Metastructure surface capable of realizing phase gradient size change through interlayer torsion

Abstract

The invention discloses a metasurface capable of realizing phase gradient size change through interlayer torsion, which comprises a plurality of layers of isomorphic surfaces rotationally connected to a central shaft, the surface comprises a plurality of element atom blocks uniformly arranged along a plurality of concentric circles, and the element atom blocks positioned on two adjacent concentric circles are spaced from each other. The element atom blocks on the surfaces of the two adjacent layers can be ingeniously changed between the parallel stacking form and the vertical stacking form through torsion, and then dynamic regulation and control over the PB phase of the metasurface are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of metasurfaces, and in particular to a metasurface that achieves phase gradient magnitude variation through interlayer twisting. Background Art

[0002] Metasurfaces are planar photonic devices composed of artificial structural units (meta-atoms) at the subwavelength scale. They achieve fine-grained control of the propagation characteristics of incident light waves, such as intensity, polarization, and phase, through artificially designed micro-nanostructure arrangements. This control capability stems from the geometric configuration and spatial distribution of meta-atoms, breaking through the limitations of traditional optical materials that rely on the inherent properties of the materials. For example, by adjusting the rotation angle or symmetry of meta-atoms, a geometric phase (Pancharatnam-Berry phase, PB phase) can be generated, thereby achieving light wavefront manipulation.

[0003] Although the geometric phase control technology has made significant progress, the meta-atom orientation and PB phase of the existing metasurfaces are fixed after preparation, and the phase cannot be dynamically adjusted or the multiple dependence can be controlled. This limits the application of the device in real-time adjustable optical systems (such as dynamic holography and adaptive beam shaping). Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a metasurface that realizes phase gradient magnitude change through interlayer twisting, which can realize dynamic regulation of PB phase.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A metasurface that achieves phase gradient size change through interlayer twisting, including a multi-layer isomorphic surface connected by rotation on a central axis, the surface including a plurality of meta-atomic blocks evenly arranged along a plurality of concentric rings, and a spacing between the meta-atomic blocks located on two adjacent concentric circles. The meta-atomic blocks on two adjacent layers of the surface are transformed between a parallel stacking state and a vertical stacking state through twisting, so as to achieve dynamic regulation of the PB phase of the metasurface.

[0007] Preferably, the number of meta-atom blocks arranged on the same concentric circle is an even number, and the central angles formed between two adjacent meta-atom blocks are equal.

[0008] Preferably, the position of each meta-atom block on the surface in the spatial coordinates is defined as follows:

[0009] g(r,θ)=qθ+g 0

[0010] Where θ is the polar coordinate azimuth, g is the orientation angle of the meta-atom block relative to the X-axis, and g 0is the fixed initial orientation angle of the meta-atom block, r is the radius of the concentric circle where the meta-atom block is located, q is a constant, and g(r,θ) is the rotation angle of the meta-atom block around its own center at the corresponding position.

[0011] Preferably, the surface further comprises a substrate, the meta-atomic block is arranged on the substrate, the substrate has a central hole, and the central hole is connected to the central axis through a bearing.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] The metasurface disclosed in the present invention is composed of multiple layers of isomorphic surfaces. By twisting, the meta-atomic blocks on two adjacent layers of the surface can cleverly change between a parallel stacking state and a vertical stacking state, thereby realizing dynamic regulation of the PB phase of the metasurface. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the meta-atom, where the material is gold and it is embedded in an isotropic nonlinear medium;

[0015] Figure 2 It is a schematic diagram of a meta-atom composed of a rectangle, an equilateral triangle, and a regular pentagonal hole from left to right;

[0016] Figure 3 It is the meta-atom in the square lattice;

[0017] Figure 4 It is a front view of the meta-surface disclosed in the present invention when the meta-atomic blocks between two adjacent layers of the surface are in a parallel stacking state;

[0018] Figure 5 It is a side view of the meta-surface disclosed in the present invention when the meta-atomic blocks between two adjacent surfaces are in a parallel stacking state;

[0019] Figure 6 It is a front view of the meta-surface disclosed in the present invention when the meta-atomic blocks between two adjacent layers of the surface are in a vertically stacked state;

[0020] Figure 7 It is a side view of the meta-atom blocks between two adjacent layers of the meta-surface disclosed in the present invention when they are in a vertically stacked state;

[0021] Figure 8 It is a schematic cross-sectional assembly diagram between two adjacent layers of the metasurface disclosed in the present invention;

[0022] Fig. 9 It is a front view of the meta-atom blocks between two adjacent layers of the meta-surface disclosed in the present invention when they are twisted into a parallel stacking state;

[0023] Fig.10It is a front view of the meta-atom block between two adjacent layers of the meta-surface disclosed in the present invention when it is twisted into a vertical stacking state;

[0024] Fig.11 It is a front view of a periodic metasurface of a meta-atom block when two adjacent layers of surfaces in the metasurface disclosed in the present invention are in a parallel stacking state;

[0025] Fig.12 It is a front view of a periodic metasurface of a meta-atom block when two adjacent layers of surfaces in the metasurface disclosed by the present invention are in a vertically stacked state;

[0026] Fig.13 is a PB phase diagram when two adjacent layers of the metasurface disclosed in the present invention are in a parallel stacked state;

[0027] Fig.14 is a PB phase diagram of a meta-atom block when two adjacent layers of the metasurface disclosed in the present invention are in a vertically stacked state;

[0028] Fig.15 It is a schematic diagram of periodic spatial variation of the angular orientation of the meta-atomic blocks in a vertically stacked form when two adjacent layers of the meta-surface disclosed in the present invention are in a vertically stacked form;

[0029] Fig.16 It is a PB phase diagram when the orientation angle space of the meta-atomic blocks in the vertically stacked form changes when two adjacent layers of the meta-surface disclosed in the present invention are in a vertically stacked form;

[0030] Fig.17 It is a phase diagram of the outgoing field when the meta-atomic blocks of two adjacent layers of the metasurface disclosed in the present invention are in a horizontally stacked form;

[0031] Fig.18 It is an outgoing field phase diagram when the meta-atomic blocks on two adjacent layers of the metasurface disclosed in the present invention are in a vertically stacked form.

[0032] Figure symbols: 1. central axis, 2. surface, 21. meta-atomic block, 22. substrate. DETAILED DESCRIPTION

[0033] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0034] In the prior art:

[0035] 1. By applying nonlinear active media on the entire metasurface to generate high-order harmonics, a larger PB phase can be generated in the high-order harmonics.

[0036] For details, see Figure 1 , where a is a schematic diagram of a meta-atom, the material is set to gold, and it is embedded in an isotropic nonlinear medium.

[0037] When the meta-atom is excited by the circularly polarized incident field, an equivalent nonlinear dipole moment can be formed:

[0038]

[0039] Where ω is the angular frequency of the incident fundamental frequency beam, is the nth harmonic nonlinear polarizability tensor of the meta-atom at the direction angle θ. represents the incident fundamental frequency light beam propagating along the +z direction, whose circular polarization state is σ, and σ=±1 represents left-handed or right-handed circular polarization state respectively.

[0040] When the local coordinate system (x′, y′) is rotated by an angle θ relative to the experimental coordinate system (x, y), the fundamental beam acquires a geometric phase due to the spin-rotation coupling effect:

[0041]

[0042] Where L represents the local coordinate system of the meta-atom. In the local coordinate system, Therefore, the nth harmonic nonlinear dipole moment can be given by:

[0043]

[0044] The above nonlinear dipole moment can be decomposed into two in-plane rotating dipoles (circular polarization states σ and -σ):

[0045]

[0046] Equation (4) can be converted back to the experimental coordinate system (x, y):

[0047]

[0048] Therefore, the nonlinear polarizability of the meta-atom can be expressed as:

[0049]

[0050] In the prior art, the material constitutive relationship is

[0051] D=ε 0 E+P (9)

[0052] Where D is the electric displacement vector, ε 0 is the dielectric constant of vacuum, E is the electric field vector, and P is the polarization intensity.

[0053] In nonlinear optics, the relationship between the nonlinear polarizability α and P can be described by the following formula:

[0054] P=ε 0 αE+ε 0 α 2 E 2 +ε 0 α 3 E 3 +... (10)

[0055] Substituting (10) into (9) yields:

[0056] D=ε 0 E+ε 0 αE+ε 0 α 2 E 2 +ε 0 α 3 E 3 +... (11)

[0057] Equation (11) can be understood as the electric field E generating high-order harmonics E in the nonlinear active medium. n , the electric susceptibility is the coupling coefficient. The electric susceptibility in equations (7) and (8) is a multiple of the PB phase, so a high-order PB phase can be generated at high-order harmonics.

[0058] From equations (7) and (8), it can be seen that the PB phases (n-1)iσθ and (n+1)iσθ are introduced into the nth-order harmonics with the same and opposite circular polarization to the fundamental beam, respectively.

[0059] After applying nonlinear active material to the metasurface, third harmonics are generated, such as Figure 1 As shown in (b), the phase of the third harmonic PB with circular polarization opposite to the fundamental beam is 4iσθ.

[0060] 2. Use meta-atoms with high rotational symmetry to produce larger PB phases.

[0061] See also Figure 2 , Figure 2 Schematic diagram of a meta-atom composed of rectangular, equilateral triangle and regular pentagonal holes. When left-handed circularly polarized light is incident, the PB phases of right-handed circularly polarized light in the outgoing field are 2φ, 6φ and -10φ respectively.

[0062] This scheme uses the equivalent principal axis of the equivalent medium theory to explain the above phenomenon, see Figure 3 , Figure 3is a meta-atom in a square lattice. The double arrows indicate the direction of the equivalent principal axis. The equivalent principal axis rotation angle of the meta-atoms with C1 and C2 rotational symmetry is approximately equal to the rotation angle of the meta-atoms. However, for meta-atoms with higher rotational symmetry, there are multiple corresponding relationships between the equivalent principal axis and the meta-atom rotation angle, which can achieve higher-order PB phases.

[0063] In the metasurfaces disclosed in the above two schemes, the orientation of the meta-atoms is fixed and the PB phase is fixed, so the PB phase cannot be dynamically controlled and the propagation characteristics of the light beam cannot be dynamically changed as needed.

[0064] Unlike traditional optical elements that need to gradually accumulate phase changes during light propagation, metasurfaces can introduce nearly abrupt phase differences in devices with subwavelength thickness. Pancharatnam-Berry (PB) phase can achieve this regulation. Different abrupt phase differences can be achieved by changing the orientation angles of meta-atoms of the same size. PB phase metasurfaces can be used to design holographic imaging, superlenses, and vortex light generators. When the polarization state of a light wave undergoes periodic changes during the spin-orbit interaction, a PB phase is generated, and its size and sign are determined by the cyclic trajectory on the Poincare sphere. Therefore, the PB phase can be precisely adjusted by changing the polarization state of the input and output, or by designing the evolution of polarization in the optical system.

[0065] Based on the above principle, the present invention discloses a metasurface that achieves phase gradient magnitude change through interlayer twisting.

[0066] Example

[0067] like Figure 8 A metasurface that achieves phase gradient magnitude variation by interlayer twisting, including a multi-layer isomorphic surface 2 connected to a central axis 1 by rotation, as shown in FIG. Figure 9-10 As shown, the surface 2 includes a plurality of meta-atom blocks 21 uniformly arranged along a plurality of concentric rings, and there is a spacing between the meta-atom blocks 21 located on two adjacent concentric circles. By twisting, the meta-atom blocks 21 on two adjacent layers of the surface 2 are transformed between a parallel stacking state and a vertical stacking state to realize PB phase control of the metasurface.

[0068] like Fig. 9 As shown, the number of the meta-atom blocks 21 arranged on the same concentric circle is an even number, and the central angle formed between two adjacent meta-atom blocks 21 is equal. The meta-atom blocks 21 are arranged along a circular ring so that the meta-surface can realize vortex beam output, and when the surface 2 is twisted, the meta-surface can realize the change of the topological charge of the output vortex beam. This structural feature is expressed by the q number, as follows:

[0069] The q number is defined as g(r,θ)=qθ+g 0

[0070] Wherein, θ is the polar coordinate azimuth, g is the orientation angle of the meta-atom block 21 relative to the X-axis, and g 0 is the fixed initial orientation angle of the meta-atom block 21, r is the radius of the concentric circle where the meta-atom block 21 is located, q is a constant, and g(r,θ) is the rotation angle of the meta-atom block 21 around its own center at the corresponding position. Specifically, Fig. 9 The orientation angle of the element block 21 in the Sure; Fig.10 The meta-atomic block 21 in the Fig. 9 The orientation angle of the meta-atom block 21 in is the same, but the orientation angle of the meta-atom block 21 is determined according to q=1.

[0071] When implementing it, Figure 9-10 As shown, by twisting, the meta-atomic blocks 21 on two adjacent layers of surfaces 2 are transformed between a parallel stacking state and a vertical stacking state, thereby realizing dynamic control of the PB phase of the metasurface.

[0072] The surface 2 mentioned above also includes a substrate 22, and the meta-atom block 21 is arranged on the substrate 22, and the substrate 22 has a central hole, and the central hole is connected to the central axis 1 through a bearing. This embodiment takes a metasurface composed of two layers of surfaces 2 as an example to show the steps of regulating the PB phase of the metasurface. Specifically, the meta-atom block 21 of the first layer of surface 2 is fixed on one of the substrates 22, and the meta-atom block 21 of the second layer of surface 2 is fixed on the other substrate 22, and the meta-atom blocks 21 on the two layers of surfaces 2 are stacked in parallel, and one of the substrates 22 is twisted so that the meta-atom blocks 21 on the two substrates 22 are stacked in a vertical state, and then one of the substrates 22 is twisted so that the meta-atom blocks 21 on the two substrates 22 are stacked in parallel so that the meta-atom blocks 21 on the two substrates 22 are mutually transformed between the parallel stacking state and the vertical stacking state to realize the dynamic regulation of the PB phase of the metasurface. In practical applications, vortex beams can be used for optical communication, optical tweezers, etc. By changing the topological charge of the vortex beam, the communication capacity can be increased and the angular velocity of the optical tweezers can be changed.

[0073] Verification Example

[0074] The PB phase of the metasurface is calculated when the meta-atomic blocks 21 on two adjacent layers of the surface 2 are in parallel stacking and vertical stacking. Specifically, the simulation uses periodic boundary conditions to simulate the following: Figure 11-12 The periodic metasurface with a lattice constant of 1.5a is composed of the meta-atomic blocks 21 in parallel stacking and vertical stacking. The incident port is set to left-handed circularly polarized light, the receiving port is set to right-handed circularly polarized light, the simulation wavelength is set to 632.8nm, the reference length a=353.52nm, and the material of the meta-atomic block 21 is TiO 2, the rest of the materials are set to SiO 2 , their refractive indices are n TiO2 =2.39, n SiO2 =1.46.

[0075] get Figure 13-14 The phase change of Arg (S21) during the transmission process describes the phase delay of the output right-handed circularly polarized light relative to the input left-handed circularly polarized light during the transmission process, representing the PB phase. The triangle represents the PB phase data calculated by simulation, and the solid line is the data fitting line. Figure 13-14 As shown in the phase diagram, the PB phase of the meta-atom block 21 in a parallel stacking state and the meta-atom block 21 in a vertical stacking state has a dual dependence on the orientation angle, N=2, where N is defined as:

[0076]

[0077] Similarly, using periodic boundary conditions, we simulated Fig.15 The vertically stacked meta-atom blocks 21 shown are oriented toward the angular space-varying periodic metasurface, with a lateral period of 7.5a and a longitudinal period of 0.94a. All stacked meta-atom blocks 21 are rotated synchronously, and the incident port is set to left-handed circularly polarized light, which is incident on the entire periodic structure, and the receiving port is set to right-handed circularly polarized light, and the receiving range is a single meta-atom block 21 in the periodic structure.

[0078] The simulation results are as follows Fig.16 As shown, the PB phase has a four-fold dependence on the orientation angle, N = 4, and a larger PB phase is achieved by changing the lattice spacing.

[0079] Fig. 9 Front view of the metasurface designed for this scheme, Figure 4-5 As shown, the meta-atomic blocks 21 are stacked in parallel at different orientation angles. The meta-atomic blocks 21 are arranged on two concentric rings. Specifically, the arrangement along the rings can realize the output of vortex beams, and the topological charge of the output vortex beams can be changed by twisting. The inner ring radius is 1.26a, and the outer ring radius is 2.544a. According to Fig.13 From the phase dependence shown, it can be seen that when the orientation angle of the parallel stacked meta-atomic blocks 21 changes by 180°, the PB phase of the control field changes by 360° accordingly. Fig. 9 The right-handed circularly polarized light outgoing field of the metasurface shown is a Fig.17 The 360° vortex shown in Figure 1 is a 360° vortex. Figure 8 As shown in FIG. 1 , when the surface 2 of the lower layer is physically twisted 180° relative to the surface 2 of the upper layer, the resulting metasurface is as shown in FIG. Fig.10 As shown, it is oriented at different angles. Figure 6-7 The figure shows a structure of a plurality of element blocks 21 arranged at different orientation angles and stacked vertically. Figure 15-16 It can be seen that the orientation angle of the vertically stacked meta-atomic block 21 changes by 180°, and the PB phase of the control field changes by 720° accordingly. Fig.10 The right-handed circularly polarized light outgoing field of the metasurface shown is a Fig.18 The vortex changes by 720° as shown in the figure. In the figure, l represents the vortex optical topological charge. Fig.17 The topological charge of is 1. Fig.18 The topological charge of is 2.

[0080] In summary, by twisting, the meta-atomic blocks 21 constituting the surface 2 can be cleverly changed between a parallel stacking state and a vertical stacking state, thereby achieving dynamic control of the PB phase.

[0081] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, technicians familiar with the field may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A metasurface that achieves phase gradient magnitude variation through interlayer twisting, characterized in that: The invention comprises a multi-layer isomorphic surface (2) connected to a central axis (1) by rotation, wherein the surface (2) comprises a plurality of meta-atomic blocks (21) uniformly arranged along a plurality of concentric rings, and a spacing exists between the meta-atomic blocks (21) located on two adjacent concentric circles, and the meta-atomic blocks (21) on two adjacent layers of the surface (2) are transformed between a parallel stacking state and a vertical stacking state by twisting.

2. The metasurface with phase gradient magnitude variation achieved by interlayer twisting according to claim 1, characterized in that: The number of the meta-atom blocks (21) arranged on the same concentric circle is an even number, and the central angle formed between two adjacent meta-atom blocks (21) is equal.

3. The metasurface with phase gradient variation achieved by interlayer twisting according to claim 2, characterized in that: The position of each of the meta-atomic blocks (21) on the surface (2) in the spatial coordinates is defined as follows: g(r,θ)=qθ+g0 In the formula, θ is the polar coordinate azimuth, g is the orientation angle of the meta-atom block (21) relative to the X-axis, g0 is the fixed initial orientation angle of the meta-atom block (21), r is the radius of the concentric circle where the meta-atom block (21) is located, q is a constant, and g(r,θ) is the rotation angle of the meta-atom block (21) around its own center at the corresponding position.

4. The metasurface with phase gradient variation achieved by interlayer twisting according to any one of claims 1 to 3, characterized in that: The surface (2) further comprises a substrate (22), the meta-atomic block (21) is arranged on the substrate (22), the substrate (22) has a central hole, and the central hole is connected to the central axis (1) via a bearing.

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