Metasurface construction method for generating any perfect vector vortex beam on high-order Poincare sphere

Abstract

The invention discloses a metasurface construction method for generating any perfect vector vortex beam on a high-order Poincare sphere, relates to the field of metasurface light field regulation and control, and aims to solve the problem that the amplitude and phase of orthogonal circularly polarized light cannot be accurately controlled when a metasurface is constructed in the prior art. The device is formed by alternately arranging two pairs of TiO2 nano columns, and based on the interference effect related to circular polarization between different nano units, the transmission phase and the geometric phase of the nano units are modulated at the same time, so that the complex amplitude of a transmission light field under left-hand circular polarization and right-hand circular polarization incident light can be accurately regulated and controlled. On the basis, a representation method of a light beam on a high-order Poincare sphere is analyzed, longitude and latitude coordinates of the light beam are in one-to-one correspondence with transmission light, and by controlling the amplitude ratio and the phase difference of a perfect vortex light beam of an orthogonal circular polarization channel, the characteristic that linearly polarized light can be decomposed into left-hand circularly polarized light and right-hand circularly polarized light is utilized; and a perfect vector vortex light beam is successfully generated when x-ray polarized light is incident.

Description

Technical Field

[0001] The present invention relates to the field of metasurface light field control technology, and specifically to a metasurface construction method for generating arbitrary perfect vector vortex beams on a high-order Poincare sphere. Background Art

[0002] Perfect vector vortex beams (PVVBs), as a special type of vector vortex beam, not only possess a spiral phase, annular intensity distribution, and non-uniform polarization distribution, but also possess a bright ring radius that is unaffected by topological charge and carry both spin angular momentum and orbital angular momentum. Due to their unique optical properties, PVVBs have broad application prospects in information processing, quantum communication, and high-precision imaging. PVVBs can be characterized using points on the surface of high-order Poincaré spheres (HOPS), where the two levels of a HOPS represent two orthogonal circularly polarized perfect vortex beams (PVBs). Each point on the sphere surface can be represented as a linear superposition of these two PVBs. Generally speaking, PVVBs can be generated using spatial light modulators or traditional interferometric systems. However, these systems suffer from large size, low integration, and sensitivity to alignment errors, making them difficult to meet the demands of miniaturization of photonic devices and system-on-chip integration.

[0003] Metasurfaces, with their nanoscale structural units' ability to coordinately control the amplitude, polarization, and phase of light fields in multiple dimensions, have broken through the bottleneck of the aforementioned traditional generation methods and achieved PVVBs by superimposing different PVBs. However, existing research generates different PVVBs by switching the polarization state of the incident light to change the amplitude of two orthogonal circularly polarized PVBs, but cannot directly control the amplitude of the transmitted light. Furthermore, genetic algorithms are used to optimize the unit structure to generate PVVBs with constant intensity, arbitrary polarization, and phase distribution under the incidence of linearly polarized light at a certain angle. This process is relatively complex and places strict demands on the angle of the incident light.

[0004] Therefore, it is necessary to design a metasurface that can precisely control the amplitude and phase of orthogonal circularly polarized light to obtain arbitrary PVVBs on HOPS. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the existing defects and provide a metasurface construction method for generating arbitrary perfect vector vortex beams on a high-order Poincare sphere, which can effectively solve the problems in the background technology.

[0006] To achieve the above objectives, the present invention discloses a method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere. The technical solution adopted is as follows:

[0007] Step 1: constructing a metasurface by using a tetraatomic supramolecule, wherein the supramolecule includes nanopillars A, nanopillars B, and a substrate, and is used to adjust the amplitude and phase of the transmitted linearly polarized light;

[0008] Step 2: Determine the longitude and latitude coordinates of the desired PVVB on the HOPS and obtain the amplitude and phase difference of the transmitted circular polarization channel;

[0009] Step 3: Determine the E1, E2, and

[0010] Step 4, calculate the phase shift and rotation angle required for nanopillars A and B through the Jones matrix of the metasurface;

[0011] Step 5: Construct a nanopillar structure unit, calculate the phase and amplitude response of the unit structure to a specific incident light using finite element analysis software (FDTD), build a database of the unit structure's geometric dimensions and transmission phase, and further determine the structural parameters of the structure unit;

[0012] In step 6, the phase obtained in step 4 is matched one-to-one with the size and rotation angle of the metastructure unit in step 5, and nanopillars A and nanopillars B are combined to construct a metasurface, which can precisely control the amplitude and phase of orthogonal circularly polarized light. The representation of the light beam on the HOPS is matched one-to-one with the transmitted light, providing a simple, feasible and flexible method for generating arbitrary PVVBs on the HOPS, which is conducive to the construction of a compact and highly integrated nanophotonics platform.

[0013] As a preferred technical solution of the present invention, in step 1, nanopillars A and nanopillars B are TiO2 nanopillars; the substrate is a SiO2 square substrate. The use of TiO2 nanopillars and SiO2 substrate avoids the high ohmic loss of metal at optical frequencies.

[0014] As a preferred technical solution of the present invention, it is characterized in that: in step 1, the linearly polarized light is a superposition of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light of equal amplitude. When the x-linearly polarized light is incident on the constructed metasurface, the transmitted light Ψ(x, y) can be expressed as:

[0015]

[0016] Among them, E1 and E2 are the amplitudes of LCP and RCP components, The phase representing the LCP and RCP components is controlled jointly by the transmission phase and the geometric phase, which can completely decouple the LCP and RCR, while generating a beam with high efficiency.

[0017] As a preferred technical solution of the present invention, in step 2, the longitude and latitude coordinates of the PVVB on the HOPS are (ψ, χ). The points on the HOPS can represent PVBs of any polarization state, and the expression is:

[0018]

[0019] Where, |PVB R ,l m > and | PVB L ,l n >Represents the PVBs of RCP distribution and LCP distribution, where each beam carries a topological charge of l m and l n ; cos(χ / 2) and sin(χ / 2) are the amplitudes of the two beams; ψ is the phase difference between the two beams.

[0020] As a preferred technical solution of the present invention, in step 4, the expression of the Jones matrix J(x,y) of the hypersurface is:

[0021]

[0022] in, As a preferred technical solution of the present invention, the expression of J(x,y) is calculated according to formula (3);

[0023] The amplitude E 1，2 (x,y) and phase Decomposed into nano-unit A and nano-unit B, and expressed as:

[0024]

[0025] The amplitude of orthogonal circularly polarized light can be expressed as

[0026]

[0027] Phase is

[0028]

[0029] and are the phases of nanopillar A and nanopillar B under LCP and RCP incident light, respectively;

[0030] The Jones matrix J(x,y) of the metasurface can be expressed as the Jones matrix J of nanopillars A and B.A (x,y) and J B (x,y) represents;

[0031] By solving the eigenvalue equations of the two Jones matrices, the eigenvalues and eigenvectors of the two matrices are obtained respectively, and the phase delay and rotation angle distribution of the two nanounits, nanopillar A and nanopillar B, are derived as follows:

[0032]

[0033] As a preferred technical solution of the present invention, the structural parameters in step 5 include a major semi-axis, a minor semi-axis, a height, and a period.

[0034] Compared with the existing technology, the beneficial effects of the present invention are: the metasurface construction method proposed in this technical solution can accurately control the amplitude and phase of orthogonal circularly polarized light, and make a one-to-one correspondence between the representation of the light beam on the HOPS and the transmitted light, providing a simple, feasible and flexible method for generating arbitrary PVVBs on the HOPS, which is conducive to the construction of a compact and highly integrated nanophotonics platform; the use of TiO2 nanorods and SiO2 substrates avoids the high ohmic loss of metals at optical frequencies; the joint regulation of transmission phase and geometric phase can completely decouple LCP and RCR, and at the same time generate light beams with high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of the function of the metasurface construction method of the present invention;

[0036] Figure 2 is the transmittance of the nanometer unit of the present invention along the x-polarized light at a wavelength of 633 nm;

[0037] Figure 3 The nanometer unit of the present invention is delayed along the x phase at a wavelength of 633 nm;

[0038] Figure 4 is the transmittance of the nanometer unit of the present invention along the y-line polarized light at a wavelength of 633 nm;

[0039] Figure 5 is the phase delay of the nanometer unit of the present invention along the y-line polarized light at a wavelength of 633 nm;

[0040] Figure 6 The transmittance and phase delay of the nanometer unit are selected in the embodiment of the present invention;

[0041] Figure 7 Schematic diagram of the three-dimensional structure of the tetraatomic molecule of the present invention;

[0042] Figure 8 Schematic diagram of the top view of the tetraatomic molecule of the present invention;

[0043] Figure 9 Specific PVVBs generated on HOPS according to an embodiment of the present invention;

[0044] Figure 10 This is the electric field intensity distribution of the generated PVVBs and the change in electric field intensity of the light beam passing through different linear polarizers in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] Example 1

[0047] like Figures 1 to 10 As shown, the present invention discloses a method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere. The technical solution adopted is as follows:

[0048] Step 1: The metasurface is composed of a tetraatomic supramolecule, wherein the supramolecule includes two pairs of alternating TiO2 nanopillars A and nanopillars B and a SiO2 substrate. The substrate is square and can adjust the amplitude and phase of the transmitted circularly polarized light.

[0049] Since linearly polarized light can be regarded as a superposition of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light of equal amplitude, when x-polarized light is incident on the metasurface, the transmitted light Ψ(x,y) can be expressed as:

[0050]

[0051] Among them, E1 and E2 are the amplitudes of LCP and RCP components, Represents the phase of the LCP and RCP components.

[0052] Step 2: Determine the longitude and latitude coordinates (ψ, χ) of the desired PVVB on the HOPS, and obtain the amplitude and phase difference of the transmitted circular polarization channel;

[0053] It is known that the points on HOPS can represent PVBs of any polarization state, namely:

[0054]

[0055] Where, |PVB R ,l m > and | PVBL ,l n >Represents the PVBs of RCP distribution and LCP distribution, where each beam carries a topological charge of l m and l n ; cos(χ / 2) and sin(χ / 2) are the amplitudes of the two beams; ψ is the phase difference between the two beams;

[0056] Step 3: Determine the E1, E2, and

[0057] Step 4: Calculate the phase shift and rotation angle required for nanopillar A and nanopillar B;

[0058] Specific operations include:

[0059] The Jones matrix J(x,y) of the hypersurface can be expressed as:

[0060]

[0061] in,

[0062] According to formula (3), calculate the expression of J(x,y);

[0063] Furthermore, the amplitude E 1，2 (x,y) and phase Decomposed into the expression of nano unit A and nano unit B

[0064]

[0065] The amplitude of orthogonal circularly polarized light can be expressed as

[0066] Phase is

[0067] and The phases of nanopillar A and nanopillar B under LCP and RCP incident light, respectively.

[0068] Therefore, the Jones matrix J(x,y) of the metasurface can be expressed as the Jones matrix J of nanopillars A and B. A (x,y) and J B (x,y) represents.

[0069] By solving the eigenvalue equations of the two Jones matrices, the eigenvalues and eigenvectors of the two matrices are obtained respectively, and then the phase delay and rotation angle distribution of the two units A and B are derived as follows:

[0070]

[0071] Step 5: Design the TiO2 nanocolumn structural unit, calculate the phase and amplitude response of the unit structure to specific incident light through finite element analysis software (FDTD), build a database of the unit structure's geometric dimensions and transmission phase, and further determine the structural parameters of the structural unit, including the major and minor axes, height, and period.

[0072] Step 6: Match the phase calculated in step 4 with the metacell size and rotation angle determined in step 5, and combine nanopillars A and B to construct the metasurface.

[0073] The working principle of the present invention is as follows: Figure 1 As shown, the metasurface can regulate the amplitude and phase of the transmitted orthogonal circularly polarized light, and can generate a specific PVVB at the Fourier plane position based on the superposition of the transmitted channels under x-polarized light.

[0074] In order to select suitable nanopillars, Figure 2-Figure 5 In this work, FDTD was used to simulate and calculate the transmittance and phase delay of the meta-unit under x- and y-polarized light incidence, where the height of the nanopillars is H = 600 nm, the lattice constant period is P = 380 nm, the operating wavelength is λ = 633 nm, and the boundary conditions of the structural unit along the x- and y-directions are set to periodic boundary conditions, and the boundary condition along the z-axis is set to a perfectly matched layer.

[0075] According to formulas (5) and (6), the phase difference of the polarized light along the x and y lines of the nanometer unit should be equal to π, that is, the function of a half-wave plate is realized, so Figure 2 The eight nanometer units marked in the figure are used as the basic units for constructing the metasurface of the present invention, and are Figure 6 The transmittance and phase retardation corresponding to the optimized selection of nanopillars are characterized in the figure. The figure shows that the transmittance of all eight nanopillars exceeds 80%, while the phase difference between x- and y-polarized light approaches π, and highly efficient polarization conversion is achieved. Therefore, the eight nanopillars described above constitute a complete structural unit set.

[0076] In order to further encode the independent amplitude and phase into two orthogonal circular polarization channels, according to formula (4), it is necessary to use Figure 6 The optimized 8 nanopillars are selected to construct a supermolecule composed of four nanounits, where each supermolecule contains two types of rectangular nanounits A and B arranged alternately, with the structure as shown in Figure 7 and Figure 8 shown.

[0077] Next, in order to generate second-order PVVB, the above-mentioned four-atom arrangement structure was used to construct an all-dielectric transmission metasurface with a size of 25μm×25μm, where the operating wavelength λ=633nm.

[0078] It is known that PVVB can be generated by the linear superposition of two orthogonal circularly polarized PVBs with opposite topological charges. Therefore, it is necessary to use metasurfaces to generate amplitude- and phase-adjustable PVBs under LCR and RCP incident light, respectively.

[0079] Since PVB can be obtained by Fourier transforming a Bessel-Gaussian beam, i.e., the incident Gaussian beam passes through a spiral phase plate, a conical lens, and a Fourier lens in sequence, the metasurface in the present invention can replace the above three optical elements. Therefore, the phase distribution of the metasurface under orthogonal circularly polarized light should satisfy:

[0080]

[0081] Where l1 and l2 are the topological charges carried by the transmitted RCP and LCP channels when LCP and RCP are incident, d represents the focal length of the conical lens, which is used to control the spot radius of the PVB, f is the focal length of the Fourier lens, and λ represents the working wavelength of the metasurface. is the phase difference between the transmitted RCP and LCP components.

[0082] In order to obtain the second-order PVVB, the parameters in the formula are set to l1=-l2=2,

[0083] d=4μm, λ=633nm, f=80μm.

[0084] Therefore, when x-polarized light is irradiated onto the metasurface, the transmitted light field satisfies:

[0085]

[0086] Then, according to formula (2), the amplitude ratio of the transmitted channel beam can be controlled to produce Figure 9 PVVBs at the middle marked point.

[0087] To generate Figure 9 Taking the PVVB represented by the midpoint i as an example, substituting its longitude and latitude coordinates into formula (2), we can obtain that the amplitudes of the transmitted RCP and LCP components are cos(π / 4) and sin(π / 4), respectively, and the corresponding phase difference is 0.

[0088] Then, the obtained values are matched one by one with formula (8), and E1, E2,

[0089] Therefore, based on the above parameters, a metasurface can be constructed to generate Figure 9 Point i represents the light beam.

[0090] Through the above steps, the super surface can be further constructed Figure 9 Midpoints ii, iii, iv of the beam. Figure 6 The first column represents the generated Figure 5 The electric field intensity distribution of the midpoints i, ii, iii, and iv of the light beam at the Fourier plane (xy plane at z = 80 μm) shows that the electric field intensity is uniformly distributed in a ring shape, and the spot radius is equal.

[0091] Next, in order to further analyze the characteristics of different PVVBs, the generated PVVBs were passed through a linear polarizer at an angle α to the x-axis to observe the change in the electric field intensity of the light beam. The angle of the linear polarizer α was set to 0°, 45°, 90° and 135° respectively, and the transmitted light intensity of the generated PVVBs through different linear polarizers was as follows: Figure 10 The second, third, fourth and fifth columns are shown.

[0092] It can be clearly observed from the figure that the electric field intensity of the light beam presents a four-lobe distribution. At the same time, the light beam rotates with the rotation of the linear polarizer.

[0093] In addition, the rotation angle (i.e., latitude) of the beam from the HOPS equator is 4 times the rotation angle of the beam spot passing through the linear polarizer. Specifically, when the latitude coordinate of the beam on the HOPS changes by π / 2 (corresponding to Figure 10 The first and second rows and the third and fourth rows) indicate that when the light beam evolves from point i to point ii or from point iii to point iv, the rotation angle of the PVVBs spot passing through the linear polarizer is π / 8; when the latitude changes by π, that is, when the light beam evolves from point i to point iii or from point ii to iv, the rotation angle of the transmitted spot is π / 4 (corresponding to Figure 10 1st, 3rd, 2nd, and 4th rows).

[0094] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A metasurface construction method for generating arbitrary perfect vector vortex beams on a high-order Poincare sphere, characterized in that: The following steps are involved: Step 1: constructing a metasurface by using a tetraatomic supramolecule, wherein the supramolecule includes nanopillars A, nanopillars B, and a substrate, and is used to adjust the amplitude and phase of the transmitted linearly polarized light; Step 2: Determine the longitude and latitude coordinates of the desired PVVB on the HOPS and obtain the amplitude and phase difference of the transmitted circular polarization channel; Step 3: Determine the E1, E2, and Step 4, calculate the phase shift and rotation angle required for nanopillars A and B through the Jones matrix of the metasurface; Step 5: Construct a nanopillar structure unit, calculate the phase and amplitude response of the unit structure to a specific incident light using finite element analysis software (FDTD), build a database of the unit structure's geometric dimensions and transmission phase, and further determine the structural parameters of the structure unit; In step 6, the phase obtained in step 4 is matched one-to-one with the size and rotation angle of the metastructure unit in step 5, and nanopillars A and nanopillars B are combined to construct a metasurface.

2. The method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere according to claim 1, characterized in that: In step 1, nanopillars A and nanopillars B are TiO2 nanopillars and the substrate is a SiO2 square substrate.

3. The method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere according to claim 1, characterized in that: In step 1, the linearly polarized light is a superposition of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light of equal amplitude. When the x-linearly polarized light is incident on the constructed metasurface, the transmitted light Ψ(x,y) can be expressed as: Among them, E1 and E2 are the amplitudes of LCP and RCP components, Represents the phase of the LCP and RCP components.

4. The method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere according to claim 1, characterized in that: In step 2, the longitude and latitude coordinates of PVVB on HOPS are (ψ,χ). Points on HOPS can represent PVBs of any polarization state, and the expression is: Where, |PVB R ,l m > and | PVB L ,l n >Represents the PVBs of RCP distribution and LCP distribution, where each beam carries a topological charge of l m and l n ; cos(χ / 2) and sin(χ / 2) are the amplitudes of the two beams; ψ is the phase difference between the two beams.

5. The method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere according to claim 1, characterized in that: In step 4, the expression of the Jones matrix J(x,y) of the hypersurface is: in, 6. The method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere according to claim 5, characterized in that: According to formula (3), calculate the expression of J(x,y); The amplitude E 1，2 (x,y) and phase Decomposed into nano-unit A and nano-unit B, and expressed as: The amplitude of orthogonal circularly polarized light can be expressed as Phase is and are the phases of nanopillar A and nanopillar B under LCP and RCP incident light, respectively; The Jones matrix J(x,y) of the metasurface can be expressed as the Jones matrix J of nanopillars A and B. A (x,y) and J B (x,y) represents; By solving the eigenvalue equations of the two Jones matrices, the eigenvalues and eigenvectors of the two matrices are obtained respectively, and the phase delay and rotation angle distribution of the two nanounits, nanopillar A and nanopillar B, are derived as follows:

7. The method for constructing a metasurface for generating an arbitrary perfect vector vortex beam on a high-order Poincare sphere according to claim 1, characterized in that: The structural parameters in step 5 include the major semi-axis, minor semi-axis, height, and period.

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