A method for producing a controllable spatial light annulus

Abstract

The application provides a method for generating controllable spatial light annulus, which adopts a 4Pi optical focusing system, the 4Pi optical focusing system comprises two high numerical aperture objectives, and further comprises an antenna array element; the antenna array element forms a virtual annular array and is placed at the center of the focal volume of the optical focusing system, the total radiation field generated by the virtual annular array is calculated, the high numerical aperture objectives collect the radiation field generated by the virtual annular array and collimate the radiation field to the pupil plane, the incident field distribution on the two pupil planes is obtained by inversely solving the radiation field; the obtained incident field is reversed and relatively phase-shifted by π to serve as the input of the whole 4Pi optical focusing system, and the input is focused from the pupil plane to the center of the 4Pi optical focusing system to form a light annulus focal field. The application of the technical scheme can realize a light annulus focal field with controllable radius, position, ring number and layer number, and is expected to meet the needs of some higher-level applications and further improve the efficiency of the light field in the field of micro-nano structure processing.

Description

Technical Field

[0001] This invention relates to the field of novel optical focal field customization technology, and in particular to a method for generating a controllable spatial optical ring. Background Technology

[0002] Based on the vector diffraction theory proposed by Richards-Wolf, it was discovered that focusing a vector beam using a high numerical aperture objective lens will yield a strong longitudinal component. This study is the first to uncover the application value of vector light fields in the field of tight focusing, which has led to a rapid increase in interest in the field of vector light field research.

[0003] In recent years, optical focal fields with specific forms, such as multifocal arrays, optical needles, and optical tubes, have shown significant applications in particle trapping and capture, particle acceleration, and photolithography. In 2009, Chen WB and Zhan QW first utilized the radiation pattern of an electric dipole antenna to generate a spherical spot in a 4Pi focusing system. In 2019, YuY Z et al. reported a method for generating a two-dimensional circular array focal spot with controllable characteristics using the radiation field of an electric dipole array antenna. In 2022, Xia XL et al. separately focused and controlled two sets of radially polarized and angularly polarized beams of cylindrical vector light, then superimposed the two sets of polarized light fields in the focal region with appropriate amplitude ratios to synthesize a quasi-spherical multifocal array. Currently, much attention has been paid to special forms of optical focal fields such as bright spots, optical needles, optical chains, and optical tubes in the field of close focusing. However, relatively little research has focused on optical annular focal fields. For some more advanced applications, the aforementioned published reports lack simplicity and flexibility, and can no longer fully meet the needs. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for generating a controllable spatial optical ring, realizing a controllable focal field of the optical ring in terms of radius, position, number of rings and number of layers, in order to meet the needs of some more advanced applications and further improve the efficiency of the optical field in the field of micro-nano structure fabrication.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for generating a controllable spatial optical ring, employing a 4Pi optical focusing system. The 4Pi optical focusing system includes two identical, symmetrically placed, and confocal high numerical aperture objectives, and two antenna elements composed of orthogonally superimposed electric dipoles placed along the X-axis and Y-axis, respectively. The antenna elements form a virtual ring array and are placed at the focal volume center of the optical focusing system. The total radiation field generated by the virtual ring array is calculated, and the radiation field generated by the symmetrically placed high numerical aperture objectives is completely collected by the left and right sides and aligned to the pupil plane. The incident field distribution on both pupil planes is obtained by solving the radiation field in reverse. The obtained incident field is inverted and phase-shifted relative to π and used as the input of the entire 4Pi optical focusing system. It is focused from the pupil plane through the lens towards the center of the 4Pi optical focusing system to form the desired optical ring focal field.

[0006] In a preferred embodiment, a circular array of orthogonal superimposed electric dipole elements is formed, and the radiation field of the orthogonal superimposed electric dipole elements is derived and calculated using antenna radiation theory. The expression is:

[0007]

[0008] C, which is independent of the radiation coefficient x and C y Normalized to 1; where It is the unit vector along the θ direction in the radiation field. It is along the radiation field The unit vector of direction; therefore, after simplification, we get the following formula:

[0009]

[0010] Combining the array factor at any spatial location, and according to the antenna array pattern product theorem, the array factor of a circular array composed of orthogonal superimposed electric dipole elements is:

[0011]

[0012] Where k = 2π / λ represents the wave number, and θ represents the angle between the antenna radiation direction and the Z-axis. H represents its azimuth angle; H represents the number of center coordinates, (x h ,y h ,z h ) represents the spatial Cartesian coordinates of the center of the annulus, M represents the number of annulus rings in the array, and R m Let N represent the radius of each ring in the circular array, and let N represent the number of orthogonal superimposed electric dipole elements required to form the corresponding ring. This condition holds when N ≥ 14R. m / λ, that is, forming a radius of R m A uniformly distributed ring of light. This represents the azimuth angle from the positive X-axis to the nth orthogonal superimposed electric dipole element in the annular array, from which the total radiation field of the spatial optical annular array is obtained. for:

[0013]

[0014] Assuming the circular array is located near the focal point of a 4Pi optical focusing system, the total radiation field generated by the virtual circular array is collected and collimated onto the pupil plane by two perfectly symmetrical high numerical aperture objectives. Using time-reversal techniques, the radiation field of the virtual circular array is solved in reverse, thus obtaining the incident field at the pupil planes on both sides. Used as input for the entire 4Pi optical focusing system.

[0015] In a preferred embodiment, for high numerical aperture lenses that satisfy the Helmholtz condition, their apodization function is utilized. The incident field distribution on the normalized pupil surface is obtained. for:

[0016]

[0017] This incident field distribution can be achieved using spatial light modulation technology and novel metasurface technology that controls micro- and nano-optical information.

[0018] In a preferred embodiment, finally, the desired incident field described above is... As the input field for the entire 4Pi optical focusing system, it propagates in reverse and is focused. The corresponding focal field is calculated using the Richards-Wolfe vector diffraction method as follows:

[0019]

[0020]

[0021]

[0022] in C0 is the amplitude constant. These represent the field components along the X, Y, and Z directions at the observation point on the focal plane, respectively.

[0023] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for generating controllable spatial optical rings. In a 4Pi optical focusing system, by reverse focusing the radiation field of a virtual ring array, the focal field of the optical ring with controllable radius, position, number of rings and layers can be flexibly realized. It is expected to meet the needs of some more advanced applications and further improve the efficiency of the optical field in the field of micro-nano structure fabrication. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the focusing principle of the circular array according to a preferred embodiment of the present invention;

[0025] Figure 2 This is a three-dimensional spatial multi-ring array, a preferred embodiment of the present invention.

[0026] Figure 3 This is a 3D image of a single-light annulus with a center position of (0, 0, 0) and a radius of 1λ, representing a preferred embodiment of the present invention.

[0027] Figure 4 This is a preferred embodiment of the present invention. Figure 3 Top view of the XY plane;

[0028] Figure 5 The image shows a 3D model of a single-light annulus with a center position of (0, 0, 0) and a radius of 2.5λ, representing a preferred embodiment of the present invention.

[0029] Figure 6 A 3D diagram of a single-light ring with a center position of (-1λ, 1λ, 0) and a radius of 1λ, representing a preferred embodiment of the present invention;

[0030] Figure 7 This is a preferred embodiment of the present invention. Figure 6 Top view of the XY plane;

[0031] Figure 8 This is a 3D diagram of a double-ring optical ring according to a preferred embodiment of the present invention;

[0032] Figure 9 This is a 3D diagram of a three-ring optical ring according to a preferred embodiment of the present invention;

[0033] Figure 10 This is a 3D diagram of a preferred embodiment of the double-layer optical ring of the present invention;

[0034] Figure 11 This is a diagram showing the incident field distribution at the pupil surface in a preferred embodiment of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0037] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0038] This invention introduces a method for flexibly generating a controllable circular focal field from a circular array of orthogonal superimposed electric dipole elements in a 4Pi optical focusing system.

[0039] The 4Pi optical focusing system used in this invention consists of two identical, perfectly symmetrical, and confocal high numerical aperture objectives. An antenna array composed of two orthogonally superimposed electric dipoles placed along the X and Y axes is used. A virtual circular array formed by these antenna elements is placed at the focal volume center of the 4Pi focusing system, and the total radiation field generated by this virtual circular array is calculated. The symmetrical high numerical aperture objectives then completely collect this radiation field and collimate it onto the pupil plane. By inverting the radiation field, the incident field distribution on both pupil planes can be obtained. The obtained incident field is inverted and phase-shifted relative to π and used as the input to the entire 4Pi optical focusing system. It is focused from the pupil plane through the lens towards the center of the 4Pi focusing system to form the desired optical circular focal field.

[0040] A circular array composed of orthogonal superimposed electric dipole elements, such as Figure 2 As shown, the radiation field of an orthogonal superimposed electric dipole array element is derived and calculated using antenna radiation theory. The expression is:

[0041]

[0042] Generally, for the sake of simplified calculation, we will consider C, which is independent of the radiation coefficient, as... x and C y Normalized to 1; where It is the unit vector along the θ direction in the radiation field. It is along the radiation field The unit vector of direction. Therefore, after simplification, we get the following formula:

[0043]

[0044] Combining the array factor at any spatial location, and according to the antenna array pattern product theorem, the array factor of a circular array composed of orthogonal superimposed electric dipole elements can be obtained as follows:

[0045]

[0046] To simplify calculations, all coefficients independent of the optical focal field shape are omitted. Here, k = 2π / λ represents the wavenumber, and θ represents the angle between the antenna radiation direction and the Z-axis (optical axis). This indicates its azimuth. H represents the number of coordinates of the center of the circle, (x... h ,y h ,z h ) represents the spatial Cartesian coordinates of the center of the annulus, M represents the number of annulus rings in the array, and R m N represents the radius of each ring in the circular array, and N represents the number of array elements of the orthogonal superimposed electric dipoles required to form the corresponding ring (when N ≥ 14R). m / λ, which can form a radius of R m A uniformly distributed light ring (of light intensity). This represents the azimuth angle from the positive half-axis of the X-axis to the nth orthogonal superimposed electric dipole element in the circular array, such as... Figure 2 As shown. From this, the total radiation field of the spatial optical ring array can be obtained. for:

[0047]

[0048] Assuming the circular array is located near the focal point of the 4Pi focusing system, such as Figure 1 As shown in the purple area, the total radiation field generated by the virtual ring array is collected and collimated to the pupil plane by two perfectly symmetrical high numerical aperture objectives. Using time-reversal techniques, the radiation field of the virtual ring array is solved in reverse, thus allowing the determination of the incident field at the pupil planes on both sides. Used as input for the entire 4Pi focusing system.

[0049] For high numerical aperture lenses that satisfy the Helmholtz condition, their apodization function can be used. The incident field distribution on the normalized pupil plane can be obtained. for:

[0050]

[0051] This incident field distribution can be achieved using spatial light modulation technology and novel metasurface technology that controls micro- and nano-optical information.

[0052] Finally, the required incident field mentioned above As the input field for the entire 4Pi focusing system, it propagates backward and is focused. The corresponding focal field is calculated using the Richards-Wolfe vector diffraction method as follows:

[0053]

[0054]

[0055]

[0056] in C0 is the amplitude constant. These represent the field components along the X, Y, and Z directions at the observation point on the focal plane, respectively.

[0057] Figure 1 In this context, a 4Pi optical focusing system is formed by two confocal, perfectly symmetrical high numerical aperture objectives. A virtual circular array is placed at the center of the 4Pi focusing system (e.g., ...). Figure 4 The purple area at the center of the Pi focusing system is shown. This system was used to achieve the total radiation field of the virtual circular array. Complete collection (as shown by the black dashed arrow in the figure), and collimated to the pupil planes on both sides through two symmetrical objective lenses, relative π phase shift (as shown by the blue realization arrow in the figure), to obtain the desired incident field. (As shown by the red dashed arrow in the figure) it propagates in reverse and is highly focused to the center of the system, so that the desired focal field can be obtained in the focal volume.

[0058] To simplify calculations, coefficients independent of the circular array radiation were normalized to 1, i.e., the amplitude constant C0 was set to 1. Furthermore, the NA value of both lenses collecting the radiation field was set to 1, meaning the maximum convergence angle was set to θ. max =π / 2, to achieve complete collection of the radiation field by the lens. This setting can be achieved by using a reflecting objective or a non-surface plane lens.

[0059] Example 1: Generation of a single-beam circular focal field

[0060] Let the number of rings in the virtual annular array be M = 1, and the number of annular centers be H = 1. At this point...

[0061] (1.1) Set the parameters x1=0, y1=0, z1=0, that is, the center coordinates are (0,0,0), and the radius R1=1λ. Substitute these into equation (3), and combine them with equations (4) and (6-8) to obtain the focal field of a single optical ring, such as Figure 3 As shown, Figure 4 yes Figure 3The top view of the XY plane shows that the center of the optical ring is located at the same coordinates (0, 0, 0) and the radius of the optical ring is 1λ, which is determined by the position parameters (x1, y1, z1) and radius parameter R1 of the ring array.

[0062] (1.2) When changing the radius parameters of the annular array, setting the radius R1 = 2.5λ, and simultaneously letting x1 = 0, y1 = 0, z1 = 0, then we obtain single optical annular focal fields with different radii and the center coordinates of the annulus (0, 0, 0), such as... Figure 5 As shown, the radius of its optical ring is consistent with the parameter values ​​set for the ring array.

[0063] (1.3) When changing the center position parameters of the annular array, setting x1 = 0, y1 = 0, z1 = 0, that is, the coordinates of the annular center are (-1λ, 1λ, 0), and simultaneously setting the radius R1 = 1λ, then the focal field of a single optical annular ring with a radius of 1λ at different positions is obtained, such as... Figure 6 As shown, Figure 7 yes Figure 6 The top view shows that the position of the optical ring is consistent with the parameter values ​​set for the ring array.

[0064] Therefore, from Figure 3 , Figure 5 and Figure 6 It can be seen that the radius and position of the optical ring can be flexibly adjusted by adjusting the radius parameter R1 and the center parameter (x1, y1, z1) of the ring array.

[0065] Example 2: Generation of a multi-beam circular focal field

[0066] (2.1) Let the parameters of the virtual circular array be H = 1, the number of centers of the circular array be x1 = 0, y1 = 0, z1 = 0, that is, the center coordinates of the circular array are (0, 0, 0).

[0067] When the ring number parameter of the circular array is changed, setting the ring number M=2, and the radii from the inside out being R1=1λ and R2=4λ respectively, substituting into equations (2-4) and (6-8), the focal field of the double-ring optical circular array can be obtained, such as... Figure 8 As shown. With the number of rings M = 3, and the radii from the inside out being R1 = 1λ, R2 = 3λ, and R3 = 5λ respectively, substituting these values ​​into equations (2-4) and (6-8) yields the focal field of the three-ring optical circle, as shown. Figure 9 As shown. By Figure 8 and Figure 9 It can be seen that the number of rings and the radius of each ring are determined by the ring number parameter M of the ring array and the corresponding radius R. m Decide.

[0068] (2.2) Let the parameters of the virtual circular array be: the number of rings M = 1, the radius R1 = 2.5λ, and the number of centers H = 2. The coordinates of the two centers are set as x1 = 0, y1 = 0, z1 = -2.5λ and x2 = 0, y2 = 0, z2 = 2.5λ, respectively. That is, the coordinates of the two centers are (0, 0, -2.5λ) and (0, 0, 2.5λ). Substituting these into equations (2-4) and (6-8), the double-layer optical circular focal field can be obtained, as follows: Figure 10 As shown. Therefore, the number of layers in the optical ring array can be controlled by adjusting the number of centers H and the position parameter (x). h ,y h ,z h (To decide)

[0069] Example 3: Different incident field distributions at the pupil plane are required for customizing different optical ring focal fields. For an objective lens that satisfies the Helmholtz condition, a single optical ring with center coordinates (0, 0, 0) and R1 = 2.5λ (i.e., Figure 5 Taking the example shown, by substituting equations (1) and (3-4) into equation (5), the required incident field distribution on the pupil surface can be calculated, such as... Figure 11 As shown.

[0070] This invention combines antenna array pattern synthesis theory and electromagnetic time reversal technology to demonstrate the effectiveness and flexibility of the proposed method for generating controllable optical rings. The proposed method can be easily implemented using the radiation field of an inverse-focusing ring array. By inverse solving, the required incident field distribution on the pupil plane for generating a three-dimensional circular optical ring can be calculated. Numerical results show that by adjusting the parameters of the ring array, a spatial optical ring focal field with controllable radius, position, number of rings, and number of layers can be flexibly constructed. The resulting controllable optical ring focal field has higher degrees of freedom in optical field manipulation, and many potential applications can be found in fields such as arbitrary orientation particle capture and guidance, multi-particle acceleration, laser guide tubes, and optical capture and manipulation.

Claims

1. A method for generating a controllable spatial optical ring, characterized in that, A 4Pi optical focusing system is employed, comprising two identical, symmetrically placed, and confocal high numerical aperture objectives, and two antenna elements composed of orthogonally superimposed electric dipoles placed along the X and Y axes, respectively. These antenna elements form a virtual circular array and are placed at the focal volume center of the optical focusing system. The total radiation field generated by this virtual circular array is calculated, and the symmetrical high numerical aperture objectives completely collect this radiation field and collimate it onto the pupil surface. By inverting the radiation field, the incident field distribution on both pupil surfaces is obtained. The obtained incident field is inverted and phase-shifted relative to π and then used as the input to the entire 4Pi optical focusing system. It is focused from the pupil surface through the lens towards the center of the 4Pi optical focusing system to form the desired optical circular focal field. The radiation field of the orthogonal superimposed electric dipole array elements, which form a circular array, is derived and calculated using antenna radiation theory. The expression is: （1） C, which is independent of the radiation coefficient x and C y Normalized to 1; where It is along the radiation field The unit vector of direction, It is along the radiation field The unit vector of direction; therefore, after simplification, we get the following formula: （2） Combining the array factor at any spatial location, and according to the antenna array pattern product theorem, the array factor of a circular array composed of orthogonal superimposed electric dipole elements is: （3） in Represents wave number, This indicates the angle between the antenna's radiation direction and the Z-axis. H represents its azimuth angle; H represents the number of center coordinates, (x h , y h , z h ) represents the spatial Cartesian coordinates of the center of the annulus, M represents the number of annulus rings in the array, and R m Let N represent the radius of each ring in the circular array, and let N represent the number of elements of the orthogonal superimposed electric dipoles required to form the corresponding ring. When N satisfies... That is, forming a radius of R m A uniformly distributed ring of light. This represents the azimuth angle from the positive X-axis to the nth orthogonal superimposed electric dipole element in the annular array, from which the total radiation field of the spatial optical annular array is obtained. for: （4） Assuming the circular array is located near the focal point of a 4Pi optical focusing system, the total radiation field generated by the virtual circular array is collected and collimated onto the pupil plane by two perfectly symmetrical high numerical aperture objectives. Using time-reversal techniques, the radiation field of the virtual circular array is solved in reverse, thus obtaining the incident field at the pupil planes on both sides. It is used as the input for the entire 4Pi optical focusing system.

2. The method for generating a controllable spatial optical ring according to claim 1, characterized in that, For high numerical aperture lenses that satisfy the Helmholtz condition, their apodization function can be used. The incident field distribution on the normalized pupil surface is obtained. for: （5） This incident field distribution can be achieved through spatial light modulation technology and novel metasurface technology that can be controlled by micro-nano optical information.

3. A method for generating a controllable spatial optical ring according to claim 2, characterized in that, Finally, the required incident field mentioned above As the input field for the entire 4Pi optical focusing system, it propagates in reverse and is focused. The corresponding focal field is calculated using the Richards-Wolfe vector diffraction method as follows: （6） （7） （8） in , Let be the amplitude constant. , ; , , These represent the field components along the X, Y, and Z directions at the observation point on the focal plane, respectively.

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