A composite phase metasurface and method for generating a tunable elliptical airy beam

Abstract

The application discloses a kind of composite phase metasurface and method for generating tunable elliptical Airy beam.The composite phase metasurface includes two coaxially stacked phase metasurfaces, each phase metasurface can be arranged rotatably, the composite phase metasurface can modulate original light beam into elliptical Airy beam, and by rotating at least one phase metasurface around the common axis, the relative rotation angle of the two phase metasurfaces is changed, the focal point position of the elliptical Airy beam can be adjusted;Two phase metasurfaces are respectively a first phase metasurface and a second phase metasurface, the first phase metasurface is located on the side of the original light beam, has a superimposed phase of cubic phase and first phase, and the second phase metasurface is located on the side of the elliptical Airy beam, has a second phase, and the first phase and the second phase are complementary.The composite phase metasurface and method in the application can generate elliptical Airy beam and dynamically adjust the light beam trajectory and the position of the focal point in the longitudinal or transverse direction in real time.

Description

Technical Field

[0001] The present invention relates to the field of metasurface technology, and in particular to a composite phase metasurface and method for generating a tunable elliptical Airy beam. Background Art

[0002] Elliptic Airy beams (EABs) are an advanced form of traditional Airy beams, exhibiting elliptical asymmetry in their cross-section. Unlike standard Airy beams, which propagate along parabolic paths and exhibit self-acceleration and non-diffracting properties, EABs propagate along elliptical trajectories, combining the unique properties of Airy beams with the flexibility of elliptical wavefronts, resulting in richer optical field distributions and phase characteristics. Furthermore, because EABs are more complex than standard Airy beams, the modulation of elliptical Airy beams is also more complex.

[0003] Traditionally, EABs are generated by complex and bulky optical devices, such as complex lens systems and spatial light modulators (SLMs). Although these devices and methods provide a way to generate EABs, they are not suitable for compact integrated systems due to limitations such as alignment issues, low efficiency, and polarization and power handling. In addition, existing optical devices also face problems such as low efficiency and difficulty in equipment alignment during beam control. Metasurfaces composed of nanoantennas can precisely control the amplitude, phase, and polarization of light. Although metasurfaces can generate elliptical Airy beams with diverse trajectories by combining cubic phase profiles with lens structures, such devices and methods lack the ability to tune EABs in real time, and are unable to flexibly and dynamically adjust the focal position and propagation characteristics of the beam.

[0004] In summary, the existing generation devices of elliptical Airy beams still have shortcomings such as being too complex and large, difficult to apply to compact integrated systems, and lacking dynamic adjustment and real-time tuning capabilities. These have posed significant limitations to the use of elliptical Airy beams in high-power application scenarios and other fields. Summary of the Invention

[0005] To overcome the limitations of existing technologies in terms of system compactness and real-time dynamic tuning, the present invention provides a composite phase metasurface and method for generating tunable elliptical Airy beams. The composite phase metasurface not only enables compact and efficient elliptical Airy beam generation and control, but also dynamically modulates the beam's focal length and propagation characteristics through relative rotation of the phase metasurface, demonstrating real-time responsiveness.

[0006] The technical solution adopted in the present invention is:

[0007] 1. A composite phase metasurface for generating tunable elliptical Airy beams

[0008] The composite phase metasurface includes two coaxially stacked phase metasurfaces, each of which is rotatable. The composite phase metasurface can modulate the original light beam into an elliptical Airy beam, and by rotating at least one phase metasurface around a common axis, the relative rotation angle of the two phase metasurfaces is changed, thereby adjusting the focal position of the elliptical Airy beam.

[0009] The two phase metasurfaces are the first phase metasurface and the second phase metasurface. The first phase metasurface is located on one side of the original light beam and has a superimposed phase of the cubic phase and the first phase. The second phase metasurface is located on one side of the elliptical Airy beam and has a second phase. The first phase and the second phase are complementary.

[0010] The cubic phase is used to modulate the original beam into an elliptical Airy beam.

[0011] Each phase metasurface includes a substrate and a nanopillar array disposed on one side of the substrate. The two phase metasurfaces, each with a nanopillar array disposed on one side, are arranged relative to each other. The nanopillar array is primarily composed of a plurality of nanopillars arranged in a ring array. The nanopillars have the same maximum arrangement radius on both phase metasurfaces. The nanopillars are cylindrical in shape, with different radii at different locations, and the radius of the cylinder increases radially from the center to the edge.

[0012] The first phase and the second phase satisfy any one of the following phase distributions:

[0013] The first type: The relationship between the superposition phase of the first phase and the second phase and the relative rotation angle θ0 satisfies the following formula:

[0014] Φ intergral =ar 2 θ0

[0015] Where, Φ intergral represents the superposition phase of the first phase and the second phase, θ0 represents the relative rotation angle, and a represents a constant related to the spatial frequency difference, which can be selected as a=100mm -2 , r represents the radial coordinate;

[0016] When the first phase and the second phase satisfy the first phase distribution, the adjusting of the focal position of the elliptical Airy beam is specifically: adjusting the focal length of the elliptical Airy beam; the relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula:

[0017] f θ =λ / (πaθ0)

[0018] Where, f θ represents the focal length of the composite phase metasurface, θ0 represents the relative rotation angle, λ represents the operating wavelength, and a represents a constant.

[0019] Type 2: The first phase is the first Fresnel holographic lens phase, and the second phase is the second Fresnel holographic lens phase. Both the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are off-axis phases and have opposite focal lengths. The off-axis distances of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are the same. When the relative rotation angle is 0°, the off-axis directions of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are opposite.

[0020] When the first phase metasurface rotates around the central axis in a first direction by an angle of θ1, and the second phase metasurface rotates around the central axis in a second direction opposite to the first direction by an angle of θ2, the phase distribution of the first Fresnel holographic lens satisfies the following formula:

[0021] P1(x,y)=-π[(x+dcosθ1) 2 +(y-dsinθ1) 2 ] / (λF0)

[0022] Wherein, P1(x, y) represents the phase distribution of the first Fresnel holographic lens phase, λ represents the operating wavelength, F0 represents the reference focal length, x and y represent the position coordinates, d represents the off-axis distance, and θ1 represents the angle of rotation of the first phase metasurface along the first direction.

[0023] The phase distribution of the second Fresnel holographic lens satisfies the following formula:

[0024] P2(x,y)=π[(x-dcosθ2) 2 +(y+dsinθ2) 2 ] / (λF0)

[0025] Wherein, P2(x, y) represents the phase distribution of the second Fresnel holographic lens phase, λ represents the operating wavelength, F0 represents the reference focal length, x and y represent the position coordinates, d represents the off-axis distance, and θ2 represents the angle of rotation of the second phase metasurface along the second direction.

[0026] The first direction and the second direction are clockwise and counterclockwise, respectively, or the first direction and the second direction are counterclockwise and clockwise, respectively.

[0027] When the first phase and the second phase satisfy the second phase distribution, the adjusting the focus position of the elliptical Airy beam specifically includes adjusting the lateral position of the focus of the elliptical Airy beam.

[0028] 2. A method for generating tunable elliptical Airy beams based on composite phase metasurfaces

[0029] The following steps are involved:

[0030] 1) Arranging the nanopillar arrays of the two phase metasurfaces based on their phase distributions, thereby manufacturing the two phase metasurfaces; aligning the two phase metasurfaces, coaxially and rotatably stacking them, to construct the composite phase metasurface. In step 1), the phase distribution of the first phase metasurface is a superposition of a cubic phase and a first phase, and the phase distribution of the second phase metasurface is a second phase, wherein the first phase and the second phase are complementary; the first phase and the second phase satisfy any of the following phase distributions:

[0031] The first type: The relationship between the superposition phase of the first phase and the second phase and the relative rotation angle θ0 satisfies the following formula:

[0032] Φ intergral =ar 2 θ0

[0033] Where, Φ intergral represents the superimposed phase of the first phase and the second phase, θ0 represents the relative rotation angle, a represents a constant, and r represents the radial coordinate.

[0034] Type 2: The first phase is a first Fresnel holographic lens phase, and the second phase is a second Fresnel holographic lens phase. Both the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are off-axis phases and have opposite focal lengths. The off-axis distances of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are the same. When the relative rotation angle is 0°, the off-axis directions of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are opposite.

[0035] When the first phase metasurface rotates around the central axis in a first direction by an angle of θ1, and the second phase metasurface rotates around the central axis in a second direction opposite to the first direction by an angle of θ2, the phase distribution of the first Fresnel holographic lens satisfies the following formula:

[0036] P1(x,y)=-π[(x+dcosθ1) 2 +(y-dsinθ1) 2 ] / (λF0)

[0037] Wherein, P1(x, y) represents the phase distribution of the first Fresnel holographic lens phase, λ represents the operating wavelength, F0 represents the reference focal length, x and y represent the position coordinates, d represents the off-axis distance, and θ1 represents the angle of rotation of the first phase metasurface along the first direction;

[0038] The phase distribution of the second Fresnel holographic lens satisfies the following formula:

[0039] P2(x,y)=π[(x-dcosθ2) 2 +(y+dsinθ2) 2 ] / (λF0)

[0040] Wherein, P2(x, y) represents the phase distribution of the second Fresnel holographic lens phase, λ represents the operating wavelength, F0 represents the reference focal length, x and y represent the position coordinates, d represents the off-axis distance, and θ2 represents the angle of rotation of the second phase metasurface along the second direction.

[0041] 2) The original light beam is vertically incident from the side surface of the first phase metasurface where the nanopillar array is not set. After being modulated by the first phase metasurface and the second phase metasurface, the generated elliptical Airy beam is emitted from the side surface of the second phase metasurface where the nanopillar array is not set.

[0042] 3) Using the common axis of the first phase metasurface and the second phase metasurface as the rotation axis, rotate at least one phase metasurface so that the relative rotation angle of the two phase metasurfaces changes, thereby adjusting the focal position of the elliptical Airy beam.

[0043] In step 3), the focus position of the elliptical Airy beam is adjusted by any of the following methods:

[0044] When the first phase and the second phase satisfy the first phase distribution, the focal length of the elliptical Airy beam is adjusted; the relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula:

[0045] f θ =λ / (πaθ0)

[0046] Where, f θ represents the focal length of the composite phase metasurface, θ0 represents the relative rotation angle, λ represents the operating wavelength, and a represents a constant.

[0047] When the first phase and the second phase satisfy a second phase distribution, the transverse position of the focus of the elliptical Airy beam is adjusted.

[0048] The beneficial effects of the present invention are:

[0049] 1. Compared with traditional complex lenses and spatial light modulators, the composite phase metasurface provided by the present invention has the advantages of small size, high efficiency in generating elliptical Airy beams, and compactness, and is suitable for integrated beam generation systems.

[0050] 2. The composite phase metasurface provided by the present invention can generate an elliptical Airy beam and realize real-time dynamic tuning of the elliptical Airy beam through a simple rotation operation, and has flexibility and versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the structure of the composite phase metasurface in the present invention; wherein (a) is a composite phase metasurface with a first phase distribution, and (b) is a composite phase metasurface with a second phase distribution;

[0052] Figure 2 Schematic diagram of the relationship between transmission efficiency and phase change and nanopillar radius in an embodiment of the present invention;

[0053] Figure 3 Schematic diagram of the structure of the nanorods and the bottom substrate in an embodiment of the present invention;

[0054] Figure 4 Schematic diagram of the phase distribution of the composite phase metasurface in Example 1 of the present invention; wherein, (a) is the phase distribution of the first phase metasurface when the spin is 0°, (b) is the phase distribution of the second phase metasurface when the spin is 0°, (c) is the combined phase distribution of the two phase metasurfaces when the relative rotation angle is 0°, (d) is the phase distribution of the second phase metasurface when the spin is 0°, (e) is the phase distribution of the second phase metasurface when the spin is 30°, and (f) is the combined phase distribution of the two phase metasurfaces when the relative rotation angle is 30°;

[0055] Figure 5 yz plane intensity distribution diagram of the elliptical Airy beam at different relative rotation angles in Example 1 of the present invention; wherein (a) is the prediction result, (b) is the simulation result, and (c) is the relationship between focal length and relative rotation angle;

[0056] Figure 6 Schematic diagram of the phase distribution of the composite phase metasurface in Example 2 of the present invention; wherein, (a) is the phase distribution of the first phase metasurface when the spin is 0°, (b) is the phase distribution of the second phase metasurface when the spin is 0°, (c) is the combined phase distribution of the two phase metasurfaces when the relative rotation angle is 0°, (d) is the phase distribution of the second phase metasurface when the spin is 0°, (e) is the phase distribution of the second phase metasurface when the spin is 30°, and (f) is the combined phase distribution of the two phase metasurfaces when the relative rotation angle is 30°;

[0057] Figure 7 : The xy-plane intensity distribution diagram of the elliptical Airy beam at different relative rotation angles in Example 2 of the present invention; wherein (a) is the prediction result and (b) is the simulation result;

[0058] Figure 8 : The xz plane intensity distribution diagram of the elliptical Airy beam at different relative rotation angles in Example 2 of the present invention; wherein (a) is a relative rotation angle of 0°, (b) is a relative rotation angle of 30°, (c) is a relative rotation angle of 60°, and (d) is a relative rotation angle of 90°;

[0059] Figure 9 is the lateral position of the focus of the elliptical Airy beam at different relative rotation angles in Example 2 of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] The present invention combines the moiré effect with a double-layer all-dielectric metasurface, replacing traditional complex lenses and spatial light modulators to achieve an efficient and compact beam generation system—a composite phase metasurface. The composite phase metasurface provided by the present invention dynamically modulates the focal length and propagation characteristics of EABs through two layers of phase metasurfaces with specific phase distributions, thereby overcoming the limitation of the existing technology that lacks real-time adjustment capabilities. The present invention uses a moiré metasurface to achieve dynamic modulation of the focal length and beam propagation through the interference effect between the two phase metasurfaces. The change in the superimposed phase produces a new phase distribution, which is controlled by the relative rotation angle and determines the focusing behavior of the beam. The moiré effect enables the gradient phase to be finely controlled on a subwavelength scale, achieving more flexible focus control than traditional optical systems. The present invention not only enables dynamic adjustment of the focal length, but also achieves lateral movement of the focus through control of the gradient phase. This flexibility allows the propagation characteristics and focal position of the beam to be adjusted in real time according to specific needs, making it suitable for fields such as high-resolution imaging and adaptive optics.

[0062] In a first aspect, the present invention provides a composite phase metasurface for generating a tunable elliptical Airy beam. A tunable elliptical Airy beam is one in which the position of the focus of the elliptical Airy beam in the horizontal (xy plane) or vertical (z direction) directions can be dynamically adjusted in real time, with the phase metasurface being the xy plane and the original beam incident in the z direction.

[0063] The initial electric field distribution U(eab) of the elliptical Airy beam is specifically:

[0064] U(eab)=Ai([r0-(y u 2 +t 2 x u 2 ) 1 / 2 ] / ω)×exp(b[r0-(y u 2 +t2 x u 2 ) 1 / 2 ] / ω)

[0065] Where Ai represents the Airy function, r0 represents the parameters related to the radius of the initial plane main ring of the elliptical Airy beam, ω represents the scale factor of the elliptical Airy beam, t represents the adjustment parameter, b represents the attenuation factor, and x u 、y u Indicates the position coordinates on the transverse plane.

[0066] Among them, the value range of the adjustment parameter t is 0 <t<1。

[0067] The parameter r0 related to the radius of the initial plane main ring of the elliptical Airy beam is set according to the following formula:

[0068] r0=R0 / 3

[0069] Where R0 represents the maximum arrangement radius of the nanopillar array on the phase metasurface.

[0070] The scale factor ω of the elliptical Airy beam is set according to the following formula:

[0071] ω=r0 / 10

[0072] Where r0 represents the relevant parameters of the radius of the main ring of the initial plane of the elliptical Airy beam.

[0073] The composite phase metasurface provided by the present invention includes two coaxially stacked phase metasurfaces, each of which is rotatably arranged on a common axis, that is, the foci of both phase metasurfaces are located on the common axis. The composite phase metasurface can modulate the original light beam into an elliptical Airy beam, and by rotating at least one phase metasurface around the common axis, the relative rotation angle of the two phase metasurfaces is changed, thereby adjusting the focal position of the elliptical Airy beam. The term "rotatable" refers to the ability of both phase metasurfaces to spin about their common axis.

[0074] Each phase metasurface includes a substrate and a nanocolumn array arranged on one side surface of the substrate. The nanocolumn array is used to realize phase modulation of the incident light of the phase metasurface to which it belongs. The two phase metasurfaces are arranged with one side surface of the nanocolumn array relative to each other. Among them, the nanocolumn array is mainly composed of a plurality of nanocolumns arranged in a ring array. The shape of the nanocolumns can be optionally a cylinder. The radius of the cylinder at different radii is different. The radius of the cylinder increases radially from the center to the edge, so that the phase of the phase metasurface can cover 0~2π, and the transmission efficiency is greater than the preset target value. In a specific implementation, the size parameters and arrangement parameters of the nanocolumn array can be obtained according to the phase distribution of the phase metasurface.

[0075] Figure 1 FIG. 1 is a schematic diagram of the structure of the composite phase metasurface of the present invention. Figure 1 As shown, the two phase metasurfaces are the first phase metasurface and the second phase metasurface. The first phase metasurface is located on one side of the original light beam and has a superimposed phase of the cubic phase and the first phase. The second phase metasurface is located on one side of the elliptical Airy beam and has a second phase. The first phase and the second phase are complementary.

[0076] The first phase metasurface is used to modulate the original light beam into an elliptical Airy beam. Specifically, the cubic phase loaded on the first phase metasurface is used to modulate the original light beam into an elliptical Airy beam. The second phase metasurface is used to adjust the focal position of the elliptical Airy beam by working in conjunction with the first phase metasurface.

[0077] With the first direction and the second direction being clockwise and counterclockwise respectively, or with the first direction and the second direction being counterclockwise and clockwise respectively:

[0078] The phase distribution of the first phase and the second phase and the focus position of the elliptical Airy beam are adjusted in either of the following two ways:

[0079] The first type: when the angle of rotation of the first phase metasurface around the central axis in the first direction is θ1, the relative rotation angle is θ0, and the angle of rotation of the second phase metasurface along the first direction is θ1-θ0, such as Figure 1 As shown in (a), the superposition phase of the first phase and the second phase satisfies the following formula:

[0080] Φ intergral =Φ(r,θ1)+(-Φ(r,θ1-θ0)

[0081] Where, Φ intergral represents the superposition phase of the first phase and the second phase, θ0 represents the relative rotation angle, θ1 represents the angle of rotation of the first phase metasurface around the central axis along the first direction, Φ(r,θ1) represents the first phase, and (-Φ(r,θ1-θ0) represents the second phase;

[0082] The first phase satisfies the following formula:

[0083] Φ(r,θ1)=2πr 2 θ1 / (λF0)

[0084] Where Φ(r,θ1) represents the phase of the radial coordinate r at the rotation angle θ1, θ1 represents the angle of rotation of the first phase metasurface along the first direction, λ represents the operating wavelength, F0 represents the reference focal length, and r represents the radial coordinate;

[0085] It can be obtained that the superposition phase of the first phase and the second phase satisfies the following formula:

[0086] Φ intergral =ar 2 θ0

[0087] Where, Φ intergral represents the superposition phase of the first phase and the second phase, θ0 represents the relative rotation angle, and a represents a constant related to the spatial frequency difference, which can be selected as a=100mm -2 , r represents the radial coordinate.

[0088] When the first phase and the second phase satisfy the first phase distribution, and when the phase distributions of the first phase metasurface and the second phase metasurface are complementary, adjusting the focal position of the elliptical Airy beam specifically involves adjusting the focal length of the elliptical Airy beam. The relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula:

[0089] f θ =λ / (πaθ0)

[0090] Where, f θ represents the focal length of the composite phase metasurface, θ0 represents the relative rotation angle, λ represents the operating wavelength, and a represents a constant.

[0091] The second type: Figure 1 As shown in (b), the first phase is the first Fresnel holographic lens phase, the second phase is the second Fresnel holographic lens phase, and both the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are off-axis phases and have opposite focal lengths.

[0092] The first Fresnel holographic lens phase and the second Fresnel holographic lens phase are both off-axis phases. When the first phase metasurface is aligned with the second phase metasurface, that is, the relative rotation angle is 0°, one of the Fresnel holographic lens phases has a positive focal length and is offset in a certain direction, while the other Fresnel holographic lens phase has a negative focal length and is offset in the opposite direction. The offset direction (i.e., the off-axis direction) of each Fresnel holographic lens phase is parallel to the transverse plane. The two Fresnel holographic lens phases are used to generate a gradient phase that changes with the relative rotation angle of the two phase metasurfaces, thereby affecting the focal length and the propagation characteristics of the light beam, resulting in dynamic changes in the focusing behavior.

[0093] When the first phase and the second phase satisfy the second phase distribution: adjusting the focus position of the elliptical Airy beam specifically includes: adjusting the lateral position of the focus of the elliptical Airy beam.

[0094] The off-axis distance of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase is the same. When the relative rotation angle is 0°, the off-axis directions of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are opposite, and the off-axis directions of each Fresnel holographic lens phase are perpendicular to the common axis of the two phase metasurfaces.

[0095] When the angle of rotation of the first phase metasurface around the central axis in the first direction is θ1, and the angle of rotation of the second phase metasurface in the second direction opposite to the first direction is θ2, the phase distribution of the first Fresnel holographic lens phase satisfies the following formula:

[0096] P1(x,y) = -π[(x + dcosθ1) 2 +(y - dsinθ1) 2 ] / (λF0)

[0097] In the formula, P1(x,y) represents the phase distribution of the first Fresnel holographic lens phase, λ represents the working wavelength, F0 represents the reference focal length, x and y represent the position coordinates in the transverse plane, d represents the off-axis distance, and θ1 represents the angle of rotation of the first phase metasurface around the central axis in the first direction.

[0098] The phase distribution of the second Fresnel holographic lens phase satisfies the following formula:

[0099] P2(x,y) = π[(x - dcosθ2) 2 +(y + dsinθ2) 2 ] / (λF0)

[0100] In the formula, P2(x,y) represents the phase distribution of the second Fresnel holographic lens phase, λ represents the working wavelength, F0 represents the reference focal length, x and y represent the position coordinates in the transverse plane, d represents the off-axis distance, and θ2 represents the angle of rotation of the second phase metasurface in the second direction.

[0101] From the relationship between the phase distribution of the two Fresnel holographic lens phases and the relative rotation angle, it can be seen that the change of the relative rotation angle will change the size of the phase gradient, and the parameters of the two off-axis Fresnel holographic lens phases determine the maximum value of the phase gradient.

[0102] In the second mode, the two off-axis Fresnel holographic lens phases are superimposed on each other to form a gradient phase. The relative positions of the two Fresnel holographic lens phases change with the relative rotation angle of the two phase metasurfaces, thereby generating an overall phase distribution that changes with the relative rotation angle of the two phase metasurfaces. Specifically, by changing the relative rotation angle of the two phase metasurfaces, the phase distribution after the superposition of the two Fresnel holographic lens phases is adjusted. This change produces a so-called "gradient phase", that is, the gradient phase is directly related to the relative rotation angle. When the relative rotation angle changes, the phase gradient also changes, thereby affecting the focal length and the propagation characteristics of the light beam.

[0103] In the present application, when the relative rotation angle changes, the size of the gradient phase changes, thereby precisely controlling the movement of the focal point in the transverse plane by affecting the focusing behavior of the light beam.

[0104] The second aspect of the present application provides a method for generating a tunable elliptical Airy beam based on the composite phase metasurface provided in the first aspect of the present application. The method specifically includes the following steps:

[0105] 1) Obtain the nanorod array arrangement parameters and size parameters of the two phase metasurfaces according to the phase distributions of the two phase metasurfaces, and then manufacture the two phase metasurfaces. After aligning the two phase metasurfaces, they are rotatably arranged on the common axis of the two phase metasurfaces.

[0106] Specifically, the alignment of the two phase metasurfaces is that the center of the two phase metasurfaces is taken as the central axis perpendicular to the direction of the phase metasurface, and the relative rotation angle is 0°.

[0107] In step 1), the phase distribution of the first phase metasurface is the superposition of the cubic phase and the first phase, the phase distribution of the second phase metasurface is the second phase, and the first phase and the second phase are complementary.

[0108] The first phase and the second phase satisfy any one of the following phase distributions:

[0109] The first one: the relationship between the superposition of the first phase and the second phase and the relative rotation angle θ0 satisfies the following formula:

[0110] Φ intergral = ar 2 θ0

[0111] In the formula, Φ intergral represents the superposition of the first phase and the second phase, θ0 represents the relative rotation angle, a represents a constant related to the difference in spatial frequency, which can be selected as a = 100 mm -2 , and r represents the radial coordinate.

[0112] When the first phase and the second phase satisfy the first phase distribution, when the phase distribution of the first phase surface and the second phase surface are complementary, the adjustment of the focal point position of the elliptical Airy beam is specifically adjusting the focal length of the elliptical Airy beam. The relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula:

[0113] f θ =λ / (πaθ0)

[0114] In the formula, f θ represents the focal length of the elliptical Airy beam, θ0 represents the relative rotation angle of the two phase surfaces, λ represents the working wavelength, and a represents a constant related to the spatial frequency difference, which can be represented as 1 / λF0.

[0115] Secondly, the first phase is a first Fresnel holographic lens phase, the second phase is a second Fresnel holographic lens phase, the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are both off-axis phases, and have opposite focal lengths; the off-axis distances of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are the same; when the relative rotation angle is 0°, the off-axis directions of the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are opposite;

[0116] When the first phase surface rotates around the central axis by an angle of θ1 in the first direction, and the second phase surface rotates by an angle of θ2 in the second direction opposite to the first direction, the phase distribution of the first Fresnel holographic lens phase satisfies the following formula:

[0117] P1(x,y)=-π[(x+dcosθ1) 2 +(y-dsinθ1) 2 ] / (λF0)

[0118] In the formula, P1(x,y) represents the phase distribution of the first Fresnel holographic lens phase, λ represents the working wavelength, F0 represents the reference focal length, x and y represent the position coordinates in the transverse plane, d represents the off-axis distance, and θ1 represents the angle of the first phase surface rotating around the central axis in the first direction.

[0119] The phase distribution of the second Fresnel holographic lens phase satisfies the following formula:

[0120] P2(x,y)=π[(x-dcosθ2) 2 +(y+dsinθ2) 2 ] / (λF0)

[0121] In the formula, P2(x, y) represents the phase distribution of the second Fresnel holographic lens phase, λ represents the working wavelength, F0 represents the reference focal length, x and y represent the position coordinates in the transverse plane, d represents the off-axis distance, and θ2 represents the angle of rotation of the second phase super surface along the second direction.

[0122] 2) The original light beam is perpendicularly incident on the side surface of the first phase super surface which is not provided with a nano pillar array, and the generated elliptical Airy beam is emitted from the side surface of the second phase super surface which is not provided with a nano pillar array after being modulated by the first phase super surface and the second phase super surface.

[0123] 3) Rotating at least one phase super surface with the common axis of the first phase super surface and the second phase super surface as the rotation axis, the relative rotation angle of the two phase super surfaces is changed, and then the focal point position of the elliptical Airy beam is adjusted.

[0124] Wherein, the adjustment of the focal point position of the elliptical Airy beam is realized by any one of the following ways:

[0125] When the first phase and the second phase satisfy the first phase distribution, the adjustment of the focal point position of the elliptical Airy beam is specifically adjusting the focal length of the elliptical Airy beam; the relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula:

[0126] f θ =λ / (πaθ0)

[0127] In the formula, f θ represents the focal length of the elliptical Airy beam, θ0 represents the relative rotation angle of the two phase super surfaces, λ represents the working wavelength, and a represents a constant related to the difference in spatial frequency, which can be represented as 1 / λF0.

[0128] When the first phase and the second phase satisfy the second phase distribution, the adjustment of the focal point position of the elliptical Airy beam is specifically adjusting the transverse position of the focal point of the elliptical Airy beam. Wherein, the obtaining method of the superimposed phase of the cubic phase and the first Fresnel holographic lens phase is specifically: using a phase superposition method to process the cubic phase and the first Fresnel holographic lens phase.

[0129] The specific embodiments of the application are as follows:

[0130] Unless otherwise specified, in the embodiments of the application, the x-y plane represents the transverse plane parallel to the two phase super surfaces, and the z direction represents the axial direction of the two phase super surfaces.

[0131] Embodiment 1

[0132] A composite phase metasurface with complementary phases is provided in the embodiment. The structure of the composite phase metasurface of the embodiment is shown in (a) of Figure 1 , and the specific parameters are as follows:

[0133] The working wavelength, i.e. the wavelength of the original light beam, is λ = 532 nm, and the reference focal length F0 = 50 μm.

[0134] The nanocolumns are arranged in a circular array on the surface of the substrate, and the maximum arrangement radius R0 of the nanocolumn array phase metasurface is 20 μm, and the arrangement period is 250 nm. Figure 3 Figure 1 is a schematic diagram of the structure of the nanocolumns and the bottom substrate in the embodiment of the present application. As shown in Figure 3 , the shape of the nanocolumns is a cylinder, the nanocolumns are made of gallium nitride, and the substrate is made of aluminum oxide.

[0135] The radii of the cylinders at different radii are different, and the radii of the cylinders gradually increase from 50 nm to 110 nm along the radial direction from the center of the substrate to the edge, the phase coverage range is 0-2π, and the transmission efficiency target value is 90%. Figure 2 Figure 2 is a schematic diagram of the relationship between the transmission efficiency (circles) and the phase change (stars) and the radius of the nanocolumns in the embodiment of the present application. As can be seen, the radius parameter setting of the cylinder in the embodiment can ensure that the phase coverage range is 0-2π, and the transmission efficiency is greater than the preset target value of 90%.

[0136] The specific parameters of the initial planar electric field distribution of the elliptical Airy beam (EAB) are as follows: the adjustment parameter t = 0.85, the position coordinates x u = [-20 μm, 20 μm], y u = [-20 μm, 20 μm], and the attenuation factor a = 0.1.

[0137] The distribution parameters of the cubic phase are set according to the initial electric field distribution of the elliptical Airy beam. Specifically, the first phase metasurface can modulate the original light beam into an elliptical Airy beam, the second phase metasurface is complementary to the first phase metasurface, and the two superimposed phases produce a Moire effect.

[0138] The superimposed phase of the first phase and the second phase satisfies the following formula:

[0139] Φ intergral = ar 2 θ0

[0140] In the formula, Φ intergral represents the superimposed phase of the first phase and the second phase, θ0 represents the relative rotation angle, r represents the radial coordinate, and a represents a constant related to the difference in spatial frequency. In the embodiment, the value of a is 100 mm -2 .

[0141] When the first phase and the second phase satisfy the first phase distribution, and when the phase distributions of the first phase metasurface and the second phase metasurface are complementary, adjusting the focal position of the elliptical Airy beam specifically involves adjusting the focal length of the elliptical Airy beam. The relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula:

[0142] f θ =λ / (πaθ0)

[0143] Where, f θ represents the focal length of the elliptical Airy beam, θ0 represents the relative rotation angle of the two phase metasurfaces, λ represents the operating wavelength, and a represents a constant related to the spatial frequency difference.

[0144] The phase distribution of the composite phase metasurface at different rotation angles (including spin angle and relative rotation angle) is calculated using MATLAB software. The prediction results are shown in Figure 4 . Figure 4 The combined phase distributions in (c) and (f) demonstrate that the relative rotation between the two layers of phase metasurface can change the overall phase distribution, thereby achieving dynamic control of the focal properties of the elliptical Airy beam.

[0145] The yz plane intensity distribution of the elliptical Airy beam at different relative rotation angles was calculated and simulated using MATLAB software and the finite difference time domain (FDTD) simulation method. The results are shown in Figure 5 (a) and (b) of the elliptical Airy beam. The relative rotation angles are 0°, 30°, 60°, and 90°, respectively. Both the prediction and simulation results confirm that adjusting the relative rotation angle of the two phase metasurfaces can cause the focal position of the elliptical Airy beam to shift longitudinally.

[0146] In addition, according to Figure 5 (a) and (b) of the diagram to obtain the relationship between the focal length (expressed as the coordinate of the focus on the z-axis) and the relative rotation angle, the results are shown in Figure 5 In this embodiment, the focal length is 28 microns when the relative rotation angle is 0°, the focal length is 26 microns when the relative rotation angle is 30°, the focal length is 22 microns when the relative rotation angle is 60°, and the focal length is 20 microns when the relative rotation angle is 90°.

[0147] As can be seen, the theoretical predictions are in good agreement with the simulation results, further confirming the effectiveness of the composite phase metasurface provided by this invention in dynamically controlling the longitudinal position of the focus of an elliptical Airy beam. By utilizing the phase metasurface in this embodiment to generate EABs with adjustable focus, precise imaging and focusing can be achieved in multiple focal planes, thereby improving the resolution and contrast of the imaging system.

[0148] Embodiment 2

[0149] In this embodiment, the parameters of the composite phase metasurface are the same as those in Embodiment 1.

[0150] The difference lies in that:

[0151] The first phase metasurface has a superimposed phase of a cubic phase and a first Fresnel holographic lens phase; and the second phase metasurface has a second Fresnel holographic lens phase.

[0152] The superimposed phase of the cubic phase and the first Fresnel holographic lens phase is obtained by a phase superposition method, and the superimposed phase of the cubic phase and the first Fresnel holographic lens phase can modulate the original light beam into an elliptical Airy beam.

[0153] The first Fresnel holographic lens phase and the second Fresnel holographic lens phase have opposite focal lengths, and both the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are off-axis phases and have opposite focal lengths. The two off-axis Fresnel holographic lens phases are used to generate a tunable gradient phase, which can flexibly adjust the propagation trajectory of the elliptical Airy beam in the longitudinal direction and adjust the focal point position in the transverse plane. As a focusing phase, the off-axis Fresnel holographic lens phase can reduce the loss of the light beam due to divergence during propagation, further ensuring that the original light beam can efficiently pass through the first phase metasurface and be smoothly transmitted to the second phase metasurface, thereby improving the generation efficiency of the elliptical Airy beam.

[0154] In this embodiment, when the first phase metasurface rotates by an angle of θ1 in the clockwise direction around the central axis, and the second phase metasurface rotates by an angle of θ2 in the counterclockwise direction, the phase distribution of the first Fresnel holographic lens phase satisfies the following formula:

[0155] P1(x,y)=-π[(x+dcosθ1) 2 +(y-dsinθ1) 2 ] / (λF0)

[0156] In the formula, P1(x,y) represents the phase distribution of the first Fresnel holographic lens phase, λ represents the working wavelength, F0 represents the reference focal length, x and y represent the position coordinates in the transverse plane, d represents the off-axis distance, and θ1 represents the angle of the first phase metasurface rotating in the clockwise direction around the central axis.

[0157] The phase distribution of the second Fresnel holographic lens phase satisfies the following formula:

[0158] P2(x,y)=π[(x-dcosθ2) 2 +(y+dsinθ2) 2 ] / (λF0)

[0159] Where P2(x,y) represents the phase distribution of the second Fresnel holographic lens phase, λ represents the operating wavelength, F0 represents the reference focal length, x and y represent the position coordinates on the transverse plane, d represents the off-axis distance, and θ2 represents the angle of rotation of the second phase metasurface in the counterclockwise direction.

[0160] In this embodiment, the first and second Fresnel holographic lens phases are set to deviate in the +x and -x directions, respectively (i.e., the off-axis directions are the +x and -x directions, respectively), with an off-axis distance of d = 0.15R0 = 3 μm. The focal length of the first Fresnel holographic lens phase is F0 = 50 μm, and the focal length of the second Fresnel holographic lens phase is -F0 = -50 μm.

[0161] The phase distribution of the composite phase metasurface at different rotation angles (including spin angle and relative rotation angle) was calculated using MATLAB software. The prediction results are shown in Figure 6 . Figure 6 The combined phase distributions in (c) and (f) demonstrate that the relative rotation between the two layers of phase metasurfaces can change the overall phase distribution, thereby achieving dynamic control of the focal properties of the elliptical Airy beam.

[0162] The xy plane intensity distribution of the elliptical Airy beam at different relative rotation angles was calculated and simulated using MATLAB software and the finite difference time domain (FDTD) simulation method. The results are shown in Figure 7 Among them, the different relative rotation angles are 0°, 30°, 60° and 90°. Figure 8 2 is the xz plane intensity distribution diagram of the elliptical Airy beam at different relative rotation angles in Example 2 of the present invention; among them, (a) is a relative rotation angle of 0°, (b) is a relative rotation angle of 30°, (c) is a relative rotation angle of 60°, and (d) is a relative rotation angle of 90°, among which the red curve is the prediction result and the blue model is the simulation result.

[0163] Combine Figure 7 and Figure 8 It can be seen that both the prediction results and the simulation results confirm that by adjusting the relative rotation angle of the two phase metasurfaces, the focal position of the elliptical Airy beam can be laterally shifted.

[0164] Figure 9 is the lateral position of the focus of the elliptical Airy beam in this embodiment at different relative rotation angles. Figure 9The left side is a schematic diagram of the three-dimensional structure of the composite phase metasurface. (a) to (i) in the three-dimensional structure diagram represent the position of the focus on the xy plane when the relative rotation angle is 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, and 270°, respectively; Figure 9 (a) to (i) on the right represent the xy-plane intensity distribution diagrams of the elliptical Airy beam when the relative rotation angles are 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, and 270°, respectively. Figure 9 In the figure, the elliptical Airy beam exhibits side lobes in different directions, which shows the flexibility of controlling the propagation path and further confirms that the direction of the EAB side lobes is controlled by the relative rotation angle.

[0165] In summary, the present invention solves the shortcomings of existing elliptical Airy beam generation methods in terms of compactness, efficiency, and real-time tuning capabilities through composite phase metasurfaces, successfully solves the technical difficulties in traditional elliptical Airy beam generation and control, and provides a more efficient and flexible method for generating and controlling elliptical Airy beams. It provides an efficient, compact, real-time tunable, multifunctional and flexible optical solution for fields such as adaptive optics and precision imaging.

Claims

1. A composite phase metasurface for generating a tunable elliptical Airy beam, characterized by: The composite phase metasurface includes two coaxially stacked phase metasurfaces, each of which is rotatably arranged. The composite phase metasurface can modulate the original light beam into an elliptical Airy beam, and by rotating at least one phase metasurface around a common axis, the relative rotation angle of the two phase metasurfaces is changed, so that the focal position of the elliptical Airy beam can be adjusted; the two phase metasurfaces are respectively a first phase metasurface and a second phase metasurface, the first phase metasurface is located on one side of the original light beam, and has a superposition phase of a cubic phase and a first phase, and the second phase metasurface is located on one side of the elliptical Airy beam and has a second phase, and the first phase and the second phase are complementary; The superposition phase of the first phase and the second phase and the relative rotation angle θ 0 The relationship satisfies the following formula: Φ intergral =ar 2 θ 0 Where, Φ intergral represents the superposition phase of the first phase and the second phase, θ 0 Represents the relative rotation angle, a represents a constant, r represents radial coordinates; The adjusting of the focal position of the elliptical Airy beam is specifically: adjusting the focal length of the elliptical Airy beam; the relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula: f θ =λ / (πaθ 0 ) Where, f θ represents the focal length of the composite phase metasurface, θ 0 Represents the relative rotation angle, λ represents the operating wavelength, a Represents a constant.

2. The composite phase metasurface for generating a tunable elliptical Airy beam according to claim 1, wherein: The cubic phase is used to modulate the original beam into an elliptical Airy beam.

3. The composite phase metasurface for generating a tunable elliptical Airy beam according to claim 1, wherein: Each phase metasurface includes a substrate and a nanocolumn array arranged on one side surface of the substrate. The surfaces of the two phase metasurfaces provided with the nanocolumn arrays are arranged relative to each other; the nanocolumn array is mainly composed of a plurality of nanocolumns arranged in a circular array, and the maximum arrangement radius of the nanocolumns on the two phase metasurfaces is the same. The shape of the nanocolumns is a cylinder, and the radius of the cylinder increases radially from the center to the edge.

4. A method for generating a tunable elliptical Airy beam based on the composite phase metasurface according to any one of claims 1 to 3, characterized in that: The following steps are involved: 1) Arranging the nanopillar arrays of the two phase metasurfaces according to the phase distribution of the two phase metasurfaces, thereby manufacturing the two phase metasurfaces; aligning the two phase metasurfaces, and coaxially and rotatably stacking them to construct the composite phase metasurface; The superposition phase of the first phase and the second phase and the relative rotation angle θ 0 The relationship satisfies the following formula: Φ intergral =ar 2 θ 0 Where, Φ intergral represents the superposition phase of the first phase and the second phase, θ 0 Represents the relative rotation angle, a represents a constant, r represents radial coordinates; 2) The original light beam is vertically incident from the side of the first phase metasurface where the nanopillar array is not provided. After being modulated by the first phase metasurface and the second phase metasurface, the generated elliptical Airy beam is emitted from the side of the second phase metasurface where the nanopillar array is not provided. 3) rotating at least one phase metasurface with the common axis of the first phase metasurface and the second phase metasurface as the rotation axis, so that the relative rotation angle of the two phase metasurfaces changes, thereby adjusting the focal position of the elliptical Airy beam; The adjusting of the focal position of the elliptical Airy beam is specifically: adjusting the focal length of the elliptical Airy beam; the relationship between the focal length of the elliptical Airy beam and the relative rotation angle satisfies the following formula: f θ =λ / (πaθ 0 ) Where, f θ represents the focal length of the composite phase metasurface, θ 0 Represents the relative rotation angle, λ represents the operating wavelength, a Represents a constant.

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