An on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography

Abstract

The application relates to the field of micro-nano optical technology, and particularly discloses a wafer-on-chip waveguide and super-structure surface integrated device for realizing arbitrary polarization holography, which comprises a super-structure surface, a waveguide and a substrate arranged in sequence from top to bottom; a complete unit of the super-structure surface comprises four nano pillars arranged on the waveguide; the nano pillars have anisotropic structures and have fixed relative positions in one unit; the nano pillars in the same row of one unit have perpendicular rotation angles; the nano pillars can extract light waves from the waveguide, the light waves extracted by the four nano pillars in the same unit interfere with each other to form scattered light with specific amplitude, phase and polarization; by changing the size and rotation angle of the nano pillars, sudden phase, geometric phase and detour phase of the fixed distance between the nano pillars can be utilized to realize holographic images with arbitrary polarization states.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of micro-nano optics, in particular to an on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography and a design method thereof. BACKGROUND

[0002] The metasurface allows complete control of electromagnetic field characteristics, including phase, amplitude and polarization. Therefore, the current development of the combination of metasurface and waveguide enhances the ability of photonic integrated circuit to manipulate light, realizes the functions of focusing, OAM, hologram, grayscale display, etc., and the metasurface is an extremely thin optical device, which matches the compactness of the photonic integrated circuit, so that the PIC can generate a complex light field. The current scheme of directly making the metasurface unit on the waveguide includes the schemes of using abrupt phase, geometric phase, detour phase and the combination of several phases. The geometric phase and the detour phase can theoretically realize continuous phase change. If the waveguide mode is a TE fundamental mode, the output light of the metasurface using the abrupt phase or the detour phase is linearly polarized light whose polarization direction is perpendicular to the propagation direction of the light wave in the waveguide. The output light of the metasurface using the geometric phase is right-handed or left-handed circularly polarized light. Although the above schemes produce more forms of free space light compared with the traditional grating coupler and end face coupler, they lack further manipulation of polarization. SUMMARY

[0003] In view of the deficiencies of the prior art, the present application provides an on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography and a design method thereof. By introducing an array of four nanometer pillars in a complete metasurface unit group on the waveguide, the interference between the scattered light extracted from the four nanometer pillars in the waveguide can realize the scattered light with 0-2π phase in a certain amplitude range, which utilizes the abrupt phase, the geometric phase and the detour phase with fixed distance between units. Moreover, only the phase library of the metasurface unit of y-polarized light needs to be established, and the structure parameters required by the phase of other polarization states can be derived using the Jones matrix, which reduces the workload of simulation and provides a new method for photonic integrated circuit to manipulate the characteristics of free space light.

[0004] To solve the above problems, the present application adopts the following technical scheme:

[0005] An on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography, which is sequentially provided with a metasurface, a waveguide and a substrate from top to bottom.

[0006] The complete unit of the metasurface includes four nanometer pillars, and the nanometer pillars are arranged on the waveguide.

[0007] The nanometer pillars have anisotropic structure and have fixed relative positions in a unit.

[0008] The rotation angles of the nanorods in the same row of a unit are perpendicular to each other.

[0009] The nanorods can extract light waves from the waveguide, and the light waves extracted by the four nanorods in the same unit interfere to form scattered light with specific amplitude, phase and polarization.

[0010] Further, the distance of the nanorods in the same row in the x direction is equal to half of the period of the complete unit in the x direction, and the distance of the nanorods in different rows of the same unit in the y direction is equal to half of the period of the complete unit in the y direction.

[0011] The period of the complete unit of the super-structure surface in the x direction is equal to the distance required for the light wave transmission in the waveguide to produce a π phase shift, and the nanorods in different rows of the same unit are staggered by a quarter of the period in the x direction.

[0012] The fixed distance between the nanorods produces a detour phase.

[0013] Further, the waveguide is a multi-mode waveguide with sufficient area to carry the super-structure surface, and the waveguide propagates a TE0 wave, which is represented by a corresponding vector E in = [0 1] T , where T represents the transpose of the vector.

[0014] When the nanorods change in size, the length offset of the two orthogonal axes of the nanorods follows a fixed proportional relationship, and the size change of the nanorods produces a sudden phase. For the fixed proportional relationship, it needs to be explained that when the variable of the offset of one of the orthogonal axes is greater than 0, the offset of the other orthogonal axis is α times the offset of the orthogonal axis; when the variable of the offset of one of the orthogonal axes is less than 0, the offset of the other orthogonal axis is 1 / α times the offset of the orthogonal axis. Specifically, when the nanorods are composed of Si, the waveguide is composed of SiN x , and the substrate part close to the waveguide is composed of SiO2, the fixed proportional relationship is specifically that when the variable of the offset of one of the orthogonal axes is greater than 0, the offset of the other orthogonal axis is 3 / 8 times the offset of the orthogonal axis; when the variable of the offset of one of the orthogonal axes is less than 0, the offset of the other orthogonal axis is 8 / 3 times the offset of the orthogonal axis.

[0015] When the rotation angle of the nanorods changes, the same nanorods in the same unit remain perpendicular to each other, and the change in the rotation angle of the nanorods produces a geometric phase.

[0016] The Jones matrix of a nanorod without rotation is as follows, where t a and tb is a complex number.

[0017]

[0018] The Jones matrix of the other nanorod in the same row in a unit is

[0019]

[0020] e iπ The distance between the two nanorods in the x direction is equal to the optical path difference of half a wavelength in the waveguide. The rotation angles of the two nanorods in the same row in a unit are perpendicular to each other, so the rotation angle of the other nanorod is π / 2, R is the rotation matrix, R(θ) is the rotation matrix with an angle of θ, and R -1 (θ) is the inverse matrix of R(θ); i is the imaginary unit.

[0021] Let t1=t a -t b The Jones matrix corresponding to the two nanorods in the upper row is:

[0022]

[0023] The nanorod in the lower row is translated by a quarter of a period relative to the nanorod in the upper row in the direction of light propagation. The Jones matrix corresponding to the nanorod in the lower row is

[0024]

[0025] Therefore, the total Jones matrix corresponding to the four nanorods is

[0026]

[0027] TE0 wave is set to propagate in the waveguide, and the corresponding vector representation is E in = [0 1] T Therefore, the output light can be represented as

[0028]

[0029] The output is y-polarized light.

[0030] Consider that the rotation angle of the nanorod in the upper row is θ1, and the corresponding Jones matrix is

[0031]

[0032] Similarly, if the rotation angle of the nanorod in the lower row is θ2, then

[0033]

[0034] When θ1=θ2

[0035]

[0036] The output light is represented as

[0037]

[0038] Thus the output light is linearly polarized light with the angle between the polarization direction and the positive direction of the y axis being 2θ1.

[0039] The following derives the general case, θ1 and θ2 are not necessarily equal, and the Jones matrix can be represented as

[0040]

[0041] The output light at this time is

[0042]

[0043] Equation (12) gives the expression of arbitrary polarized light, especially non-linearly polarized light, and the following gives a solution. Assume that the electric field amplitude of the elliptically polarized light to be achieved in the x direction is A1, the electric field amplitude in the y direction is A2, and the phase difference between the electric fields in the two directions is

[0044] (t1 cos 2θ1) 2 +(t2 cos2θ2) 2 =A2 2 (13)

[0045] (t1 sin 2θ1) 2 +(t2 sin 2θ2) 2 =A1 2 (14)

[0046]

[0047] Because the light intensity of the input light is 1, there is the following restriction condition.

[0048] A1 2 +A2 2 =1(18)

[0049] By solving the equation group of (13) to (17), the required θ1, θ2, t1 and t2 can be obtained.

[0050] It is convenient to first consider a type of polarized ellipse whose long axis direction is in the x axis or y axis. When , it represents right-handed, and the variable k1 is defined:

[0051]

[0052] The relationship between θ1 and k1 is

[0053]

[0054] θ1 can be obtained according to the above formula, and a variable k2 is defined:

[0055]

[0056] θ2 can be derived in the same way. When , it indicates left-handedness, and a variable k1 is defined:

[0057]

[0058] The relationship between θ1 and k1 is

[0059]

[0060] θ1 can be obtained according to the above formula, and a variable k2 is defined:

[0061]

[0062] θ2 can be derived in the same way.

[0063] After θ1 and θ2 are obtained, t1 2 and t2 2 are calculated according to formula (13) and (14). For right-handed light, t1>0, t2>0, and for left-handed light, t1>0, t2<0. In order to unify t1 and t2 to be greater than 0, θ2 is added by π / 2 for left-handed light. When the long axis direction of the polarization ellipse is not on the x-axis or y-axis, the rotation angle required is half of the polarization angle plus θ1 and θ2 calculated above. This provides a method for generating non-linearly polarized light.

[0064] Further, the phase required for the generated holographic image is obtained by the GS algorithm based on Fresnel diffraction, and is given to the super-structured surface unit.

[0065] A phase library of super-structured surface units for y-polarized light is established. When constructing a hologram for y-polarized light, the structural parameters of the super-structured surface are selected from the phase library of y-polarized light. The super-structured surface for other polarized light can be derived by referring to the phase library of y-polarized light using the Jones matrix described above. Therefore, the design method can obtain holograms of any polarization.

[0066] The super-structured surface unit with phase has a group of super-structured surface units for refractive index matching at each end, and the nanocolumns of the super-structured surface units for refractive index matching do not have a size offset in the orthogonal axis. The nanocolumns of the super-structured surface units for refractive index matching linearly increase in radius as the distance from the super-structured surface unit with phase decreases.

[0067] Compared with the prior art, the present application has the following advantages:

[0068] 1. Compared with the free-space metasurface, the polarization state of the input light of the on-chip metasurface is often limited, and the input light in the waveguide is TE or TM mode, corresponding to the output y-polarized or x-polarized light. The present application provides a polarization conversion method, so that the metasurface can generate scattered light of any polarization state, especially elliptical polarization state with arbitrary ellipticity and polarization direction not on the x-axis or y-axis.

[0069] 2. Generally, the metasurface with abrupt phase can only select a limited number of phase-generating units from the phase library. If polarization conversion is required, the number of functional units will be smaller. The size of the nanocolumn of the metasurface unit of the present application can be continuously changed, so that a continuously changing phase can be generated. Through the interference between the scattered light of the four units in a complete metasurface unit group on the waveguide, the metasurface generates scattered light of any polarization state, which can carry a 0-2π phase by using abrupt phase, geometric phase and detour phase with fixed distance between units. Combined with the GS algorithm based on Fresnel diffraction, a hologram of any polarization can be realized.

[0070] 3. The present application only needs to establish a phase library of y-polarized light metasurface units, and then the structure parameters of the metasurface unit required for other polarization states can be derived by using the Jones matrix, which reduces the workload of simulation.

[0071] 4. Because the phase of the scattered light is mainly affected by the anisotropy of the same row nanocolumn and the interference of the scattered light from the upper and lower nanocolumns, the abrupt phase of a single nanocolumn does not play a decisive role, and a large aspect ratio is not required. This means that the process tolerance of the device manufacturing process is large.

[0072] 5. The metasurface unit with phase of the present application has a group of metasurface units for refractive index matching at each end. The nanocolumns of the refractive index matching unit do not have a size offset in the orthogonal axis, so that the scattered light of the refractive index matching unit can be reduced as much as possible. BRIEF DESCRIPTION OF DRAWINGS

[0073] Figure 1 Fig. 1 is a three-dimensional schematic diagram of the on-chip waveguide and metasurface integrated device for realizing arbitrary polarization hologram of the present application, and the insert is a schematic diagram of a complete metasurface unit.

[0074] Figure 2 Fig. 2 is a top view schematic diagram of a complete metasurface unit.

[0075] Figure 3Simulation results for super-structured surface structure parameter scanning. (a) Size variation of two nanorods, and the relationship of (b) amplitude and (c) phase of the escaped light Ey with δ 1a and δ 1b . D is the original diameter. (d) Size variation of the complete super-structured surface unit cell, and the relationship of (e) amplitude and (f) phase of the escaped light Ey with δ1 and δ2. (g) Rotation angle variation of the complete super-structured surface unit cell, and the relationship of (h) ψ and (i) χ of the escaped light with θ1 and θ2, ψ and χ represent the angle between the long axis of the polarization ellipse and the x-axis and the ellipticity, respectively.

[0076] Figure 4 Simulation results for holographic images. (a)-(c), (d)-(f), (g)-(i) and (j)-(l) are the total intensity, x-polarized light intensity and y-polarized light intensity of holographic image letter “A” for y-polarized light, holographic image letter “B” for x-polarized light, holographic image letter “C” for right-handed circularly polarized light and holographic image letter “D” for left-handed elliptically polarized light, respectively.

[0077] Figure 5 Super-structured surface unit cells for generating (a) x-polarized light, (b) right-handed circularly polarized light and (c) left-handed elliptically polarized light with 0, π / 2, π and 3π / 2 phase.

[0078] Figure 6 Process flow chart for device fabrication.

[0079] Figure 7 Real images of fabricated on-chip waveguide and super-structured surface integrated devices for arbitrary polarization holography. (a) Optical microscope image of the fabricated device. (b) Scanning electron microscope image of the fabricated device.

[0080] Figure 8 Schematic diagram of the measurement setup.

[0081] Figure 9 Measurement results for holographic images. (a)-(c), (d)-(f), (g)-(k) and (m)-(q) are the measurement results of holographic image letter “A” for y-polarized light, holographic image letter “B” for x-polarized light, holographic image letter “C” for right-handed circularly polarized light and holographic image letter “D” for left-handed elliptically polarized light, respectively. Pol represents polarizer, QWP represents quarter-wave plate, and the angle is the angle between the pass axis of the polarizer and the positive direction of the x-axis, which coincides with the horizontal direction. (l) and (r) are the optical setups for the disappearance of holographic image letter “C” and holographic image letter “D”.

[0082] Figure 10 Simulation results for holographic image letter “B” for x-polarized light in special cases.

[0083] (a)-(c), (d)-(f) and (g)-(i) are total intensity, x-polarized light intensity and y-polarized light intensity of 200 nm high silicon nanopillar, 400 nm high silicon nanopillar and 300 nm high silicon nanopillar with 400 nm thick HSQ layer, respectively.

[0084] The reference signs are as follows:

[0085] 1, metasurface; 2, waveguide; 3, substrate; 4, nanopillar. DETAILED DESCRIPTION

[0086] The technical solutions in the embodiments will be described clearly and completely below with reference to the drawings in the embodiments. Obviously, the described embodiments are only a part of the embodiments, not all the embodiments.

[0087] EMBODIMENT

[0088] As shown in Figure 1 and 2 , an on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography is provided, in which a metasurface 1, a waveguide 2 and a substrate 3 are sequentially arranged from top to bottom.

[0089] The complete unit of the metasurface 1 includes four nanopillars 4, and the nanopillars 4 are arranged on the waveguide 2. It should be noted that, as shown in Figure 1 , the nanopillars 4 in this embodiment are composed of Si, the waveguide 2 is composed of SiN x , and the part of the substrate 3 close to the waveguide 2 is composed of SiO2. The nanopillars 4 are single material.

[0090] The nanopillars 4 have anisotropic structure and have fixed relative positions in a unit;

[0091] The nanopillars 4 in the same row in a unit are perpendicular to each other in rotation angle;

[0092] The nanopillars 4 can extract light waves from the waveguide 2, and the light waves extracted by the four nanopillars 4 in the same unit will interfere to form scattered light with specific amplitude, phase and polarization.

[0093] Specifically, the distance of the nanopillars 4 in the same row in the x direction is equal to half of the period of the complete unit in the x direction, and the distance of the nanopillars 4 in different rows in the same unit in the y direction is equal to half of the period of the complete unit in the y direction.

[0094] Specifically, the period of the complete unit of the metasurface in the x direction is equal to the distance required for the light wave transmission in the waveguide 2 to produce a π phase shift, and the nanopillars 4 in different rows in the same unit are staggered by a quarter of the period in the x direction.

[0095] The fixed distance between the nanorods 4 produces a meandering phase.

[0096] In this embodiment, the waveguide 2 is a multimode waveguide with enough area to carry the metasurface 1, and the TE0 wave propagates in the waveguide 2, which is represented by the vector E in = [0 1] T .

[0097] In this embodiment, when the nanorods 4 change in size, the two orthogonal axis length offsets of the nanorods 4 follow a fixed proportional relationship, and the size change of the nanorods 4 produces a sudden phase change.

[0098] When the rotation angle of the nanorods 4 changes, the same nanorod 4 in the same unit remains perpendicular to each other, and the rotation angle change of the nanorods 4 produces a geometric phase.

[0099] In this embodiment, when the nanorods 4 in the upper and lower rows of a unit rotate by the same angle, the scattering light of the unit can be described by the following Jones matrix:

[0100]

[0101] t1 and t2 reflect the size changes of the nanorods 4 in the upper and lower rows of the unit, respectively, and θ1 and θ2 reflect the rotation angle changes of the nanorods in the upper and lower rows of the unit, respectively. The scattering light of the metasurface unit is linearly polarized light, and the polarization direction of the scattering light is determined by the rotation angle, and the phase of the scattering light is determined by the size change.

[0102] In this embodiment, when the nanorods 4 in the upper and lower rows of a unit rotate by different angles, the scattering light of the unit can be described by the following Jones matrix:

[0103]

[0104] The scattering light of the metasurface unit is non-linearly polarized light, and the scattering light and the phase are jointly determined by the rotation angle and the size change.

[0105] In this embodiment, the nanorods 4 are silicon nanorods. The waveguide 2 is a silicon nitride waveguide. The substrate 3 is a silicon dioxide substrate.

[0106] In this embodiment, the height of the nanorods 4 is 300 nm. The period of the nanorods is 950 nm in the x direction and 700 nm in the y direction.

[0107] In this embodiment, the thickness of the waveguide 2 is 300 nm.

[0108] In this embodiment, the working wavelength of the device is 1570 nm.

[0109] The finite-difference time-domain (FDTD) method is used for numerical simulation. A TE mode light source is set in the silicon nitride waveguide, and the light escapes from the waveguide in the form of an elliptic cylinder with two rotation angles that differ by 90°, as shown in Fig. 1(a), Figure 3 Fig. 1(b) and Fig. 1(c) reflect the amplitude and phase of the y-polarized scattered light. The elliptic cylinder is changed from a circular cylinder with a radius of 110 nm by adding an offset to the orthogonal axes respectively, so that the circular cylinder becomes an elliptic cylinder. The two offsets δ 1a and δ 1b range from -150 nm to 150 nm. The simulation results are as follows. Figure 3 Most of the phase values in Fig. 1(c) are near 0 and π, only the positive and negative of the electric field are changed. According to the amplitude change in Fig. 1(b) and the simulation verification, when δ 1a > 0, δ 1b = 3δ 1a / 8; δ 1a < 0, δ 1b = 8δ 1a / 3 (i.e. the dashed line in Fig. 1(b)), the complete metasurface unit can produce a larger amplitude change range.

[0110] The simulation results of the amplitude and phase of the y-polarized scattered light of the complete metasurface unit composed of four elliptic cylinders are as follows Figure 3 Fig. 1(e) and Fig. 3(f), and the size changes of the elliptic cylinders are shown in Fig. 1(d). When δ 1a > 0, δ 1a 1 = δ 1a , and when δ 1b < 0, δ 2 1 = δ 2 . Figure 3 The results in Fig. 1(e) and Fig. 3(f) are basically consistent with formula (6), and δ Figure 3 1 and δ Figure 3 2 are proportional to t Figure 3 1 and t 2 respectively. As shown in Fig. 1(g), the size offsets of the upper and lower rows of elliptic cylinders are fixed, so that δ

[0111] 1 = δ 2 = 75 nm, and they are rotated respectively, so that the polarization of the scattered light changes, and the changes of the long axis angle ψ and the ellipticity χ of the polarization ellipse are as shown in Fig. 1(h) and Fig. 1(i). Therefore, through the previous Jones matrix derivation and the parameter scanning results of formula (6), we can control the polarization of the scattered light, and all types of polarized light have the same amplitude under the phase control range of π.

[0112] In order to verify the effect, the holographic images of different polarizations generated by the metasurface in four different waveguides are simulated and measured by experiments in this embodiment.

[0113]

[0112] In this embodiment, the holographic phase map is obtained by GS (Gerchberg-Saxton) algorithm based on Fresnel diffraction, and the holographic image is designed at 100 μm above the metasurface 1.

[0113] In this embodiment, 40x30 metasurface units form the holographic phase, the radius of the cylinder is 110 nm, and sqrt(δ1 2 +δ2 2 )=150 nm to keep the amplitude unchanged.

[0114] In this embodiment, the effective refractive index is gradually increased by adding several complete metasurface units with increasing radius, and δ1=δ2=0 nm to minimize the scattered light amplitude. The radius of the cylinder increases linearly from 100 nm to 110 nm.

[0115] In this embodiment, the effective refractive index is matched by four periods at both ends, so there are 48x30 complete metasurface units.

[0116] Specifically, the metasurface parameters are set in FDTD according to the phase map, and the far-field results are obtained in FDTD. According to the amplitude and phase relationship of (e) and (f) in Figure 3 , the metasurface structure for generating reconstructed images using y-polarized light can be designed. Figure 4 (a)-(c) in are the simulation results of the y-polarized light holographic image letter "A", and there is almost no x-polarized component. According to formula (10), combined with the simulation results of Figure 3 , the required structure parameters of linearly polarized light hologram can be obtained, and the nanocolumn needs to be rotated by 45° to generate x-polarized light. Figure 4 (e)-(g) in are the simulation results of the x-polarized light holographic image letter "B", and there is almost no y-polarized component, indicating that polarization conversion has occurred. More generally, the holographic image letter "C" of right circularly polarized light and the holographic image letter "D" of left elliptically polarized light are designed, where the A1:A2=1:2 of left elliptically polarized light, and the polarization angle is 60°. Figure 4 (g)-(i) in and Figure 4 (j)-(l) in respectively show the simulation results of right circularly polarized light and left elliptically polarized light, both of which exist x-polarized component and y-polarized component.

[0117] Figure 5Super-structured surface units providing 0, π / 2, π and 3π / 2 phase shifts for x-polarized light, right-handed circularly polarized light and left-handed elliptically polarized light, respectively, are given. Generally, the nano-pillars producing linearly polarized light have the same rotation direction and only the size is changed to produce phase shift; the nano-pillars producing circularly polarized light have the same size and the same rotation angle of four nano-pillars in a super-structured surface unit is changed to produce phase shift; the nano-pillars producing elliptically polarized light with phase shift need to change both the size and the rotation angle.

[0118] Devices are fabricated to verify the simulation results above, as shown in Figure 6 First, 300 nm thick silicon nitride is deposited on a thermal oxide wafer at low temperature of 300 °C by inductively coupled plasma chemical vapor deposition (ICP-CVD). Alignment marks are defined by electron beam lithography (EBL) followed by evaporation of 5 nm titanium adhesion layer and 100 nm gold and then lift-off. Silicon nitride waveguides are defined on the thermal oxide wafer by electron beam lithography and reactive ion etching (RIE). 300 nm thick amorphous silicon is deposited and super-structured surfaces are defined on the waveguides by electron beam lithography and inductively coupled plasma (ICP) etching. Figure 7 Figures (a) and Figure 7 show optical microscope images and scanning electron microscope (SEM) images of the fabricated devices.

[0119] The samples are tested by the optical setup shown in Figure 8 . Laser light exits from a tapered fiber and is coupled into the waveguide by an end-face coupler. Light is scattered out of the super-structured surface and is collected by an x- objective and finally captured by an infrared camera. Polarizers and quarter- wave plates are used in the optical setup as needed for the tests. Polarizers and quarter- wave plates are used in the optical setup as needed for the tests.

[0120] Figure 9 Test results of holographic images are shown. The x-polarized light can pass through when the polarizer is at 0° and the y-polarized light can pass through when the polarizer is at 90°. Therefore, the y-polarized letter "A" cannot be shown when the polarizer is at 0° and the x-polarized letter "B" cannot be shown when the polarizer is at 90°, which is consistent with the simulation results in Figure 4 . Figure 9 The ratio of the light intensity in Figure 9 (b) is large because of the y-polarized background light that does not undergo polarization conversion. Right-handed circularly polarized light can be converted to linearly polarized light no matter what the angle between the optical axis of the quarter- wave plate and the x-axis is. When the quarter- wave plate is set to 135°, right-handed circularly polarized light is converted to x-polarized light, as shown in Figure 9As shown in (j) and (k), the letter "C" can be visualized when the polarizer is at 0°, but not when the polarizer is at 90°. For left-handed elliptically polarized light, the optical axis of the quarter wave plate needs to be aligned with either the major axis or the minor axis of the polarization ellipse to convert it into linearly polarized light. With the quarter wave plate set at 60°, the angle between the linearly polarized light converted from the left-handed elliptically polarized light and the x-axis is

[0121] arctan(2 / 1)-60°≈-3.43°. As shown in (p) and (q), the letter "D" is not visualized when the polarizer is at 86°, but is visualized when the polarizer is at -4°. Figure 9

[0122] As shown in (j) and (k), the letter "C" can be visualized when the polarizer is at 0°, but not when the polarizer is at 90°. For left-handed elliptically polarized light, the optical axis of the quarter wave plate needs to be aligned with either the major axis or the minor axis of the polarization ellipse to convert it into linearly polarized light. With the quarter wave plate set at 60°, the angle between the linearly polarized light converted from the left-handed elliptically polarized light and the x-axis is Figure 10 As shown in (p) and (q), the letter "D" is not visualized when the polarizer is at 86°, but is visualized when the polarizer is at -4°.

[0123] Although the embodiments of the present application have been shown and described above, the scope of the present application is not limited to the above, and any changes or substitutions not involving inventive labor are intended to be covered by the scope of the present application. Unless explicitly stated, any element, action or instruction used herein should not be interpreted as critical or essential.​

Claims

1. An on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography, characterized in that, include: The metasurface (1), waveguide (2) and substrate (3) are arranged sequentially from top to bottom. The complete unit of the metasurface (1) comprises four nanopillars (4) arranged on the waveguide (2); The nanopillars (4) have an anisotropic structure and a fixed relative position in a unit cell; The nanopillars (4) are in the same row of a unit, and their rotation angles are perpendicular to each other; The nanopillars (4) extract light waves from the waveguide (2). The light waves extracted by the four nanopillars (4) in the same unit will interfere to form scattered light with specific amplitude, phase and polarization. The distance between the nanopillars (4) in the same row in the x direction is equal to half the period of the complete unit in the x direction, and the distance between the nanopillars (4) in different rows of the same unit in the y direction is equal to half the period of the complete unit in the y direction; The period in the x-direction of the complete unit of the metasurface is equal to the distance required for the optical wave transmission to generate a π phase shift in the waveguide (2), and the nanopillars (4) in different rows of the same unit are staggered by a quarter of a period in the x-direction; The fixed distance between the nanopillars (4) creates a meandering phase; When the size of the nanopillar (4) changes, the length offset of the two orthogonal axes of the nanopillar (4) follows a fixed proportional relationship, and the size change of the nanopillar (4) produces an abrupt phase change. When the rotation angle of the nanopillar (4) changes, the same nanopillar (4) within the same unit remains perpendicular to each other, and the change in the rotation angle of the nanopillar (4) generates a geometric phase; By utilizing abrupt phase, geometric phase, and detour phase with fixed distance between units, the scattered light of arbitrary polarization states generated by the metasurface carries a 0-2π phase.

2. The on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography according to claim 1, characterized in that, The waveguide (2) is a multimode waveguide with sufficient area to support the metasurface. The waveguide (2) propagates a TE0 wave, the corresponding vector of which is E. in =[0 1] T , where T represents the transpose of the vector.

3. The on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography according to claim 1, characterized in that, The fixed proportional relationship is specifically as follows: when the variable of the offset of one orthogonal axis is greater than 0, the offset of the other orthogonal axis is α of the offset of the orthogonal axis; when the variable of the offset of one orthogonal axis is less than 0, the offset of the other orthogonal axis is 1 / α of the offset of the orthogonal axis.

4. The on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography according to claim 3, characterized in that, When the nanopillars are composed of Si, the waveguide is composed of SiN x When the substrate portion near the waveguide is composed of SiO2, the fixed proportional relationship is specifically as follows: when the variable of the offset of one orthogonal axis is greater than 0, the offset of the other orthogonal axis is 3 / 8 of the offset of the orthogonal axis; when the variable of the offset of one orthogonal axis is less than 0, the offset of the other orthogonal axis is 8 / 3 of the offset of the orthogonal axis.

5. The on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography according to claim 1, characterized in that, When the two rows of nanopillars within a single cell are rotated by the same angle, the scattered light from the cell is described by the following Jones matrix: t1 and t2 respectively reflect the size changes of the nanopillars in the upper and lower rows of the unit, and θ1 and θ2 respectively reflect the rotation angle changes of the nanopillars in the upper and lower rows of the unit; the scattered light of the unit is linearly polarized light, the polarization direction of the scattered light is determined by the rotation angle, and the phase of the scattered light is determined by the size change; Where i is the imaginary unit.

6. The on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography according to claim 1, characterized in that, When the two rows of nanopillars within a single cell are rotated at different angles, the scattered light from the cell is described by the following Jones matrix: t1 and t2 respectively reflect the size changes of the nanopillars in the upper and lower rows of the unit, and θ1 and θ2 respectively reflect the rotation angle changes of the nanopillars in the upper and lower rows of the unit. The scattered light from the unit is non-linearly polarized light, and its phase is determined by the rotation angle and size change.

7. The on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography according to claim 1, characterized in that, The phase required to generate the holographic image is obtained by a Fresnel diffraction-based GS algorithm and is assigned to the metasurface unit.

8. The on-chip waveguide and metasurface integrated device for realizing arbitrary polarization holography according to claim 1, characterized in that, Each end of the phase-equivalent metasurface unit has a set of metasurface units for refractive index matching, and the nanopillars of the metasurface units for refractive index matching do not have dimensional offsets on orthogonal axes. The radius of the nanopillars of the metasurface unit used for refractive index matching increases linearly as the distance from the metasurface unit with phase decreases.

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