Method for manipulating arbitrary optical trajectories and their longitudinal polarization changes based on on-chip metasurfaces

Abstract

The application discloses a method for manipulating arbitrary optical trajectories and longitudinal polarization changes based on a super surface on a chip. The application first integrates a two-dimensional array of square nanostructures in a unit structure on a super surface on a chip above a waveguide, designs displacement of each nano brick based on a detour phase principle to meet mapping of points on a trajectory from a transverse phase to a longitudinal phase, thereby extracting a guided wave to free space and shaping into an arbitrary optical trajectory; the application uses a super surface on a chip composed of double-atom nano bricks arranged orthogonally in a unit structure to realize simultaneous and independent control of a wave front and polarization of the extracted guided wave, and finally designs and experimentally realizes an arbitrary optical trajectory with a longitudinal predefined polarization state change. The optical trajectory obtained by the application is not interfered by zero-order diffraction and has a high signal-to-noise ratio; the method can extend the application of the optical trajectory in the fields of complex optical manipulation, advanced laser manufacturing, microscopic imaging and biophysics, and provide a new photonic chip manipulation platform.

Description

Technical Field

[0001] This invention belongs to the fields of micro-nano optics and integrated photonics, and particularly relates to a method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces. Background Technology

[0002] The study of self-accelerating optical trajectories has broad application potential in fields such as microfabrication, optical tweezers, photoelasticity, and medical imaging, thus attracting great interest. Among these, Bessel-like beams, as a novel type of self-accelerating beam, can propagate along predefined arbitrary trajectories and possesses three characteristics: self-acceleration, diffraction-free propagation, and self-healing, thus revealing an emerging research direction. Traditional optical devices, such as spatial light modulators, can be used to generate Bessel-like beams. However, these devices are bulky, have low diffraction efficiency, and lack flexible trajectory control capabilities. These shortcomings make them difficult to miniaturize and integrate into chips, hindering their multifunctional practical applications. The emergence of metasurfaces with ultrathin planar structures alleviates these problems and provides a method for generating self-accelerating beams by modulating free-space light. However, the above scheme relies on the incident beam directly illuminating the phase plane, so the quality of the generated beam may be affected by strong background light.

[0003] Recently, some hot research has focused on integrating metasurfaces onto optical waveguides (called on-chip metasurfaces) to manipulate guided waves, providing a new approach for micro-system-on-a-chip (SPC) and integrated photonic devices, and enabling various functions and applications, including on-chip superlenses, on-chip multiplexed holographic displays, vortex light generators, augmented reality displays, and screen displays. In particular, due to the on-chip optical propagation mechanism, the holographic display and imaging functions of on-chip metasurfaces are uniquely free from zero-order background interference, producing images with high contrast and quality. Most current work and efforts in this field focus on achieving holographic or near-field displays, but methods for manipulating arbitrary optical trajectories on such novel on-chip platforms have not yet been realized and remain to be explored. Furthermore, manipulating optical parameters along light trajectories on-chip also shows great promise, but due to a lack of coding freedom and feasible solutions, this technology is still in its infancy. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to integrate an optical waveguide with a metasurface composed of an array of nanostructures and to realize a method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on an on-chip metasurface.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] In a first aspect, the present invention provides a design method for realizing arbitrary optical trajectories and their longitudinal polarization changes based on on-chip metasurfaces, comprising the following steps:

[0007] S1: A metasurface is formed by arranging silicon nanounit structures into a two-dimensional periodic array; the silicon nanounit structure includes a single nanobrick and a waveguide and substrate below it;

[0008] S2: Establish an xoy coordinate system with the two sides parallel to the working surface of the optical waveguide layer, designated as the x-axis and y-axis respectively; the sides of the silicon nanounit structure are parallel to the x-axis and y-axis; the metasurface is used to extract guided waves to free space; for guided waves propagating along the x-direction, the working wavelength is λ, and the corresponding period P is calculated based on the waveguide propagation constant β. x P x The period of the silicon nanounit structure along the x-axis;

[0009] S3: The positional arrangement of the nanobricks is calculated using the principle of detour phase;

[0010] S4: After the guided wave from step S2 passes through the on-chip metasurface array, it is point-mapped along the z-direction to obtain a preset light trajectory intensity distribution in the free space above the waveguide.

[0011] S5: Achieving arbitrary light trajectories and their longitudinal polarization variations: Replace the individual nanobricks in step S1 with orthogonally and staggered biatomic nanobricks; wherein, the spacing between the biatomic nanobricks along the x-direction is designed as P. x / 2, the spacing between the two-atom nanobricks along the y-direction is designed as P y / 2; The overall displacement of each pair of diatomic nanobricks is also calculated using the detour phase principle, and the phase distribution of the corresponding trajectory is also obtained using the calculation method in step S3; The polarization state of the guided wave is modulated by setting the rotation angle of the diatomic nanobricks;

[0012] S6: Following the calculation process described in step S5, the positional arrangement and corresponding rotation angle of all the two-atom nanostructures are encoded to obtain the final on-chip metasurface two-dimensional array.

[0013] S7: Following the same method as in step S4, a guided wave with wavelength λ is incident along the x-direction. After passing through the on-chip metasurface array in step S6, the same light trajectory intensity distribution as preset in step S4 is obtained in the free space above the waveguide, and a linear polarization state distribution that varies along the transmission path is obtained.

[0014] Furthermore, in step S1, the nanobrick is a cuboid with a square top surface, and its period is a square formed by the projection of the waveguide and the substrate below it, with an area larger than the top surface of the nanobrick.

[0015] Furthermore, in step S4, any point on the trajectory in free space is regarded as the vertex of a conical beam of light emitted from a circle on the metasurface plane, and interference occurs along a predefined path, thereby creating an arbitrary light trajectory intensity distribution.

[0016] Furthermore, in step S3, the phase formula for calculating the positional arrangement of the nanobricks using the detour phase principle is as follows:

[0017]

[0018]

[0019] The predefined trajectory can be represented as (F, G, z) in the coordinate system, where x and y are the position coordinates of the metasurface plane, λ is the free space wavelength, and γ is the divergence factor of the Bessel-like beam.

[0020] Furthermore, in step S5, the diatomic nanobrick is composed of two identical cuboid nanobricks, with the long sides of the top surfaces of the nanobricks forming an orthogonal arrangement.

[0021] Furthermore, in step S5, the displacement of the diatomic nanobricks is defined as follows: D is the overall displacement of the diatomic structure along the x-direction from the leftmost element of the unit period within one period; S is the spacing between the diatomic nanobricks along the x-direction; and the spacing between two orthogonally arranged nanobricks along the y-direction is designed as P. y / 2.

[0022] Furthermore, in step S5, the rotation angle of the nanobrick is set using the following formula:

[0023] θ = π × z / 100 - 3π / 10

[0024] Where θ is the rotation angle of the diatomic nanobrick, the angle between the long side of the nanobrick and the x-axis, 0°≤θ≤180°, and z is the z-direction coordinate of the corresponding point on the trajectory, 30μm≤z≤100μm.

[0025] Furthermore, the arbitrary light trajectory includes, but is not limited to, parabolic, hyperbolic, and cosine types.

[0026] Secondly, the present invention provides the application of the design method described in the first aspect for realizing arbitrary optical trajectories and their longitudinal polarization changes based on on-chip metasurface manipulation in the fields of extended optical trajectories, advanced laser manufacturing, microscopic imaging, and biophysics.

[0027] The beneficial effects of this invention are as follows:

[0028] 1. The method of the present invention arranges an array of silicon nanobricks above an optical waveguide and designs the displacement of each silicon nanobrick based on a detour phase to satisfy the mapping of the transverse phase to a point on the longitudinal trajectory. This allows the guided wave to be extracted into free space and shaped into arbitrary optical trajectories (e.g., parabolic, hyperbolic, and cosine curves).

[0029] 2. The method described in this invention utilizes an on-chip metasurface composed of two orthogonally arranged diatomic nanobricks to simultaneously and independently achieve wavefront extraction and polarization control of guided waves. Therefore, based on this on-chip diatomic metasurface, an optical trajectory with a predefined longitudinal polarization state change was successfully designed and experimentally realized.

[0030] 3. The on-chip optical transmission mechanism adopted in this invention, compared with the traditional free-space metasurface, results in an optical trajectory that is not affected by zero-order diffraction, thus having a high signal-to-noise ratio. The on-chip metasurface configuration proposed in this invention has the advantages of miniaturization and multi-dimensional optical manipulation, which can expand the application of optical trajectories in complex optical manipulation, advanced laser manufacturing, microscopic imaging and biophysics, and provide them with a new photonic chip manipulation platform. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of a method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on an on-chip metasurface, provided by an embodiment of the present invention.

[0032] Figure 1 In the diagram, the height H1 of the nanobrick is 380 nm, the thickness H2 of the silicon nitride waveguide is 220 nm, and the thickness of the silicon dioxide substrate is 500 μm; L and W are the length and width of the nanobrick, θ is the rotation angle of the nanobrick, and P... x P is the period in the x-direction of the unit structure. y The period in the y-direction of the unit structure is denoted as .

[0033] Figure 2 This invention relates to an on-chip metasurface array design method for generating diffraction-free Bessel-like beams with predefined trajectories and longitudinal polarization variations. The phase... Used to generate Bessel-like beams with preset arbitrary trajectories, phase Its function is to modulate and extract the polarization state of the guided wave.

[0034] Figure 3 This is a top view of an on-chip biatomic metasurface pixel composed of two orthogonal nanorods in an embodiment of the present invention, and a simulated electric field intensity distribution diagram when a TEO mode guided wave is incident from the x-direction.

[0035] Figure 4 This is a schematic diagram of the principle of generating a light trajectory with longitudinal polarization change on the chip in an embodiment of the present invention.

[0036] Figure 5 These are scanning electron microscope (SEM) images of the samples processed and manufactured in the embodiments of the present invention.

[0037] Figure 6 This invention relates to the theoretical, simulation, and experimental characterization of three different predefined optical trajectories—parabolic, hyperbolic, and cosine—designed in the embodiments of the present invention.

[0038] Figure 7 This is an experimental measurement characterization of a parabolic light trajectory with longitudinal polarization variation in an embodiment of the present invention. Detailed Implementation

[0039] The present invention will be further described below with reference to specific embodiments and accompanying drawings. The scope of the present invention is not limited thereto.

[0040] Example

[0041] This embodiment provides a specific implementation process for a method of manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces. The steps are as follows:

[0042] S1: A metasurface is formed by arranging silicon nanounit structures into a two-dimensional periodic array; the silicon nanounit structure includes a single nanobrick and a waveguide and a substrate below it.

[0043] The nanobrick is a cuboid with a square top surface; the period is a square formed by the projection of the waveguide and the substrate below it, with an area larger than the top surface of the nanobrick.

[0044] S2: Establish an xoy coordinate system with the two sides parallel to the working surface of the optical waveguide layer, designated as the x-axis and y-axis respectively; the sides of the silicon nanounit structure are parallel to the x-axis and y-axis; the metasurface is used to extract guided waves to free space; for guided waves propagating along the x-direction, the working wavelength is λ, and the corresponding period P is calculated based on the waveguide propagation constant β. x P x The period of the silicon nanounit structure along the x-axis;

[0045] S3: The positional arrangement of the nanobricks is calculated using the principle of detour phase;

[0046] The phase formula for calculating the positional arrangement of the nanobricks using the detour phase principle is as follows:

[0047]

[0048]

[0049] The predefined trajectory can be represented as (F, G, z) in the coordinate system, where x and y are the position coordinates of the metasurface plane, λ is the free space wavelength, and γ is the divergence factor of the Bessel-like beam.

[0050] S4: After the guided wave from step S2 passes through the on-chip metasurface array, it generates a corresponding trajectory by point mapping along the z-direction, so as to obtain a preset light trajectory intensity distribution in the free space above the waveguide.

[0051] S5: Achieving arbitrary light trajectories and their longitudinal polarization variations: Replace the individual nanobricks in step S1 with orthogonally and staggered biatomic nanobricks; wherein, the spacing between the biatomic nanobricks along the x-direction is designed as P. x / 2, the spacing between the two-atom nanobricks along the y-direction is designed as P y / 2; The overall displacement of each pair of diatomic nanobricks is also calculated using the detour phase principle, and the phase distribution of the corresponding trajectory is also obtained using the calculation formula in step S3; The polarization state of the guided wave is modulated by setting the rotation angle of the nanobricks;

[0052] The diatomic nanobrick is composed of two identical cuboid nanobricks, with the long sides of the top surfaces of the nanobricks forming an orthogonal shape.

[0053] In the displacement of the diatomic nanobricks, D is defined as the overall displacement of the diatomic structure, S is the spacing between the diatomic nanobricks along the x-direction, and the spacing between two orthogonally arranged nanobricks along the y-direction is designed as P. y / 2.

[0054] The rotation angle of the nanobrick is set by the following formula:

[0055] θ = π × z / 100 - 3π / 10

[0056] Where θ is the rotation angle of the diatomic nanobrick, the angle between the long side of the nanobrick and the x-axis, 0°≤θ≤180°, and z is the z-coordinate of the corresponding point on the trajectory, 30μm≤z≤100μm. For example, if the rotation angle of one nanobrick is θ, then the rotation angle of the other nanobrick is θ+90°.

[0057] S6: Following the calculation process described in step S5, the positional arrangement and corresponding rotation angle of all the two-atom nanostructures are encoded to obtain the final on-chip metasurface two-dimensional array.

[0058] S7: Following the same method as in step S4, a guided wave with wavelength λ is incident along the x-direction. After passing through the on-chip metasurface array in step S6, a light trajectory with the same intensity distribution as preset in step S4 is obtained in the free space above the waveguide, exhibiting optical characteristics of a linear polarization state distribution that varies along the trajectory. The guided wave is extracted into free space after passing through the metasurface, forming an arbitrarily curved light trajectory in free space, such as... Figure 1 As shown.

[0059] The above method will be illustrated in more detail below:

[0060] Figure 1 Figure a schematically illustrates the generation of arbitrary optical trajectories using the proposed on-chip metasurface configuration integrated on a waveguide. Specifically, a guided wave propagating along the x-direction is extracted using an on-chip detour-phase metasurface array to generate an arbitrary predefined trajectory along the z-direction. Any point on the trajectory can be viewed as the vertex of a conical beam emanating from a circle on the metasurface plane, interfering along a predefined path to create an arbitrary optical trajectory. Furthermore, as... Figure 1 As shown in Figure b, by integrating a two-atom nanostructure array above the waveguide, it is possible to design and generate structures with similar characteristics to those shown in Figure b. Figure 1 The trajectory of a Bessel-like beam is the same as that of the beam in the image, but its polarization state changes along the propagation path. The corresponding polarization state changes near the equator of the Poincaré sphere, that is, it is mainly linearly polarized light. Figure 1 c and Figure 1 In the diagram, d is the corresponding unit structure diagram. The nanostructure that makes up the on-chip metasurface is amorphous silicon nanobricks. The optical waveguide is Si3N4 (thickness is 220nm) (other materials can also be used for the waveguide, such as lithium niobate waveguide, which has a higher refractive index than silicon dioxide). The refractive index of the waveguide is ~2.05. The substrate is a silicon dioxide layer (thickness is ~500μm). Figure 1 The nanobricks in the middle c are square, with a length and width of W = 90 nm, and periods P in the x and y directions, respectively. x =P y =400nm; Figure 1 The nanobricks in d are rectangular, with a length of L = 140 nm and a width of W = 70 nm, and the two nanobricks are perpendicular to each other.

[0061] Figure 2 This describes the design flow for on-chip metasurfaces with predefined arbitrary trajectories and polarization state changes along the propagation path. The phase superimposed on the metasurface includes phase... and phase Used to generate Bessel-like beams with preset arbitrary trajectories, phase Its function is to modulate the polarization state of the extracted guided wave. A common method for generating self-accelerating Bessel-type beams is based on a conical beam emitted from a circle on the input phase plane.

[0062] To obtain these conical beams, this embodiment uses the on-chip detour phase principle to manipulate the extracted guided wave through the displacement of nanostructures, thereby guiding the light beam to form arbitrary light trajectories. Specifically, this embodiment first calculates the phase profile required for a predefined trajectory using MATLAB. The phase formula is as follows:

[0063]

[0064]

[0065] The predefined trajectory can be represented as (F, G, z) in the coordinate system, where x and y are the position coordinates of the metasurface plane, λ is the free-space wavelength, and γ is the divergence factor of the Bessel-like beam. The trajectory coordinates and the metasurface position coordinates are in the same coordinate system.

[0066] Further according to Calculate the displacement x of the nanostructure m , where x m This indicates that the m-th nanostructure along the x-direction is in P x The displacement of the leftmost element within the period of the unit cell can ultimately be used to encode the positional arrangement of the nanostructures on the entire on-chip metasurface, thereby enabling the realization of any preset light trajectory.

[0067] Due to a single square nanobrick ( Figure 1 c) Only the phase of the extracted guided wave can be manipulated, making it difficult to achieve polarization operation along the beam trajectory. Therefore, a new design strategy for on-chip nanostructures with flexible and multi-polarization control capabilities is needed. To achieve on-chip full-phase and polarization control, this embodiment replaces a single nanobrick with two orthogonally arranged nanobricks (i.e., diatomic nanobricks), such as... Figure 1 d and Figure 3 As shown in Figure a, where D is the overall displacement of a diatomic structure along the x-direction from the leftmost edge of the unit period within a period, and S is the spacing between diatomic nanobricks along the x-direction. To avoid near-field coupling and overlap of the diatomic structures at certain locations, the spacing between two orthogonally arranged nanobricks along the y-direction is designed to be P. y / 2. Here, each nanobrick can be considered as a dipole antenna, with the polarization of the light extracted from the waveguide along the long axis of the nanobrick.

[0068] The electric field characteristics of the diatomic nanobrick were simulated using the electromagnetic simulation software FDTD Solutions, with the fundamental mode TE0 as the guiding wave. The in-plane electric field intensity |E| of the simulated diatomic nanobrick at turning angles θ=0 and θ=π / 4 was calculated. 2 The distributions are as follows: Figure 3 b and Figure 3 As shown in c. This indicates that the strongly anisotropic nanobricks respond only to light waves polarized along their long axis. When S = P x At / 2, the phase difference of the extracted light propagation between the two-atom nanobricks is This means that the phase difference between the two orthogonal field components parallel to the two nanobricks is also π. Therefore, each unit of the on-chip diatomic metasurface exhibits half-wave plate characteristics. Different orientation angles θ mean that rotating the half-wave plate by an angle θ will also cause the incident linearly polarized light to rotate by 2θ. For the TE0 mode propagating along the x-direction, it can be regarded as a linearly polarized wave in the y-direction of the plane. Therefore, arbitrary linear polarization state conversion can be achieved by simply rotating the half-wave plate composed of the above diatomic structure (i.e., rotating the entire unit structure composed of diatomic nanobricks).

[0069] In addition to polarization control via rotating the orientation angle of the diatomic nanobricks, this embodiment can also achieve additional phase modulation simultaneously and independently by designing the overall displacement D of the diatomic nanobricks. Here, the overall displacement D of the diatomic nanobricks can be determined according to... The design aims to provide the phase required to achieve a predefined arbitrary beam trajectory. Notably, by employing a one-to-one mapping between the transverse phase plane and the longitudinal propagation direction—that is, the polarization modulation design on the annulus of radius r within the metasurface phase plane—the polarization state along the beam trajectory propagation path will be correspondingly altered. To achieve the preset longitudinal polarization state change of the beam trajectory, this embodiment adds an additional polarization control term by customizing diatomic nanobricks with different orientation angles on each annulus in the transverse plane. This is also related to transmission distance. For example... Figure 4 As shown, the in-plane y-linearly polarized guided wave can be decomposed into left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) components. The phase shifts of the extracted RCP and LCP guided wave components can be expressed as follows: and When the LCP and RCP components superimpose again, it means that the guided wave can be extracted as a free-space light wave with a new linear polarization state. In summary, this embodiment can achieve this by modulating the detour phase. With polarization control By combining these methods, an on-chip two-atom metasurface can be designed, enabling the manipulation of arbitrary light trajectories and their longitudinal polarization changes.

[0070] This embodiment uses plasma-enhanced chemical vapor deposition (PECVD) and conventional electron beam lithography (EBL) to fabricate the designed on-chip metasurface integrated on the waveguide. Figure 5 a and Figure 5 Figure b shows a scanning electron microscope (SEM) image of the fabricated sample. An on-chip laser source coupled with fiber optics was used to incident the laser from the edge of the waveguide. An optical microscope with a 50x objective and a charge-coupled device (CCD) camera was used to collect the light intensity distribution of the guided wave decoupled from the on-chip metasurface and to record the position of the beam center along the propagation path.

[0071] like Figure 6 As shown, this embodiment is based on Figure 5 The experiment with sample a demonstrated three different predefined light trajectories, namely the parabolic y=z... 2 / 900, hyperbolic y = (3 × z) 2 / 16-15z+800) 1 / 2 -800 1 / 2 , as well as cosine forms y=0 (0≤z≤15μm), y=3cos(π(z-15) / 65)-3 (15μm≤z≤80μm) and y=-6 (z≥80μm). Figure 6 The AD model demonstrates the simulation and experimental results of a predefined parabolic light trajectory. Figure 6 The paper presents simulations and experimental results of a predefined hyperbolic light trajectory. Figure 6 The image shows the simulation and experimental results of a predefined cosine-type optical trajectory. As can be seen from the figure, the experimentally measured transmitted optical trajectory is in good agreement with the theoretical and simulation results. The trajectory design here is theoretically arbitrary, not limited to the three types of curves mentioned above. Compared with optical trajectories generated by traditional free-space metasurfaces, the integration of such on-chip metasurfaces with waveguide chips can achieve predefined arbitrary trajectories unaffected by zero-order diffraction, thus achieving a higher signal-to-noise ratio.

[0072] Based on this, in order to achieve arbitrary light trajectories and their longitudinal polarization changes, such as Figure 7 As shown, this embodiment uses a parabolic trajectory as an example to experimentally verify the longitudinal linear polarization rotation performance of the trajectory. The designed polarization rotation angle α and the transmission distance z are related as follows: α = π × z / 100 - 3π / 10 (30μm ≤ z ≤ 100μm). Figure 7 Figure a shows the intensity distribution of the guided wave at the yz section extracted without an analyzer, compared with... Figure 6 The trajectories of C and C are basically consistent. Subsequently, polarization modulation is achieved by rotating a polarizer added in front of the CCD, obtaining the yz cross-sectional intensity distributions of the extracted light's x and y polarization components, respectively. Figure 7 b and Figure 7 (c) It can be seen that the x-polarization component ( Figure 7 The trajectory intensity of b) changes from strong to weak, while the y-polarization component ( Figure 7 c) changes in the opposite way, indicating that as the propagation distance increases, the polarization state of the extracted guided wave changes from x-polarization to y-polarization. To illustrate the evolution of the polarization state more intuitively, as... Figure 7 As shown in d, this embodiment starts from... Figure 7 The normalized intensities of the x and y polarization components are extracted from a and used as a function of the propagation distance z. Furthermore, Figure 7 Figure e shows the transverse cross-sectional intensity distribution of the x and y polarization components measured at z = 60 μm and z = 90 μm. It can be seen that in the z = 60 μm plane, the center spot of the trajectory is mainly composed of the x polarization component, while in the z = 90 μm plane, the y polarization component is dominant. Figure 7 f and Figure 7 The middle g showed from Figure 7 The transverse intensity cross-sectional plots extracted from different z-planes in the middle e show an average half-width at half-maximum of approximately 1.7 μm. Due to manufacturing and measurement errors, the measured polarization-dependent intensity variation trend along the trajectory deviates slightly from the theoretical design.

[0073] Based on the above tests and analyses, the on-chip metasurface technology described in this embodiment is compatible with current photonic integrated circuit technology and can also be easily integrated with on-chip photonic devices, which will provide a new platform for the extended application of self-accelerating light trajectories.

[0074] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the invention.

Claims

1. A design method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces, characterized in that, Includes the following steps: S1: A metasurface is formed by arranging silicon nanounit structures into a two-dimensional periodic array; the silicon nanounit structure includes a single nanobrick and a waveguide and substrate below it; S2: Establish an xoy coordinate system with the two sides parallel to the working surface of the optical waveguide layer, designated as the x-axis and y-axis respectively; the sides of the silicon nanounit structure are parallel to the x-axis and y-axis; the metasurface is used to extract guided waves to free space; for guided waves propagating along the x-direction, the working wavelength is λ, and the corresponding period P is calculated based on the waveguide propagation constant β. x P x The period of the silicon nanounit structure along the x-axis; S3: The positional arrangement of the nanobricks is calculated using the principle of detour phase; S4: After the guided wave from step S2 passes through the on-chip metasurface array, it is point-mapped along the z-direction to obtain a preset light trajectory intensity distribution in the free space above the waveguide. S5: Achieving arbitrary light trajectories and their longitudinal polarization variations: Replace the individual nanobricks in step S1 with orthogonally and staggered biatomic nanobricks; wherein, the spacing between the biatomic nanobricks along the x-direction is designed as P. x / 2, the spacing between the two-atom nanobricks along the y-direction is designed as P y / 2; The overall displacement of each pair of diatomic nanobricks is also calculated using the detour phase principle, and the phase distribution of the corresponding trajectory is also obtained using the calculation method in step S3; The polarization state of the guided wave is modulated by setting the rotation angle of the diatomic nanobricks; S6: Following the calculation process described in step S5, the positional arrangement and corresponding rotation angle of all the two-atom nanostructures are encoded to obtain the final on-chip metasurface two-dimensional array. S7: Following the same method as in step S4, a guided wave with wavelength λ is incident along the x-direction. After passing through the on-chip metasurface array in step S6, the same light trajectory intensity distribution as preset in step S4 is obtained in the free space above the waveguide, and a linear polarization state distribution that varies along the transmission path is obtained.

2. The design method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces according to claim 1, characterized in that, In step S1, the nanobrick is a cuboid with a square top surface, and its period is a square formed by the projection of the waveguide and the substrate below it, with an area larger than the top surface of the nanobrick.

3. The design method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces according to claim 1, characterized in that, In step S4, any point on the trajectory in free space is regarded as the vertex of a conical beam of light emanating from a circle on the metasurface plane, and interference occurs along a predefined path, thereby creating an arbitrary light trajectory intensity distribution.

4. The design method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces according to claim 1, characterized in that, In step S3, the phase formula for calculating the positional arrangement of the nanobricks using the detour phase principle is as follows: The predefined trajectory can be represented as (F, G, z) in the coordinate system, where x and y are the position coordinates of the metasurface plane, λ is the free space wavelength, and γ is the divergence factor of the Bessel-like beam.

5. The design method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces according to claim 1, characterized in that, In step S5, the diatomic nanobrick is composed of two identical cuboid nanobricks, with the long sides of the top surfaces of the nanobricks forming an orthogonal arrangement.

6. The design method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces according to claim 1, characterized in that, In step S5, the displacement of the diatomic nanobricks is defined as follows: D is the overall displacement of the diatomic structure along the x-direction from the leftmost element of the unit period within one period; S is the spacing between the diatomic nanobricks along the x-direction; and the spacing between two orthogonally arranged nanobricks along the y-direction is designed as P. y / 2.

7. The design method for manipulating arbitrary light trajectories and their longitudinal polarization changes based on on-chip metasurfaces according to claim 1, characterized in that, In step S5, the rotation angle of the nanobrick is set by the following formula: θ = π × z / 100 - 3π / 10 Where θ is the rotation angle of the diatomic nanobrick, the angle between the long side of the nanobrick and the x-axis, 0°≤θ≤180°, and z is the z-direction coordinate of the corresponding point on the trajectory, 30μm≤z≤100μm.

8. The design method for realizing arbitrary optical trajectories and their longitudinal polarization changes based on on-chip metasurface manipulation as described in any one of claims 1-7 is applied in the fields of extended optical trajectories, complex optical manipulation, advanced laser manufacturing, microscopic imaging, and biophysics.

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