequency.

[0021] (4) The phase gradient metasurface can ensure the control of a single in-plane transport mode and has high working efficiency. Attached Figure Description

[0022] Figure 1 This is based on the phase design principle.

[0023] Figure 2 This is a schematic diagram of the focused phase.

[0024] Figure 3 (Top view) of an artificial metamorphic unit.

[0025] Figure 4 This is a side view of an artificial metamorphic unit.

[0026] Figure 5 This is the intrinsic structure (top view).

[0027] Figure 6 This is the intrinsic structure (side view).

[0028] Figure 7 This is an array diagram of artificial metacellular units.

[0029] Figure 8 This is a diagram illustrating the intrinsic structural region.

[0030] Figure 9 This is the reflection phase curve of an artificial meta-unit. "Expt." indicates an experiment, and "FDTD" indicates the finite-time difference method.

[0031] Figure 10 This represents the surface wave dispersion relation curve for the intrinsic structure. "Expt." indicates experimental results, and "TMM" represents the transfer matrix method.

[0032] Figure 11 The images show sample images of metasurface-1. Among them, (a) is a global view of metasurface-1, and (b) is a magnified view of a local part of metasurface-1.

[0033] Figure 12 The images show sample images of metasurface-2. Among them, (a) is a global view of metasurface-2, and (b) is a magnified view of a local part of metasurface-2.

[0034] Figure 13The results represent the characterization of surface wave directional deflection wavefront modulation. "FDTD" indicates the finite-time difference method, and "Expt." indicates the experiment.

[0035] Figure 14 The results represent the characterization of surface wave focusing wavefront modulation. "FDTD" indicates the finite-time difference method, and "Expt." indicates the experiment.

[0036] Figure 15 This is a schematic diagram of the near-field surface wavefront modulation device based on metasurface of the present invention. Detailed Implementation

[0037] The key to this invention is how to reconstruct surface waves incident on a metasurface into surface waves with a pre-designed wavefront distribution, specifically involving phase distribution design and metasurface design. The design process of this invention includes principle analysis, simulation optimization, and experimental verification, as detailed below:

[0038] I. Principle Analysis

[0039] 1. Design principles of metasurface phase distribution

[0040] To control the propagation direction of surface waves within a surface, the design principles should satisfy the following: Figure 1 The in-plane wave vector conservation condition is shown below:

[0041]

[0042] To satisfy the conditions for surface waves to propagate in-plane, the scattered wave vector... It should satisfy:

[0043]

[0044] In equation (1), This represents the phase gradient of the metasurface; Denotes the gradient operator, Φ MS (x,y) represents the phase distribution of the metasurface; Let k represent the propagation wave vector of the incident surface wave. This invention specifies that its propagation direction is along the positive x-axis. In equation (2), k... SW This represents the eigenvector of a surface wave. According to... Figure 1 Based on the geometric relationships, we can deduce that the phase gradients of the metasurface in the x and y directions should be as follows:

[0045] ξ x (x,y)=k SW (-1+cosθ r ), (3-a)

[0046] ξ y (x,y)=kSW sinθ r (3-b)

[0047] In equations (3-a) and (3-b), θ r (x,y) represents the deflection angle of the surface wave at any point (x,y) in the metasurface region, defined as positive when rotated counterclockwise from the x-axis. Finally, the phase distribution of the metasurface is:

[0048]

[0049] Equation (4) is the design principle for the phase distribution of metasurfaces.

[0050] 2. Specific case design

[0051] This invention specifically introduces two types of in-plane wavefront manipulation cases: directional deflection and focusing.

[0052] For a directional deflection system, the deflection angle at each location after a surface wave is incident on the metasurface is a constant θ. r (x,y)=θ0. According to equations (3) and (4), the phase distribution of the metasurface of the directional deflection device can be obtained as follows:

[0053] Φ MS (x,y)=(-k SW x+k SW cosθ0)x+k SW sinθ0y, (5).

[0054] For a focused system, such as Figure 2 As shown, after a surface wave is incident on the metasurface, the deflection angle at each location is a function related to the coordinates (x, y):

[0055]

[0056] At this point, the phase gradient of the metasurface is:

[0057]

[0058]

[0059] Substituting equations (7-a) and (7-b) into equation (4) yields the phase distribution of the metasurface in the focusing system:

[0060]

[0061] In equation (8), F represents the focal length, which is defined as the distance from the focal point to the outermost boundary of the metasurface.

[0062] 3. Calculation of geometric phase

[0063] This study investigates the phase modulation of circularly polarized incident light by the rotation of unit cells in a total reflection system (actually a perfect metal (PEC) substrate). The unit cell structure is as follows: Figure 3 As shown. The plane formed by the periodic expansion of the element structure is the xoy plane, and the direction perpendicular to this plane is the z-axis. The principal axes of the element are respectively... and Assumption:

[0064] The incident signal is in left-circularly polarized (LCP) mode:

[0065]

[0066] Reflected waves exist in mirror-symmetric systems:

[0067]

[0068] The artificial meta-units that make up the array are rotated collectively by α to obtain new unit principal axes. and At this time, the original incident wave is In a coordinate system, it can be represented as:

[0069]

[0070] Reflected waves at In the coordinate system:

[0071]

[0072] Simplifying, we get:

[0073]

[0074] Then convert the reflected wave to From the coordinate system, we can obtain:

[0075]

[0076] Simplifying this expression, we get:

[0077]

[0078] Among them, E i For the incident electric field, E r Let k be the reflected electric field, and k0 be the wave vector of electromagnetic wave propagation in vacuum. They are and Directional phase delay, They are and Phase delay in direction. As can be seen from the above derivation, when LCP is incident on the electromagnetic array after the artificial meta-unit is rotated, the reflected wave has both LCP, which we call the normal mode, and right-hand circularly polarized (RCP), which we call the anomalous mode. Here, the anomalous mode is RCP, and it has an additional phase related to the geometric rotation angle α: 2α. This phase is the geometric phase.

[0079] Finally, the rotation angle distribution of all elements on the metasurface is as follows:

[0080] α(x,y)=Φ MS (x,y) / 2 (14).

[0081] II. Simulation Optimization

[0082] Artificial meta-units and intrinsic region structures were designed using electromagnetic wave computation packages based on finite-time difference (FTLD) simulations. An artificial meta-unit with twofold symmetry was designed for this invention, such as... Figure 3 and Figure 4 As shown, its geometric parameters are: p = 3mm, r1 = 1.2mm, r2 = 1.4mm, w = 0.2mm, β = 90°, d = 2mm, h = 0.1mm;

[0083] The intrinsic unit cell corresponding to the artificial metacellular unit has no metallic structure in its upper layer, and is composed only of the second and third layers of the artificial metacellular unit, such as... Figure 5 As shown in Figure 6.

[0084] The reflection phases of the two principal axes of the artificial metaunit were obtained through simulation using the finite-difference time-domain (FDTD) method, as shown below. Figure 9 As shown. The dispersion curve of the surface wave is calculated using the transfer matrix method (TMM), as shown below. Figure 10 As shown.

[0085] Metasurface-1 (directional deflection wavefront manipulation metasurface) and metasurface-2 (focusing wavefront manipulation metasurface) were constructed based on artificial metaunits and intrinsic cells. Metasurface-1 consists of 100 x 30 units, has dimensions of 300 mm x 90 mm, and operates at a frequency of f = 12 GHz. The phase distribution of metasurface-1 is shown below. The parameters of the metasurface-1 are calculated according to formula (5), where k is: SW =1.07k0, θ0=90°, x=[-150mm,150mm],y=[-45mm,45mm]; Metasurface-2 is: 80*25 units, with dimensions of 240×75mm2 The operating frequency is f = 12 GHz. Phase distribution of metasurface-2. The parameters of the metasurface-2 are calculated according to formula (8): F = 125 mm, x = [-120 mm, 120 mm], y = [-37.5 mm, 37.5 mm].

[0086] Specifically, the metasurface is obtained by rotating an artificial unit cell by a corresponding angle based on a calculated phase; wherein, if the position (x i ,y j The calculated phase is Φ. MS (x,y), then the local rotation azimuth angle of the primitive cell at that position is Φ. MS (x,y) / 2; The rotation angle of the metasurface unit cell refers to the angle between the axis of symmetry of the metal microstructure (i.e., the middle vertical rod) and the Y direction; The initial angle of the metasurface unit cell is defined as the angle where the included angle is 0.

[0087] Next, we performed FDTD to simulate the in-plane propagation behavior of surface waves at f = 12 GHz. The simulation results are as follows: Figure 13 (a) Figure 14 As shown in (a).

[0088] Next, the experimental sample metasurface-1 was fabricated using printed circuit board technology, and its global image is shown below. Figure 11 As shown in (a), the partial view is as follows: Figure 11 As shown in (b), the experimental sample metasurface-2 was fabricated using printed circuit board technology, and its global view is shown below. Figure 12 As shown in (a), the partial view is as follows: Figure 12 As shown in (b);

[0089] Next, experiments were conducted to test and verify the results, as follows: Figure 13 (b) and Figure 14 (b)

[0090] III. Experimental Verification

[0091] 1. Measurement of the reflection coefficient of artificial metamorphic units

[0092] Artificial metamorphic unit design such as Figure 3 As shown in Figure 4, the experimental sample is as follows: Figure 6 As shown. When measuring the reflection coefficient of the artificial metamorphic unit, the sample was placed 1m away from the antenna. One linearly polarized horn antenna emitted the signal, and the other linearly polarized horn antenna received the signal, with both antennas maintaining the same polarization state. The experimental results of the unit reflection phase are shown below. Figure 9 As shown, the results are consistent with the simulation results.

[0093] 2. Measurement of intrinsic structure dispersion curves

[0094] Intrinsic structural design such as Figure 5 As shown in Figure 6, the intrinsic structure experimental sample is as follows: Figure 8 As shown. During the experiment, a probe perpendicular to the metasurface was placed 3 mm directly above it. Samples were taken every 1 mm along the surface wave propagation direction (positive x-axis), for a total of 100 points. The surface wave electric field distribution information (E) obtained from the test was then analyzed. z The wavelength λ is obtained, and finally the surface wave vector is obtained from the wavelength. Experimental results of surface wave dispersion relation are as follows Figure 10 As shown, the results are consistent with theoretical calculations.

[0095] 3. Surface wave near-field test

[0096] Surface waves undergo in-plane scattering after being incident on the metasurface region. To measure near-field information (E... z Near-field information needs to be obtained using near-field scanning technology. During the experiment, a probe perpendicular to the metasurface is placed 3 mm directly above it. Samples are taken every 3 mm within the target area in the xy-plane, and scanning the entire target area yields the corresponding near-field distribution information. The near-field test results are as follows: Figure 13 (b) and Figure 14 As shown in (b).

Claims

1. A near-field surface wavefront modulation device based on metasurfaces, characterized in that, Surface waves incident on a metasurface can be reconstructed into surface waves with a pre-designed target wavefront distribution; and by designing the phase distribution of the metasurface, various complex surface wavefront distributions can be constructed; specifically, it is composed of an electromagnetic geometric phase metasurface region and a surface wave eigenregion spliced ​​together; wherein, the electromagnetic geometric phase metasurface region is composed of a series of metasurface units arranged according to the calculated phase distribution. A two-dimensional array region formed by rotational arrangement; the intrinsic surface wave region is a two-dimensional array region composed of intrinsic unit cells periodically extended in the X and Y directions; wherein, the metasurface unit cell is a three-layer structure of metal microstructure-dielectric thin film-metal thin film; the intrinsic unit cell is the structure after removing the upper metal microstructure from the metasurface unit cell, that is, a two-layer structure composed of dielectric thin film and metal thin film; the intrinsic region is used to support lossless transmission of surface waves; the metasurface unit cell and the intrinsic unit cell have the same size, both being square; The metasurface unit cells have a double rotationally symmetric geometry, and the metasurface unit cells are distributed according to phase. Rotational arrangement, the rotation angle refers to the angle between the left and right symmetry axes of a metal microstructure with a double rotational symmetry geometry and the y direction; surface waves propagate along the x-axis and are incident from the intrinsic region of surface waves into the electromagnetic geometric phase metasurface region; The near-field surface waves include: surface plasmons and artificial surface plasmons; The upper metal microstructure of the metasurface unit cell is required to satisfy double symmetry. Specifically, the structure is I-shaped, with symmetrical arcs at its upper and lower ends. Its geometric parameters are: unit period p, inner diameter of the arc ring r1, outer diameter of the arc ring r2, linewidth w = r2 - r1, and the central angle between the upper and lower arc rings is... The thickness of the medium is d, and the thickness of the metal is h; The size of the metasurface region is M×N, and the value of M / N is between 3 and 4; the size of the intrinsic region is M×Q, where M and Q are the number of intrinsic unit cells; the width of the intrinsic region is the same as the width of the metasurface region, that is, they are mutually matched and connected. In a surface wave-excited system, near-field surface wave wavefront modulation is achieved, and the phase design of the metasurface satisfies the following: ， （1） in, and The phase gradients obtained according to the in-plane wave vector conservation principle are as follows: ， ， It represents the deflection angle of the surface wave at any point (x, y) in the metasurface region, and is defined as positive when rotated counterclockwise from the x-axis. The eigenvectors of surface waves are represented.

2. The near-field surface wavefront modulation device based on metasurface according to claim 1, characterized in that, In the metasurface unit cell, the metal microstructure is metallic copper, the dielectric film is an isotropic homogeneous medium, and the metal thin layer is a complete metal layer.

3. The near-field surface wavefront modulation device based on metasurfaces according to claim 1, characterized in that, To achieve in-plane: (1) directional deflection of the wavefront, and (2) focusing of the wavefront, the phases of the metasurface are respectively: （2） （3） Formula (2) represents the phase distribution of the directional deflection wavefront, where θ0 is the directional deflection angle, which is a constant; Formula (3) represents the phase distribution of the focused wavefront, where F is the focal length, i.e., the distance from the focal point to the outer boundary of the metasurface.

4. The near-field surface wavefront modulation device based on metasurface according to claim 3, characterized in that, Specific calculation of geometric phase: This study investigates the phase modulation of circularly polarized incident light by the rotation of unit cells in a total reflection system. Let the plane formed by the periodic expansion of the unit cell structure be... A plane, and the direction perpendicular to this plane is The axis and the unit spindle are respectively and Assume the incident signal is a left-handed circular deflection mode: ， Reflected waves exist in mirror-symmetric systems: ， Rotate the metasurface units that make up the array collectively A new unit spindle is obtained. and At this time, the original incident wave is Represented in coordinate system as: ， Reflected waves at In the coordinate system: ， Simplifying, we get: , Then convert the reflected wave to Coordinate system, we get: ， Simplifying this expression, we get: ， in, For the incident electric field, For the reflected electric field, The wave vector for electromagnetic wave propagation in a vacuum. , They are and Directional phase delay, , They are and Phase delay in direction; As can be seen, when a left-handed circularly polarized electromagnetic array is incident on a rotated metasurface unit cell, the reflected wave exhibits both left-handed circular polarization (called the normal mode) and right-handed polarization (called the anomalous mode), and carries a polarization angle relative to the geometric rotation angle. Related additional phases: This phase is the geometric phase; ultimately, the rotation angle distribution of all unit cells on the metasurface is as follows: 。 5. The near-field surface wavefront modulation device based on metasurface according to claim 4, characterized in that, The directional deflection wavefront modulated metasurface, constructed based on metasurface unit cells and intrinsic cells, is... It consists of several units, with a size of The operating frequency is f=12GHz, and the directional deflection angle is Focused wavefront-tuned metasurfaces constructed based on metasurface unit cells and intrinsic cells are... It consists of several units, with a size of The operating frequency is f=12GHz, and the focal length is F=125mm; among which, the propagation wave vector of the surface wave is... .

6. The near-field surface wavefront modulation device based on metasurface according to claim 5, characterized in that, The optimized geometric parameters of the metasurface unit cell are: p = 3 mm, r1 = 1.2 mm, r2 = 1.4 mm, w = 0.2 mm. d=2mm, h=0.1mm; where the dielectric constant of the dielectric layer is 3.

Images