Composite phase metasurface and method for generating tunable elliptical Airy beam

Abstract

The invention discloses a composite phase metasurface and method for generating a tunable elliptical Airy beam. The composite phase metasurface comprises two coaxially stacked phase metasurfaces, each phase metasurface is rotatably arranged, the composite phase metasurface can modulate an original light beam into an elliptical Airy light beam, and the relative rotation angle of the two phase metasurfaces is changed by rotating at least one phase metasurface around a common axis. The focus position of the elliptical Airy beam can be adjusted; the two phase metasurfaces are a first phase metasurface and a second phase metasurface respectively, the first phase metasurface is located on one side of an original light beam and has a superposition phase of a cubic phase and the first phase, the second phase metasurface is located on one side of an elliptical Airy light beam and has a second phase, and the first phase and the second phase are complementary. According to the composite phase metasurface and the method, the elliptical Airy beam can be generated, and the track of the beam and the position of the focus in the longitudinal or transverse direction can be dynamically adjusted 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, with elliptical asymmetric characteristics in their cross-section. Unlike standard Airy beams that propagate along parabolic paths and have self-acceleration and non-diffraction characteristics, EABs propagate along elliptical trajectories, combining the unique characteristics of Airy beams with the flexibility of elliptical wavefronts, resulting in richer light field distribution and phase characteristics. On the other hand, since 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 accurately 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 cannot 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, which pose an important limitation to the use of elliptical Airy beams in high-power application scenarios and other fields. Summary of the invention

[0005] In order to overcome the limitations of the prior art in terms of system compactness and real-time dynamic tuning, the present invention provides a composite phase metasurface and method for generating a tunable elliptical Airy beam. The composite phase metasurface in the present invention can not only realize compact and efficient elliptical Airy beam generation and control, but also can realize dynamic modulation of the focal length and propagation characteristics of the beam by relative rotation of the phase metasurface, and has real-time response capability.

[0006] The technical solution adopted by 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 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, thereby adjusting the focal position of the elliptical Airy beam.

[0009] 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 superimposed phase of a cubic phase and a 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 nanocolumn array disposed on one side surface of the substrate, and the one side surfaces of the two phase metasurfaces on which the nanocolumn array is disposed are arranged relative to each other. The nanocolumn array is mainly composed of a plurality of nanocolumns arranged in a ring array, and the maximum arrangement radius of the nanocolumns on the two phase metasurfaces is the same, and the shape of the nanocolumns is a cylinder, and the radius of the cylinder is different at different radii, 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] In the formula, 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] In the formula, 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] The second type: the first phase is the first Fresnel holographic lens phase, the second phase is the 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 distance 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 angle of rotation of the first phase metasurface around the central axis in a first direction is θ1, and the angle of rotation of the second phase metasurface in a second direction opposite to the first direction is θ2, the phase distribution of the first Fresnel holographic lens phase 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 working 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 phase 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 working 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 focal position of the elliptical Airy beam specifically includes: adjusting the lateral position of the focal point of the elliptical Airy beam.

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

[0029] The following steps are involved:

[0030] 1) According to the phase distribution of the two phase metasurfaces, the nanocolumn array arrangement of the two phase metasurfaces is obtained, thereby manufacturing the two phase metasurfaces; after aligning the two phase metasurfaces, they are coaxially and rotatably stacked to construct the composite phase metasurface. In the step 1), the phase distribution of the first phase metasurface is the superposition phase of the cubic phase and the first phase, and the phase distribution of the second phase metasurface is the second phase, and 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] In the formula, 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] The second type: the first phase is the first Fresnel holographic lens phase, the second phase is the 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 distance 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 angle of rotation of the first phase metasurface around the central axis in a first direction is θ1, and the angle of rotation of the second phase metasurface in a second direction opposite to the first direction is θ2, the phase distribution of the first Fresnel holographic lens phase 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 working 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 phase 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 working 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 nanocolumn 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 nanocolumn array is not set.

[0042] 3) Taking 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 the step 3), the focal 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] In the formula, 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 the second phase distribution, the lateral 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 generating 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 nanocolumn radius in an embodiment of the present invention;

[0053] Figure 3 Schematic diagram of the structure of the nanorod 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 diagram between the focal length and the 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 : is 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] Fig. 9 It 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 is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] The present invention combines the moiré effect and a double-layer all-dielectric metasurface to replace the traditional complex lenses and spatial light modulators, and realizes an efficient and compact beam generation system-a composite phase metasurface. The composite phase metasurface provided by the present invention realizes dynamic modulation of the focal length and propagation characteristics of EABs through two layers of phase metasurfaces with specific phase distribution, thereby overcoming the limitation of the lack of real-time adjustment capability in the prior art. The present invention adopts a moiré metasurface to realize dynamic modulation of the focal length and beam propagation through the interference effect between two phase metasurfaces. The change of 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 allows the gradient phase to be finely controlled on a subwavelength scale, achieving more flexible focus control than traditional optical systems. The present invention can not only dynamically adjust the focal length, but also realize lateral movement of the focus through the control of the gradient phase. This flexibility enables the propagation characteristics and focal position of the beam to be adjusted in real time according to specific needs, and is suitable for fields such as high-resolution imaging and adaptive optics.

[0062] The first aspect of the present invention provides a composite phase metasurface for generating a tunable elliptical Airy beam. The tunable elliptical Airy beam means that the plane where the phase metasurface is located is the xy plane, the incident direction of the original beam is the z direction, and the position of the focus of the elliptical Airy beam in the horizontal direction (xy plane) or the vertical direction (z direction) can be dynamically adjusted in real time.

[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 Represents the position coordinates on the transverse plane.

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

[0067] Among them, the relevant parameter r0 of 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 nanorod 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 the two phase metasurfaces are both 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, and the focal position of the elliptical Airy beam can be adjusted. Among them, rotatable means that both phase metasurfaces can spin with their common axis as the rotation axis.

[0074] Each phase metasurface includes a substrate and a nanocolumn array arranged on one side surface of the substrate, and 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 relative to each other on one side surface with nanocolumn arrays. Among them, the nanocolumn array is mainly composed of a plurality of nanocolumns arranged in a ring array, and the shape of the nanocolumns can be selected as cylinders. The radius of the cylinders at different radii is different, and the radius of the cylinders increases radially from the center to the edge, so that the phase of the phase metasurface can cover 0 to 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, respectively. The first phase metasurface is located on one side of the original light beam and has a superimposed phase of a cubic phase and a 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 any of the following two ways:

[0079] The first type: when the first phase metasurface rotates around the central axis in the first direction at an angle of θ1, the relative rotation angle is θ0, and the second phase metasurface rotates around the central axis in the first direction at an angle of 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] In the formula, 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] Among them, the first phase satisfies the following formula:

[0083] Φ(r,θ1)=2πr 2 θ1 / (λF0)

[0084] Wherein, 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 working 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] In the formula, 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 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:

[0089] f θ =λ / (πaθ0)

[0090] In the formula, 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, 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.

[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, and causing a dynamic change 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 is the same as that of the second Fresnel holographic lens phase. 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 direction of each Fresnel holographic lens phase is perpendicular to the common axis of the two phase metasurfaces.

[0095] When the first phase metasurface rotates around the central axis in a first direction at an angle of θ1, and the second phase metasurface rotates in a second direction opposite to the first direction at an angle of 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] Wherein, 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 on 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 along 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] Wherein, 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 on the transverse plane, d represents the off-axis distance, and θ2 represents the rotation angle of the second phase metasurface along 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 magnitude of the phase gradient, while the parameters of the two off-axis Fresnel holographic lens phases determine the maximum value of the phase gradient.

[0102] In the second method, the phases of two off-axis Fresnel holographic lenses are superimposed on each other to form a gradient phase. The relative position of the two Fresnel holographic lens phases changes 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 to adjust the phase distribution after the two Fresnel holographic lens phases are superimposed, this change produces the 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 will also change, thereby affecting the focal length and the propagation characteristics of the light beam.

[0103] In the solution of the present invention, when the relative rotation angle changes, the magnitude of the gradient phase changes, thereby affecting the focusing behavior of the light beam, thereby accurately controlling the movement of the focus on the transverse plane.

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

[0105] 1) The nanocolumn array arrangement parameters and size parameters of the two phase metasurfaces are obtained according to the phase distribution of the two phase metasurfaces, and then the two phase metasurfaces are manufactured; after the two phase metasurfaces are aligned, they are rotatably coaxially arranged on the common axis of the two phase metasurfaces.

[0106] Among them, the alignment of two phase metasurfaces specifically means: taking the centers of the two phase metasurfaces perpendicular to the direction of the phase metasurface as the central axis, and the relative rotation angle is 0°.

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

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

[0109] 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:

[0110] Φ intergral =ar 2 θ0

[0111] In the formula, 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;

[0112] 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 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 metasurfaces, λ represents the operating wavelength, and a represents a constant related to the spatial frequency difference, which can be expressed as 1 / λF0.

[0115] The second type: the first phase is the first Fresnel holographic lens phase, the second phase is the 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 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;

[0116] When the first phase metasurface rotates around the central axis in a first direction at an angle of θ1, and the second phase metasurface rotates in a second direction opposite to the first direction at an angle of θ2, 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] Wherein, 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 on 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 along 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] Wherein, 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 on the transverse plane, d represents the off-axis distance, and θ2 represents the rotation angle of the second phase metasurface along the second direction.

[0122] 2) The original light beam is vertically incident on the side surface of the first phase metasurface where the nanocolumn 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 nanocolumn array is not set.

[0123] 3) Taking 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.

[0124] The focal position of the elliptical Airy beam is adjusted by any of the following methods:

[0125] When the first phase and the second phase satisfy the first phase distribution, adjusting the focal position of the elliptical Airy beam specifically includes: 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 metasurfaces, λ represents the operating wavelength, and a represents a constant related to the spatial frequency difference, which can be expressed as 1 / λF0.

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

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

[0130] Unless otherwise specified, in the embodiments of the present invention, the xy plane represents the lateral plane parallel to the two phase metasurfaces, and the z direction represents the axial direction of the two phase metasurfaces.

[0131] Example 1

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

[0133] Working wavelength, i.e. wavelength of original light beam λ = 532nm, reference focal length F0 = 50μm;

[0134] The nanorods are periodically arranged in a ring array on the substrate surface. The maximum arrangement radius R0 of the nanorod array on the phase metasurface is 20 μm, and the arrangement period is 250 nm. Figure 3 FIG. 1 is a schematic diagram of the structure of the nanorod and the bottom substrate in an embodiment of the present invention. Figure 3 It can be seen that the shape of the nanorod is a cylinder, the nanorod is made of gallium nitride, and the substrate is made of aluminum oxide.

[0135] The radius of the cylinder is different at different radii. From the center to the edge of the substrate, the radius of the cylinder gradually increases from 50nm to 110nm along the radial direction. The phase coverage range is 0 to 2π, and the transmission efficiency target value is 90%. Figure 2 Schematic diagram of the relationship between transmission efficiency (circles) and phase change (stars) and nanocolumn radius in an embodiment of the present invention. It can be seen that the radius parameter setting of the cylinder in this embodiment can ensure that the phase coverage range is 0 to 2π and the transmission efficiency is greater than the preset target value of 90%.

[0136] The specific parameters of the initial plane electric field distribution of elliptical Airy beams (EABs) are: adjustment parameter t = 0.85, position coordinate x on the transverse plane u =[-20μm,20μm],y u =[-20μm, 20μm], 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 beam into an elliptical Airy beam, the second phase metasurface is complementary to the first phase metasurface, and the superposition of the two produces a moiré effect.

[0138] The superposition 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 superposition 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 spatial frequency difference. In this 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 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:

[0142] f θ =λ / (πaθ0)

[0143] In the formula, 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 the 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). The different relative rotation angles are 0°, 30°, 60° and 90°. 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 longitudinally shifted.

[0146] In addition, according to Figure 5 (a) and (b) of the paper 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°, 26 microns when the relative rotation angle is 30°, 22 microns when the relative rotation angle is 60°, and 20 microns when the relative rotation angle is 90°.

[0147] It can be seen that the theoretical prediction results are in good agreement with the simulation results, which further confirms the effectiveness of the composite phase metasurface provided by the present invention in dynamically controlling the longitudinal position of the focus of the elliptical Airy beam. By using the phase metasurface in this embodiment to generate EABs with adjustable focus, accurate imaging and focusing can be achieved on multiple focal planes, thereby improving the resolution and contrast of the imaging system.

[0148] Example 2

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

[0150] The difference is:

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

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

[0153] Among them, the first Fresnel holographic lens phase and the second Fresnel holographic lens phase have opposite focal lengths, and the first Fresnel holographic lens phase and the second Fresnel holographic lens phase are both off-axis phases and have opposite focal lengths. The two off-axis Fresnel holographic lens phases are used to generate adjustable gradient phases, so that the propagation trajectory of the elliptical Airy beam in the longitudinal direction can be flexibly adjusted, and the focal position can be adjusted in the transverse plane. The off-axis Fresnel holographic lens phase, as a focusing phase, can reduce the loss of the light beam caused by divergence during the propagation process, further ensure 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 angle of the first phase metasurface rotating around the central axis in the clockwise direction is θ1, and the angle of the second phase metasurface rotating around the central axis in the counterclockwise direction is θ2, 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] Wherein, 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 on 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 clockwise direction;

[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 working 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 Fresnel holographic lens phase and the second Fresnel holographic lens phase are set to deviate in the +x direction and the -x direction respectively (that is, the off-axis directions are the +x direction and the -x direction respectively), and the off-axis distance is d=0.15R0=3μm. The focal length of the first Fresnel holographic lens phase is F0=50μm, and the focal length of the second Fresnel holographic lens phase is -F0=-50μm.

[0161] 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 6 . Figure 6 The combined phase distributions in (c) and (f) demonstrate that the relative rotation between the two layers of the phase metasurface 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 : 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°, wherein the red curve is the prediction result and the blue model is the simulation result.

[0163] Combination 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 shifted laterally.

[0164] Fig. 9 is the lateral position of the focus of the elliptical Airy beam in this embodiment at different relative rotation angles. Fig. 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 schematic diagram represent the positions of the focus on the xy plane when the relative rotation angle is 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, and 270°, respectively; Fig. 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. Fig. 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 capability through a composite phase metasurface, 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 in that: 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 superimposed 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.

2. The composite phase metasurface for generating a tunable elliptical Airy beam according to claim 1, characterized in that: The first phase and the second phase satisfy any one of the following phase distributions: 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: F intergral =ar 2 θ0 In the formula, Φ intergral represents the superposition 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; The second type: the first phase is a first Fresnel holographic lens phase, and the second phase is a 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.

3. The composite phase metasurface for generating a tunable elliptical Airy beam according to claim 2, characterized in that: 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: f θ =λ / (πaθ0) In the formula, 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.

4. The composite phase metasurface for generating a tunable elliptical Airy beam according to claim 2, characterized in that: When the first phase and the second phase satisfy the second phase distribution, the adjusting the focal position of the elliptical Airy beam specifically includes: adjusting the lateral position of the focal point of the elliptical Airy beam.

5. The composite phase metasurface for generating a tunable elliptical Airy beam according to claim 2, characterized in that: 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; When the first phase metasurface rotates along a first direction at an angle of θ1, and the second phase metasurface rotates along a second direction opposite to the first direction at an angle of θ2, the phase distribution of the first Fresnel holographic lens phase satisfies the following formula: P1(x,y)=-π[(x+dcosθ1) 2 +(y-dsinθ1) 2 ] / (λF0) Wherein, 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, d represents the off-axis distance, and θ1 represents the angle of rotation of the first phase metasurface along the first direction; The phase distribution of the second Fresnel holographic lens phase satisfies the following formula: P2(x,y)=π[(x-dcosθ2) 2 +(y+dsinθ2) 2 ] / (λF0) Wherein, 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, d represents the off-axis distance, and θ2 represents the angle of rotation of the second phase metasurface along the second direction.

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

7. The composite phase metasurface for generating a tunable elliptical Airy beam according to claim 1, characterized in that: Each phase metasurface includes a substrate and a nanocolumn array arranged on one side surface of the substrate, and the one side surfaces of the two phase metasurfaces provided with the nanocolumn array 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, and the shape of the nanocolumns is a cylinder, and the radius of the cylinder increases radially from the center to the edge.

8. A method for generating a tunable elliptical Airy beam based on the composite phase metasurface according to any one of claims 1 to 7, characterized in that: The following steps are involved: 1) obtaining the nanocolumn array arrangement 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, coaxially and rotatably stacking them, and constructing the composite phase metasurface; 2) The original light beam is vertically incident from the side surface of the first phase metasurface where the nanocolumn array is not set, and 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 nanocolumn array is not set; 3) Taking 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.

9. The method for generating a tunable elliptical Airy beam according to claim 8, characterized in that: In the step 1), the phase distribution of the first phase metasurface is a superposition phase of a cubic phase and a first phase, the phase distribution of the second phase metasurface is a second phase, and the first phase and the second phase are complementary; the first phase and the second phase satisfy any one of the following phase distributions: 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: F intergral =ar 2 θ0 In the formula, Φ intergral represents the superposition 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; The second type: the first phase is the first Fresnel holographic lens phase, the second phase is the 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 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; When the first phase metasurface rotates along a first direction at an angle of θ1, and the second phase metasurface rotates along a second direction opposite to the first direction at an angle of θ2, the phase distribution of the first Fresnel holographic lens phase satisfies the following formula: P1(x,y)=-π[(x+dcosθ1) 2 +(y-dsinθ1) 2 ] / (λF0) Wherein, 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, d represents the off-axis distance, and θ1 represents the angle of rotation of the first phase metasurface along the first direction; The phase distribution of the second Fresnel holographic lens phase satisfies the following formula: P2(x,y)=π[(x-dcosθ2) 2 +(y+dsinθ2) 2 ] / (λF0) Wherein, 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, d represents the off-axis distance, and θ2 represents the angle of rotation of the second phase metasurface along the second direction.

10. The method for generating a tunable elliptical Airy beam according to claim 8, characterized in that: In the step 3), the focal position of the elliptical Airy beam is adjusted by any of the following methods: 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: f θ =λ / (πaθ0) In the formula, f θ represents the focal length of the composite phase metasurface, θ0 represents the relative rotation angle, λ represents the working wavelength, and a represents a constant; When the first phase and the second phase satisfy the second phase distribution, the lateral position of the focus of the elliptical Airy beam is adjusted.

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