Method for generating multi-focus circular light beam based on all-dielectric metasurface

Abstract

The invention discloses a method for generating a multi-focus circular beam based on an all-dielectric metasurface, and the method specifically comprises the following steps: 1, constructing the all-dielectric metasurface which is composed of a plurality of arranged super atoms; the super atom comprises a square SiO2 substrate, and a rectangular Si nanorod is arranged on the SiO2 substrate; and 2, irradiating the all-dielectric metasurface by using left-hand circularly polarized light as incident light, and modulating the incident light by using a geometric phase and a propagation phase, so that emergent light of the all-dielectric metasurface forms a right-hand circularly polarized multi-focus circular light beam. According to the invention, the circularly symmetrical light beams with a plurality of self-focusing focuses can be efficiently and flexibly generated, and the number and the focal depth of the focuses can be adjusted as required.

Description

Technical Field

[0001] The present invention belongs to the field of optical engineering technology, and specifically relates to a method for generating multi-focal circular light beams based on an all-dielectric metasurface. Background Art

[0002] Beam focusing technology has key application value in the fields of laser processing, bio-imaging and optical capture. Traditional multi-focused beams are usually obtained through a complex optical path and a combination of multiple optical elements, such as spatial light modulators and lenses, which have problems such as bulky systems and low integration. Although the development of metasurface technology has provided a new way for beam control, the existing metasurface-based beam generation methods have the problem of difficulty in flexibly achieving multi-focus control, especially in terms of the dynamic adjustment of the number of focal points and depth of focus. For example, traditional methods can only achieve one or two focal points on the optical axis, which may not meet the diverse needs of long-distance imaging and optical manipulation. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for generating a multi-focal circular beam based on an all-dielectric metasurface. The present invention can efficiently and flexibly generate a circularly symmetric beam with multiple self-focusing focal points, and the number of focal points and focal depth can be adjusted as needed.

[0004] The technical solution of the present invention is a method for generating a multi-focus circular beam based on an all-dielectric metasurface, which specifically includes the following steps: Step 1: constructing an all-dielectric metasurface, wherein the all-dielectric metasurface is composed of a plurality of metaatoms arranged; the metaatoms include a square SiO2 substrate, on which rectangular Si nanorods are arranged; Step 2: Irradiate the all-dielectric metasurface with left-handed circularly polarized light as incident light, and modulate the incident light using geometric phase and propagation phase so that the outgoing light from the all-dielectric metasurface forms a right-handed circularly polarized multi-focal circular beam.

[0005] In the aforementioned generation of multi-focus circular beams based on all-dielectric metasurfaces, in step 1, the period of the meta-atom is ; The height of the Si nanorods is , the length is , with a width of The angle between the long side of the cross section of the Si nanorod and the side of the SiO2 substrate is the rotation angle .

[0006] In the aforementioned generation of multi-focus circular beams based on all-dielectric metasurfaces, the height of the Si nanorods is =0.8μm, period =0.7μm, length =0.24μm, width is 0.25-0.46 μm to achieve 2π phase coverage.

[0007] In the aforementioned generation of multi-focal circular beams based on all-dielectric metasurfaces, in step 2, the initial electric field of the incident light is defined by a hyperbolic umbilical caustic field, and its initial electric field distribution satisfies: ; Where, and is a scalar value in the transverse space coordinate, is the radial coordinate, is the interpolation intercept, is the scaling factor, is the interpolation direction, is a constant parameter, is the Gaussian attenuation factor, parameter It is related to power. represents the caustic field, and the formula is: ; in, is the spatial coordinate scalar of the light field in the propagation direction, and is the integral variable introduced in the hyperbolic umbilical caustic field, It is the imaginary unit in mathematics.

[0008] In the aforementioned generation of multi-focus circular beams based on all-medium metasurfaces, by adjusting the interpolation intercept and parameters To regulate the number of focal points and focal depth of the multi-focal circular beam.

[0009] In the aforementioned generation of multi-focal circular beams based on the all-dielectric metasurface, the relationship between the outgoing polarization state and the incident polarization state of the incident light is: ; Where, and Describe the incident polarization state and the outgoing polarization state respectively Jones vector in the basis, is the rotation angle of the all-dielectric metasurface metaatom, is the angle by which the unit vector in the plane is rotated A 2×2 matrix, is the matrix of the outgoing amplitude and propagation phase of light polarized along the ordinary and extraordinary axes, respectively; The matrix The formula is: ; Where, is the outgoing amplitude of light polarized along the ordinary axis, is the outgoing amplitude of light polarized along the extraordinary axis, is the propagation phase of light polarized along the ordinary axis, is the propagation phase of light polarized along the extraordinary axis, It is the imaginary unit in mathematics; The propagation phase of the light polarized along the ordinary axis The formula is: ; The propagation phase of the light polarized along the extraordinary axis The formula is: ; Where, is the height of the Si nanorods, and Represents the refractive index of the ordinary axis and extraordinary axis; is the wave number in vacuum, ; is the wavelength of the incident light.

[0010] In the aforementioned generation of multi-focal circular beams based on the all-dielectric metasurface, the geometric phase and propagation phase modulate the incident light to satisfy the formula: ; Where, represents the right-handed circularly polarized component signal, is the mathematical imaginary unit, Represents the physical polarization state of right-handed circularly polarized light RCP, Represents the physical polarization state of left-handed circularly polarized light LCP.

[0011] In the aforementioned generation of multi-focus circular beams based on the all-dielectric metasurface, the all-dielectric metasurface generates an off-axis distance of of A multi-focus circular beam array; The position vector of the beam Expressed as: ; Where, Indicates the The position vector of the beam in the x-axis direction, Indicates the The position vector of the beam in the y-axis direction; ; ; Where, is the number of outgoing beams, It is the number of foci of the multi-focus circular beam array generated by the rotationally symmetrical arrangement of metaatoms on the all-dielectric metasurface.

[0012] Compared with the prior art, the present invention has the following beneficial effects: By cleverly combining the dual modulation mechanisms of geometric phase and propagation phase, the present invention achieves coordinated control of lightwave amplitude and propagation phase, thereby outputting a right-handed circularly polarized multi-focal circular beam with a specific amplitude and phase distribution. Furthermore, the present invention innovatively employs a rotationally symmetric arrangement method, successfully achieving the generation of a multi-focal circular beam array through a carefully designed superatomic structure arrangement. This invention frees itself from the constraints of bulky optical components, facilitating integration into micro-optical systems, improving the accuracy of beam manipulation, and expanding its applicability in complex optical systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Schematic diagram of the metasurface of the MFCB of the present invention that generates right-handed polarization when incident light is incident; wherein (a) is a schematic diagram of the metasurface of the MFCB that generates right-handed polarization when incident left-handed light is incident, (b) is a schematic diagram of the unit structure, and (c) is a top view of the unit structure; Figure 2 The initial light intensity distribution diagram under different parameters on the initial plane of the present invention; wherein (a) is the initial plane =8, =30 The initial light intensity distribution, (b) is the initial plane =8, =50 The initial light intensity distribution, (c) is the initial plane =11、 =30 The initial light intensity distribution, (d) is the initial plane =11、 =30 Initial light intensity distribution; Figure 3 The unit structure of the scanning parameters of the present invention and the amplitude and phase of the transmitted light field simulated by the scanning parameters vary with the width and rotation angle of the silicon nanorod; wherein (a) is a unit structure diagram of the scanning parameters, and (b) is a diagram showing the amplitude and phase of the transmitted light field simulated by the scanning parameters as they vary with the width and rotation angle of the silicon nanorod; Figure 4 The present invention is in the parameters =0.002, =0.0016mm, =-0.05π, =8, and = Simulation diagram of MFCB beam propagation when Figure 4 (a) is the curve of self-focusing efficiency changing with propagation distance z. Figure 4 (b) is the side view of the light intensity within 300μm in the xz plane. Figure 4 (c) and (e) correspond to the lateral light intensity distribution of the two highest intensity planes marked in (a) and (b). Figure 4 (d) and (f) correspond to the light intensity distribution at the bottom of the trough adjacent to the highest peak of the curve in Figure (a); Figure 5 The present invention is in the parameters =0.002, =0.0016mm, =-0.05π, =8, =30 and =50 Simulation diagram of MFCB beam propagation when Figure 5 (a) and (b) are the side views of the light intensity within 300 μm in the xz plane. Figure 5 (c) and (d) are the curves of self-focusing intensity changing with propagation distance z. Figure 5 (e) and (g) show =30 When the main and secondary focus positions (corresponding to Figure 5 (a) and Figure 5 The xy-plane light intensity distribution (dashed lines z1 and z2 in (c)) is Figure 5 (f) and (h) show =50 When the main and secondary focus positions (corresponding to Figure 5 (b) and Figure 5 (d) The xy-plane light intensity distribution of z3 and z4 (dashed lines); Figure 6 The present invention is in the parameters =0.002, =0.0016mm, =-0.05π, =30 , =10 and Simulation diagram of MFCB beam propagation when = 12, Figure 6 (a) and (b) are the side views of the light intensity within 300 μm in the xz plane. Figure 6 (c) and (d) Curves of normalized light intensity changing with propagation distance z, Figure 6 (e)-(g) display =10 when the main and secondary focal positions (corresponding to Figure 6 (a) and Figure 6 (c) The xy plane light intensity distribution (dashed lines z1 and z2 in the middle), Figure 6 (f)-(h) display =12 when the main and secondary focal positions (corresponding to Figure 6 (b) and Figure 6 (d) The xy-plane light intensity distribution of z3 and z4 (dashed lines); Figure 7 The MFCB beam of the present invention is = 0.002, = 10, =0.0016mm, =30 and =-0.05π propagation simulation diagram, where Figure 7 (a) Figure is =42.14 µm, =3, the xy plane distribution, Figure 7 (b) Figure is =42.14µm, =4, the xy plane distribution, Figure 7 (c) Figure corresponds to Figure 7 (a) Intensity distribution diagram, Figure 7 (d) Figure corresponds to Figure 7 (b) Intensity distribution diagram. DETAILED DESCRIPTION

[0014] The present invention will be further described below with reference to the accompanying drawings and examples, but they are not intended to limit the present invention.

[0015] Example: A method for generating multi-focus circular beams based on an all-dielectric metasurface, such as Figure 1 As shown, the specific steps include: Step 1: constructing an all-dielectric metasurface, wherein the all-dielectric metasurface is composed of a plurality of metaatoms arranged; the metaatoms include a square SiO2 substrate, on which rectangular Si nanorods are arranged; In this step, the period of the superatom is ; The height of the Si nanorods is , the length is , with a width of The angle between the long side of the cross section of the Si nanorod and the side of the SiO2 substrate is the rotation angle .

[0016] In this embodiment, Si nanorods are =0.8μm, period =0.7μm, length =0.24μm, width is 0.25-0.46 μm to achieve 2π phase coverage.

[0017] Step 2: Irradiate the all-dielectric metasurface with left-handed circularly polarized light as incident light, and modulate the incident light using geometric phase and propagation phase so that the outgoing light from the all-dielectric metasurface forms a right-handed circularly polarized multi-focal circular beam.

[0018] Based on the catastrophe theory, the hyperbolic umbilical caustic field is defined, the initial electric field distribution is generated, and the initial electric field distribution is mapped to the superatomic arrangement; catastrophe theory is a mathematical tool for studying sudden changes in the state of a system. In optics, it is used to describe the singularity distribution of the light field caused by phase singularities (such as focus and vortex). In catastrophe theory, the cusp caustic field is defined as the standard diffraction integral. The canonical potential function is a polynomial, which is a vector or scalar of the parameterized potential. For hyperbolic umbilical caustics belonging to the umbilical cord catastrophe, using Thom's standard form of the potential function, the corresponding caustic field expression can be obtained as: ; in, and is a scalar value in the transverse space coordinate, and is the integral variable introduced in the hyperbolic umbilical caustic field, is the imaginary unit in mathematics. The hyperbolic umbilical caustic field can generate an asymmetric multi-focus structure, which is suitable for circularly symmetric beam arrays. or When the value is large, rapid oscillation will occur. Through the Airy function transformation, a more efficient single integral form is obtained. For Multi-Focus Self-Focusing Light Bounding (MFCB), select The single integral form of =0 plane, the initial electric field of the beam is defined, and the distribution of the initial electric field satisfies: ; Where, is the radial coordinate, is the interpolation intercept, is the scaling factor, is the interpolation direction, is a constant parameter, is the Gaussian attenuation factor, parameter Related to power (PIB), represents a caustic field.

[0019] In this embodiment, adjust The value of 1 mW is used to adjust the optical power to 1 mW while maintaining the proportionality factor =0.0016 mm unchanged. Figure 2 Shown when =0.002, =0.0016mm, =0.05π, and (a) =8, =30 , (b) =8, =50 , (c) =10, =30 , (d) =12, =30 hour, =0 plane. The process of mapping the initial electric field distribution to the superatom arrangement is to adjust the interpolation intercept and parameters To regulate the number of focal points and focal depth of the multi-focal circular beam; wherein, when When it increases, the number of focal points decreases; when As it increases, the number of focal points increases.

[0020] In this embodiment, the polarization state of the incident light is LCP light, and the wavelength of the incident light is The optical wave amplitude is 1.55μm, based on the principle of joint control of the metasurface complex amplitude of the geometric phase (Pancharatnam-Berry Phase) and the propagation phase. The core of this principle is to achieve coordinated control of the light wave amplitude and propagation phase by designing the structural parameters and rotation of the birefringent meta-atom. When linearly polarized light passes through the rotating anisotropic meta-atom, its polarization direction changes with the rotation angle of the meta-atom. changes, resulting in a phase delay of 2 (Geometric phase). This phenomenon originates from the geometric path integral of the polarization state on the Poincare sphere, which has nothing to do with the propagation distance and depends only on the rotation angle of the superatom. By rotating the angle of the Si nanorod , regulating the polarization state conversion of the incident light (such as left-handed circularly polarized light LCP), thereby introducing the geometric phase (such as the phase 2 of right-handed circularly polarized light RCP) ).

[0021] However, the relationship between the outgoing polarization state and the incident polarization state of the incident light is: ; Where, and Describe the incident polarization state and the outgoing polarization state respectively Jones vector in the basis, is the rotation angle of the all-dielectric metasurface metaatom, is the angle by which the unit vector in the plane is rotated A 2×2 matrix, is the matrix of the output amplitude and propagation phase of light polarized along the ordinary axis and extraordinary axis respectively; the polarization direction of the light along the ordinary axis (o axis) is parallel to the long side of the Si nanorod, and the refractive index is ; The polarization direction of the extraordinary axis (e-axis) light is perpendicular to the long side of the Si nanorod, and the refractive index is (The birefringence of silicon causes ).

[0022] The matrix The formula is: ; Where, is the outgoing amplitude of light polarized along the ordinary axis, is the outgoing amplitude of light polarized along the extraordinary axis, is the propagation phase of light polarized along the ordinary axis, is the propagation phase of light polarized along the extraordinary axis, It is the imaginary unit in mathematics; The propagation phase of the light polarized along the ordinary axis The formula is: ; The propagation phase of the light polarized along the extraordinary axis The formula is: ; Where, is the height of the Si nanorods, which directly determines the optical path difference of light propagation in the o-axis / e-axis, thereby achieving phase delay (such as ), and Represents the refractive index of the ordinary axis and extraordinary axis; is the wave number in vacuum, ; is the wavelength of the incident light.

[0023] The geometric phase and propagation phase modulate the incident light to satisfy the formula: ; Where, represents the right-handed circularly polarized component signal, is the mathematical imaginary unit, Represents the physical polarization state of right-handed circularly polarized light RCP, Represents the physical polarization state of left-handed circularly polarized light LCP.

[0024] Therefore, the right circular polarization component signal A complex value with amplitude and phase. The amplitude depends only on the sine term, the argument of which depends inter alia on the degree of birefringence of the variable atom ( and ). This magnitude can also be thought of as the conversion magnitude: ; in, Represents the polarization conversion efficiency (or conversion amplitude) from left-handed circularly polarized light (LCP) to right-handed circularly polarized light (RCP), and is used to describe the efficiency or amplitude of polarization state conversion after the incident light passes through the all-dielectric metasurface.

[0025] In this example, the geometric parameters of the meta-atom are scanned using a finite-difference time-domain solver, and the optimized rectangular Si nanorod length is set to = 0.24µm, basically meets = =1. According to the geometric phase principle, when the incident light is left-handed circularly polarized (LCP), the right-handed circularly polarized (RCP) component in the transmitted light is generated through geometric phase control. In the present work, the finite-difference time-domain method (FDTD solution, Lumerical Inc.) in Lumerical software was used. Periodic boundary conditions were used in the xy-axis direction, and perfectly matched layer (PML) boundary conditions were used in the z-axis direction. and After the range of values ​​is determined, the rotation angle is introduced according to the geometric phase principle. , that is, the phase change is twice the unit superatom rotation angle. The superatomic rotation angle changes from 0.25µm to 0.46µm Starting from 0° and changing to 180°, the meta-atom amplitude changes from 0 to 1, and the phase delay of the transmitted light is sufficient to cover the entire 2 region, e.g. Figure 3 After designing a single Si nanorod, the initial light field of the multi-focus circular beam is then reproduced, and the constructed meta-atoms are arranged into an all-dielectric metasurface.

[0026] Step 4: The incident light is incident on the modulated all-dielectric metasurface to obtain a multi-focus circular beam.

[0027] The all-dielectric metasurface generates an off-axis distance (such as the radial distance from the focus to the optical axis) by arranging the metaatoms in a rotationally symmetrical manner. of A multi-focus circular beam array; The position vector of the beam Expressed as: ; Where, Indicates the The position vector of the beam in the x-axis direction, Indicates the The position vector of the beam in the y-axis direction; ; ; Where, is the number of outgoing beams, It is the number of foci of the multi-focus circular beam array generated by the rotationally symmetrical arrangement of metaatoms on the all-dielectric metasurface.

[0028] Figure 4 In the parameter =0.002, =0.0016mm, =-0.05π, =8, and = Simulation diagram of MFCB beam propagation when Figure 4 (a) is the curve of self-focusing efficiency changing with propagation distance z. Figure 4 (b) is the side view of the light intensity within 300μm in the xz plane. Figure 4 (c) and (e) correspond to the lateral light intensity distribution of the two highest intensity planes marked in (a) and (b). Figure 4 (d) and (f) correspond to the light intensity distribution at the bottom of the trough adjacent to the highest peak of the curve in Figure (a).

[0029] Figure 5 In the parameter =0.002, =0.0016mm, =-0.05π, =8, =30 and =50 Simulation diagram of MFCB beam propagation when Figure 5 (a) and (b) are the side views of the light intensity within 300 μm in the xz plane. Figure 5 (c) and (d) are the curves of self-focusing intensity changing with propagation distance z. Figure 5 (e) and (g) show =30 When the main and secondary focus positions (corresponding to Figure 5 (a) and Figure 5 The xy-plane light intensity distribution (dashed lines z1 and z2 in (c)) is Figure 5 (f) and (h) show =50 When the main and secondary focus positions (corresponding to Figure 5 (b) and Figure 5 (d) The xy-plane light intensity distribution of z3 and z4 (dashed lines).

[0030] Figure 6 In the parameter =0.002, =0.0016mm, =-0.05π, =30 , =10 and Simulation diagram of MFCB beam propagation when = 12, Figure 6 (a) and (b) are the side views of the light intensity within 300 μm in the xz plane. Figure 6 (c) and (d) Curves of normalized light intensity changing with propagation distance z, Figure 6 (e)-(g) display =10 when the main and secondary focal positions (corresponding to Figure 6 (a) and Figure 6 (c) The xy plane light intensity distribution (dashed lines z1 and z2 in the middle), Figure 6 (f)-(h) display =12 when the main and secondary focal positions (corresponding to Figure 6 (b) and Figure 6 (d) The xy-plane light intensity distribution of z3 and z4 (dashed lines).

[0031] In studying the interpolation intercept When regulating MFCB, by precisely adjusting this parameter, the longitudinal distribution characteristics of MFCB in the xz plane generated when left-handed light at a wavelength of 1.55μm is incident on the metasurface are characterized in detail. Figure 5 (a) and (b) show the =8 unchanged, corresponding to =30 and =50 The xz longitudinal field diagram of =30 When the ratio increases to 50, the beam forms eight focal points, and when the ratio increases to 50, the number of focal points decreases to five. The decrease in the number of focal points is not only related to the ratio but also to the The size of is not very close to 0, which leads to a decrease in the number of foci. This change reveals the important role of the interpolation intercept in regulating the number of foci. Figure 5(c) and (d) further show the focus intensity curves of the longitudinal field at different ratios. The self-focusing efficiencies are 68.3 for z1, 57.36 for z2, 78.98 for z3, and 59.23 for z4. Figure 5 (e) to (f) show the focal planes at different dashed lines (z = 43.14 μm, 64.21 μm, 34.11 μm, 71.24 μm) in the longitudinal xz plane, combined with Figure 5 The dotted lines in (c) and (d) are the locations of the focal maximum and the focal secondary maximum. These figures reveal the lateral distribution characteristics of the beam under different parameter settings. It is worth noting that there are significant differences in the beam convergence characteristics under the two parameter settings: =30 When , the beam shows weak convergence, and its light intensity basically decays to zero after propagating to 300µm. In contrast, when =50 When the beam is transmitted, the convergence of the beam is significantly enhanced, and the light intensity decays to a negligible level after only 200µm propagation distance. Figure 5 The corresponding FWHM values ​​of (e)-(f) are 1.44, 1.64, 1.09, and 1.34 μm, respectively, indicating that the difference in FWHM values ​​at different distances is small, and the energy variation during the transmission of the beam along the z-axis is relatively uniform and highly concentrated.

[0032] To analyze the parameters in depth Impact on MFCB propagation characteristics by system changes A detailed simulation study was conducted on the value of . Figure 6 (a) and (b) show the different Under the condition of the value, the electric field diagram of the focal intensity on the xz plane changes with the propagation distance. It can be seen that as As the value gradually increases, the number of foci tends to increase. Figure 6 (c) and (d) show The focus intensity curves for different longitudinal field values ​​show that the self-focusing efficiencies are 51.57 for z1, 51.78 for z2, 27.02 for z3, and 26.16 for z4. Figure 6 (e) to (f) show different dashed lines in the longitudinal xz plane ( =42.14μm, 55.18μm, 42.14μm and 62.14μm), combined Figure 6 The dotted lines in (a) and (b) are the selected focal points. As the value of increases, the number of outer rings increases. Figure 6 The corresponding FWHM values ​​of (e)-(f) are 1.36μm, 1.48μm, 1.34μm and 1.43μm, respectively.

[0033] In order to generate the MFCB array, a method based on rotating electric field modulation is adopted. Figure 7 As shown in (a), when left-handed circularly polarized light (LCP) is incident, three evenly distributed focal spots are successfully generated at the maximum focal plane (distance is 42.14 μm). The value is 3. These MFCBs maintain the complete waveform characteristics and show excellent intensity uniformity and focusing performance. Figure 7 As shown in (b), when the parameter When the value is 4, four evenly distributed focal points are observed at the maximum focal plane. In addition, Figure 7 (c) and (d) show the Figure 7 The lateral intensity distribution at the corresponding positions (a) and (b) further verifies the uniformity of the beam array. These results show that high-performance MFCB arrays can be achieved by combining the MFCB optical field with the rotating electric field modulation technique.

[0034] In summary, the present invention can efficiently and flexibly generate a circularly symmetric light beam with multiple self-focusing focal points, and the number of focal points and focal depth can be adjusted as needed.

Claims

1. A method for generating multi-focus circular beams based on an all-dielectric metasurface, characterized in that: The specific steps include: Step 1: constructing an all-dielectric metasurface, wherein the all-dielectric metasurface is composed of a plurality of metaatoms arranged; the metaatoms include a square SiO2 substrate, on which rectangular Si nanorods are arranged; Step 2: Irradiate the all-dielectric metasurface with left-handed circularly polarized light as incident light, and modulate the incident light using geometric phase and propagation phase so that the outgoing light from the all-dielectric metasurface forms a right-handed circularly polarized multi-focal circular beam.

2. The method for generating a multi-focus circular beam based on an all-dielectric metasurface according to claim 1, characterized in that: In step 1, the period of the superatom is ; The height of the Si nanorods is , the length is , with a width of The angle between the long side of the cross section of the Si nanorod and the side of the SiO2 substrate is the rotation angle .

3. The method for generating a multi-focal circular beam based on an all-dielectric metasurface according to claim 2, characterized in that: The height of the Si nanorods =0.8μm, period =0.7μm, length =0.24μm, width is 0.25-0.46 μm to achieve 2π phase coverage.

4. The method for generating a multi-focal circular beam based on an all-dielectric metasurface according to claim 1, characterized in that: In step 2, the initial electric field of the incident light is defined by a hyperbolic umbilical caustic field, and its initial electric field distribution satisfies: ； Where, and is a scalar value in the transverse space coordinate, is the radial coordinate, is the interpolation intercept, is the scaling factor, is the interpolation direction, is a constant parameter, is the Gaussian attenuation factor, parameter It is related to power. represents the caustic field, and the formula is: ； in, is the spatial coordinate scalar of the light field in the propagation direction, and is the integral variable introduced in the hyperbolic umbilical caustic field, It is the imaginary unit in mathematics.

5. The method for generating a multi-focus circular beam based on an all-dielectric metasurface according to claim 4, characterized in that: By adjusting the interpolation intercept and parameters To regulate the number of focal points and focal depth of the multi-focal circular beam.

6. The method for generating a multi-focal circular beam based on an all-dielectric metasurface according to claim 1, characterized in that: The relationship between the outgoing polarization state and the incident polarization state of the incident light is: ； Where, and Describe the incident polarization state and the outgoing polarization state respectively Jones vector in the basis, is the rotation angle of the all-dielectric metasurface metaatom, is the angle by which the unit vector in the plane is rotated A 2×2 matrix, is the matrix of the outgoing amplitude and propagation phase of light polarized along the ordinary and extraordinary axes, respectively; The matrix The formula is: ； Where, is the outgoing amplitude of light polarized along the ordinary axis, is the outgoing amplitude of light polarized along the extraordinary axis, is the propagation phase of light polarized along the ordinary axis, is the propagation phase of light polarized along the extraordinary axis, It is the imaginary unit in mathematics; The propagation phase of the light polarized along the ordinary axis The formula is: ； The propagation phase of the light polarized along the extraordinary axis The formula is: ； Where, is the height of the Si nanorods, and Represents the refractive index of the ordinary axis and extraordinary axis; is the wave number in vacuum, ; is the wavelength of the incident light.

7. The method for generating a multi-focal circular beam based on an all-dielectric metasurface according to claim 6, characterized in that: The geometric phase and propagation phase modulate the incident light to satisfy the formula: ； Where, represents the right-handed circularly polarized component signal, is the mathematical imaginary unit, Represents the physical polarization state of right-handed circularly polarized light RCP, Represents the physical polarization state of left-handed circularly polarized light LCP.

8. The method for generating a multi-focal circular beam based on an all-dielectric metasurface according to claim 1, characterized in that: The all-dielectric metasurface is generated by arranging superatoms in a rotationally symmetrical manner with an off-axis distance of of A multi-focus circular beam array; The position vector of the beam Expressed as: ； Where, Indicates the The position vector of the beam in the x-axis direction, Indicates the The position vector of the beam in the y-axis direction; ； ； Where, is the number of outgoing beams, It is the number of foci of the multi-focus circular beam array generated by the rotationally symmetrical arrangement of metaatoms on the all-dielectric metasurface.

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