WO2024221601A1 - 一种产生携带任意指向轨道角动量涡旋焦场的方法 - Google Patents
一种产生携带任意指向轨道角动量涡旋焦场的方法 Download PDFInfo
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- 230000005855 radiation Effects 0.000 claims abstract description 78
- 210000001747 pupil Anatomy 0.000 claims abstract description 47
- 230000003287 optical effect Effects 0.000 claims abstract description 44
- 238000005452 bending Methods 0.000 claims abstract description 7
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- 230000010363 phase shift Effects 0.000 claims abstract description 6
- 238000004364 calculation method Methods 0.000 claims description 19
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- 238000005457 optimization Methods 0.000 description 3
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- 238000012576 optical tweezer Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
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- 102100023591 Polyphosphoinositide phosphatase Human genes 0.000 description 1
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
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- G—PHYSICS
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- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
Definitions
- the invention relates to the technical field of generating a vortex focal field, and in particular to a method for generating a vortex focal field carrying an angular momentum of an orbit in any direction.
- angular momentum includes both spin angular momentum related to the circular polarization of light and orbital angular momentum (OAM) related to the spiral phase structure of light.
- OAM orbital angular momentum
- the earliest research on orbital angular momentum can be traced back to 1992 when Allen et al. published an article on the conversion of orbital angular momentum of light and Laguerre-Gaussian laser mode in the journal Physical Review A, establishing the relationship between the spiral phase structure of light and the orbital angular momentum it carries, opening the era of studying the orbital angular momentum of photons.
- the orbital angular momentum of photons provides a new degree of freedom for the application of light, and because the vortex light of different topological charges is orthogonal to each other, it can carry different optical information, and has great application potential in the field of optical communications. At the same time, it also has a wide range of applications in light manipulation, light processing, quantum information and super-resolution microscopy, and still attracts the attention of many scientific researchers.
- the present invention provides a method for generating a vortex focal field carrying orbital angular momentum in an arbitrary direction.
- the method only utilizes the radiation field of a dipole, superimposes a spatial spiral phase on it, and combines time reversal technology and Debye diffraction integral theory to generate a vortex focal field carrying OAM in an arbitrary direction.
- the technical solution adopted by the present invention is: a method for generating a vortex focal field carrying an arbitrarily directed orbital angular momentum, the method comprising the following steps:
- Step 1 Create a confocal area using two objective lenses Optical focusing system
- Step 2 A dipole is placed in the confocal region of the optical focusing system
- Step 3 calculate the radiation field of the dipole, and on this basis superimpose the spiral phase factor with the same spatial orientation to obtain the superimposed radiation field;
- Step 4 The optical focusing system collects and collimates the superimposed radiation field to The entrance pupil surface of the optical focusing system, and the radiation field of the entrance pupil surface is obtained based on the bending effect of the lens on the light;
- Step 5 Based on the time reversal technique, the radiation field at the entrance pupil is reversed and the relative 180-degree phase shift is used to obtain the The two sides of the entrance pupil plane of the optical focusing system propagate toward the confocal area of the two objective lenses, and a directional vortex focal field carrying orbital angular momentum with a specified topological charge can be formed in the confocal area.
- the The optical focusing system consists of two high numerical aperture objective lenses with exactly the same dimensions and optical parameters.
- the optical axes of the two objective lenses are on the same straight line and are placed confocally.
- the origin O of the reference rectangular coordinate system is the common focus of the two objective lenses;
- the direction of the optical axis is the Z axis, and the Z axis is perpendicular to the XOY plane;
- the Y axis is vertically upward, and the X axis is perpendicular to the YOZ plane.
- step 2 the center of the dipole is located at the origin O of the reference rectangular coordinate system, and the oscillation direction parameter of the dipole is ,in is the angle between the oscillation direction of the dipole and the Z axis of the reference rectangular coordinate system, It is the angle between the projection of the dipole's oscillation direction on the XOY plane and the positive direction of the X-axis.
- step 3 the radiation field generated by the dipole is obtained based on the electromagnetic radiation theory, and the calculation method is as follows:
- C is the constant coefficient of the radiation field,
- the coefficient of the component For the radiation field
- the coefficient of the component is an imaginary unit, is the dipole oscillation angular frequency, is the magnetic permeability in vacuum, is the magnitude of the dipole oscillating current, is the length of the dipole, is the spatial spherical coordinate of the radiation field, and is the unit vector in spherical coordinates.
- step 3 The calculation method of the spiral phase factor of the direction is as follows:
- topological charge number is the azimuth along the Z axis in the reference rectangular coordinate system, and its calculation formula is: ;
- the calculation process of the spiral phase factor is as follows: 1) Taking the XYZ reference rectangular coordinate system as the rotating whole, taking the origin O of the reference rectangular coordinate system as the rotation point, the Z axis rotates along the dipole oscillation direction and the plane where OZ is located in one step to direction, forming a rotated axis; 2) The X-axis and Y-axis of the reference rectangular coordinate system rotate synchronously to and axis, , and are the three principal axes of the new coordinate system after rotation; 3) The spatial direction is derived
- the spiral phase factor is:
- the azimuth angle of the axis direction is calculated as .
- the calculated coordinate is located at the origin and points to the space
- the radiation field of the dipoles is superimposed and the spiral phase factor with the same spatial orientation is calculated.
- the radiation field expression after superposition is as shown in the formula:
- step 4 the radiation field of the entrance pupil plane is calculated as follows:
- Two identical high numerical aperture objective lenses are placed parallel to each other in the Z-axis direction of the reference rectangular coordinate system, with the origin O as their confocal point and the XOY plane as their confocal plane.
- the calculated superposition radiation field radiates outward from the confocal area of the objective lens, and propagates outward after being collimated by two identical high numerical aperture objective lenses. According to the bending effect of the lens on the light, if the apodization function of the objective lens is , then the radiation field at the entrance pupil of the objective can be obtained as:
- step 5 based on the Debye vector diffraction integral formula, the focal field distribution in the confocal area can be calculated:
- step 5 based on the calculated electric field in the confocal area, the formula for calculating the spatial orientation of the OAM carried by the electric field in the confocal area is as follows:
- the present invention has the following advantages:
- the present invention integrates the radiation field of the dipole, ingeniously superimposes the corresponding spatial spiral phase, time reversal technology and Debye vector diffraction integral theory, and places a dipole at the origin of the reference rectangular coordinate system, and its spatial pointing parameter is ,in is the angle between the dipole axis and the Z axis, is the angle between the projection of the dipole on the XOY plane and the X-axis; set Its spatial orientation can be adjusted arbitrarily; on the basis of the dipole radiation field, the spiral phase with the same spatial orientation is superimposed; the superimposed radiation field is
- the focusing system collects and collides the radiation field at the entrance pupil plane, and uses a relative 180-degree phase shift from The entrance pupils on both sides of the focusing system propagate toward the confocal area, and a directional vortex focal field carrying an orbital angular momentum with a specified topological charge can be formed in the confocal area.
- the radiation field of a dipole is used to cleverly superimpose the corresponding spatial spiral phase to obtain an analytical expression for the required entrance pupil light field. Therefore, the method of the present invention does not require a complex optimization process, and the OAM direction of the constructed vortex focal field can be flexibly customized, and the topological charge of the OAM can also be customized.
- the calculation model of the method proposed in the present invention isaki and concise, and the calculation workload is small.
- the vortex field customized according to the method has broad application potential in the fields of optical tweezers, optical processing, etc.
- FIG. 1 is a schematic diagram of the present invention. Schematic diagram of the optical focusing system
- FIG. 2 is a diagram showing the focal field light intensity of the first embodiment of the present invention when it is half of the maximum value ( )’s 3D contour map;
- FIG3 is a light intensity distribution diagram of the focal field Z component in the XOY plane according to the first embodiment of the present invention
- FIG4 is a phase distribution diagram of the focal field Z component in the XOY plane according to the first embodiment of the present invention.
- FIG5 is a diagram showing the light intensity and polarization distribution of the second embodiment of the present invention.
- FIG. 6 is an entrance pupil field of the second embodiment of the present invention. Phase distribution diagram of components
- FIG. 7 is a diagram showing the focal field light intensity of the second embodiment of the present invention. 3D contour map of
- FIG. 8 is a diagram showing the focal field intensity of the confocal area of the third embodiment of the present invention. 3D contour map of
- FIG. 9 is a diagram showing the focal field light intensity of the fourth embodiment of the present invention. 3D contour map of the
- a method for generating a vortex focal field carrying an arbitrarily directed orbital angular momentum comprises the following steps: establishing a Optical focusing system; A dipole is placed in the confocal area of the optical focusing system; the radiation field of the dipole is calculated, and on this basis, a spiral phase factor with the same spatial orientation is superimposed to obtain a superimposed radiation field; The optical focusing system collects and collimates the superimposed radiation field to The entrance pupil plane of the optical focusing system is used to obtain the radiation field of the entrance pupil plane based on the bending effect of the lens on the light.
- the radiation field of the entrance pupil plane is reversed at this time, and the relative 180-degree phase shift is used to obtain the radiation field of the entrance pupil plane.
- the two sides of the entrance pupil plane of the optical focusing system propagate toward the confocal area of the two objective lenses, and a directional vortex focal field carrying orbital angular momentum with a specified topological charge can be formed in the confocal area.
- the present invention integrates the radiation field of the dipole, ingeniously superimposes the corresponding spatial spiral phase, time reversal technology and Debye vector diffraction integral theory, and places a dipole at the origin of the reference rectangular coordinate system, and its spatial pointing parameter is ,in is the angle between the dipole axis and the Z axis, is the angle between the projection of the dipole on the XOY plane and the X-axis; set Its spatial orientation can be adjusted arbitrarily; on the basis of the dipole radiation field, the spiral phase with the same spatial orientation is superimposed; the superimposed radiation field is
- the focusing system collects and collides the radiation field at the entrance pupil plane, and uses a relative 180-degree phase shift from The entrance pupils on both sides of the focusing system propagate toward the confocal area, and a directional vortex focal field carrying an orbital angular momentum with a specified topological charge can be formed in the confocal area.
- the radiation field of a dipole is used to cleverly superimpose the corresponding spatial spiral phase to obtain an analytical expression for the required entrance pupil light field. Therefore, the method of the present invention does not require a complex optimization process, and the OAM direction of the constructed vortex focal field can be flexibly customized, and the topological charge of the OAM can also be customized.
- the calculation model of the method proposed in the present invention isaki and concise, and the calculation workload is small.
- the vortex field customized according to the method has broad application potential in the fields of optical tweezers, optical processing, etc.
- the optical focusing system consists of two high numerical aperture objective lenses with exactly the same dimensions and optical parameters.
- the optical axes of the two objective lenses are on the same straight line and are placed confocally.
- a reference rectangular coordinate system is established in the optical focusing system; wherein the origin O of the reference rectangular coordinate system is the common focus of the two objective lenses; the direction of the optical axis is the Z axis, and the Z axis is perpendicular to the XOY plane; the Y axis is vertically upward, and the X axis is perpendicular to the YOZ plane;
- the center of the dipole is located at the origin O of the reference rectangular coordinate system, and the oscillation direction parameter of the dipole is ,in is the angle between the oscillation direction of the dipole and the Z axis of the rectangular coordinate system in the reference space, is the angle between the projection of the dipole's oscillation direction on the XOY plane and the positive direction of the X axis; the direction parameter is The direction of the dipole in 3D space can be uniquely determined.
- topological charge number is the azimuth along the Z axis in the reference rectangular coordinate system, and its calculation formula is: .
- the calculation process of the spiral phase factor is as follows: 1) Taking the XYZ reference rectangular coordinate system as the rotating whole, taking the origin O of the reference rectangular coordinate system shown in Figure 1 as the rotation point, the Z axis rotates one step along the dipole oscillation direction and the plane where OZ is located to direction, forming a rotated axis; 2) The X-axis and Y-axis of the reference rectangular coordinate system rotate synchronously to and axis, , and are the three principal axes of the new coordinate system after rotation; 3) The spatial direction is derived
- the spiral phase factor is:
- the azimuth angle of the axis direction is calculated as .
- the calculated coordinate system located at the origin and pointing to The radiation field of the dipoles is superimposed and the spiral phase factor with the same spatial orientation is calculated.
- the radiation field expression after superposition is as shown in the formula:
- Two identical high numerical aperture objective lenses are placed parallel to the Z axis direction of the reference rectangular coordinate system shown in Figure 1, with the origin O as their confocal point and the XOY plane as their confocal plane; the calculated superposition radiation field radiates outward from the confocal area, and propagates outward after being collimated by two identical high numerical aperture objective lenses; due to the bending of the radiation light by the lens, if the apodization function of the objective lens is , then the radiation field at the entrance pupil of the objective can be obtained as:
- the analytical expression of the radiation field at the entrance pupil plane of the objective lens has been calculated. Based on the time reversal technology, it is assumed that the radiation field is reversed at the entrance pupil planes of the two objective lenses and converges to the origin of the confocal area of the two objective lenses. The expected optical focal field will be formed in the confocal area. The incident field phases of the entrance pupil surfaces on both sides of the optical focusing system differ by 180 degrees. The focal field distribution in the confocal area can be calculated by the Debye diffraction integral formula:
- the objective lens that satisfies the sine condition is used as the objective lens used in the embodiment of the present invention, and its apodization function is .
- Example 1 Generating a vortex focal field carrying Z-axis OAM:
- the dipole is placed at point O of the reference rectangular coordinate system, and the spatial pointing parameters are set.
- topological charge number the electric field distribution in the confocal area is calculated using the formula
- Figure 2 shows the electric field distribution in the confocal area when the focal field intensity is half of the maximum value ( ) 3D contour diagram;
- the generated focal field is a hollow vortex structure pointing along the Z axis; It is precisely because of the OAM in the Z axis direction that the focal field is a hollow structure along the Z axis.
- focal field component is dominated by the Z direction component, and the size of the X and Y components can be ignored; the light intensity distribution of the focal field Z component in the XOY plane is shown in Figure 3, and the corresponding phase distribution is shown in Figure 4.
- the OAM data is calculated by equations (9) and (10) as follows: , , ,in is the reduced Planck constant; from the above data, it can be seen that the OAM carried by Example 1 points along the Z axis, and its size is approximately equal to the topological charge .
- the required entrance pupil field is calculated using formula (8), and its light intensity and polarization distribution are shown in Figure 5.
- the polarization of the entrance pupil field is radially symmetrically distributed; the light intensity of the entrance pupil field changes regularly along the radial direction, the light intensity in the central area is zero, and the light intensity gradually increases along the periphery; the entrance pupil field is mainly Component,
- Figure 6 is the entrance pupil field From the phase distribution diagram of the component, it can be clearly seen that its phase changes continuously twice within a cycle, which is consistent with the set topological charge.
- Example 2 Generating a vortex focal field carrying X-axis OAM:
- FIG. 7 is the focal field intensity 7, the generated focal field is a hollow vortex structure pointing along the X-axis; analyzing the focal field data, it is found that the focal field components are mainly in the X direction, and the magnitudes of the Y and Z components are negligible; the intensity distribution and phase distribution of the focal field X component in the YOZ plane are similar to the law of the first embodiment.
- the OAM data is calculated by equations (9) and (10) as follows: , , ; From the above data, it can be seen that the OAM carried by Example 2 points along the X-axis, and its size is approximately equal to the topological charge .
- Example 3 Generating a vortex focal field carrying Y-axis OAM:
- the focal field of the confocal area is calculated using the formula;
- Figure 8 shows the focal field intensity of the confocal area 8, the generated focal field is a hollow vortex structure pointing along the Y axis; analyzing the focal field data, it is found that the focal field components are mainly in the Y direction, and the magnitudes of the X and Z components are negligible; the intensity distribution and phase distribution of the focal field Y component in the XOZ plane are similar to those of the first embodiment.
- the OAM data is calculated by equations (9) and (10) as follows: , , ; From the above data, it can be seen that the OAM carried by Example 3 points along the Y axis, and its size is approximately equal to the topological charge .
- Example 4 Generating a vortex focal field carrying arbitrary spatially directed OAM:
- the above-mentioned embodiments 1, 2 and 3 demonstrate the effectiveness of the method proposed in the present invention in realizing the generation of a three-axis pointing vortex focal field carrying OAM; in order to demonstrate the effectiveness of the method in customizing a vortex focal field with other arbitrary spatial pointing OAM, without loss of generality, the pointing parameter , topological charge number
- the focal field of the confocal area is calculated using the formula;
- Figure 9 shows the focal field intensity 3D contour diagram; it can be seen from Figure 9 that the generated focal field is a hollow vortex structure along the non-main axis direction; compared with Figures 2, 7 and 8, it is found that the hollow part of the vortex focal field shown in Figure 9 is larger. This is because the topological charge number 4 set in this embodiment 4 is greater than the topological charge number 2 set in embodiments 1, 2 and 3.
- the OAM data is calculated by equations (9) and (10) as follows: , , ; From the above data, we can calculate The size is , slightly less than the topological charge number 4 set in the fourth embodiment of the present invention; in addition, it can be calculated that Direction angle , the spatial pointing parameter set by the fourth embodiment , the theoretical direction angle can be calculated as It can be seen that the OAM spatial orientation of the vortex focal field generated in the fourth embodiment is approximately equal to the set value. The spatial direction of the OAM carried by the vortex focal field can be determined.
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Abstract
一种产生携带任意指向轨道角动量涡旋焦场的方法，包括由两个具有共焦区的物镜建立光学聚焦系统；在光学聚焦系统的共焦区放置偶极子；计算该偶极子的辐射场，并在此基础上叠加相同空间指向的螺旋位相因子，以获得叠加辐射场。光学聚焦系统将叠加辐射场收集并准直到光学聚焦系统的入瞳面，并根据透镜对光线的弯折效应以求得入瞳面的辐射场；基于时间反演技术，反转此时入瞳面的辐射场，并用相对180度相移从光学聚焦系统的入瞳面两侧向两物镜共焦区方向传播，可在共焦区形成携带指定拓扑荷数的轨道角动量的定向涡旋焦场。所构建的涡旋焦场的OAM指向可灵活定制，并且OAM的拓扑荷数亦可定制。
Description
本发明涉及涡旋焦场的生成技术领域，尤其涉及一种产生携带任意指向轨道角动量涡旋焦场的方法。
光子具有沿光传播方向的线性动量和角动量，其中角动量既包括与光的圆偏振有关的自旋角动量，也包括与光的螺旋位相结构有关的轨道角动量(Orbital Angular Momentum: OAM)。关于轨道角动量的研究，最早可追溯到1992年Allen等人在期刊《Physical Review A》发表了关于光的轨道角动量和拉盖尔-高斯激光模式的转换的文章，建立了光的螺旋位相结构与其携带的轨道角动量之间的关系，开启研究光子轨道角动量的时代。光子的轨道角动量为光的应用提供一个全新的自由度，并且由于不同拓扑荷的涡旋光之间彼此正交，因此可以携带不同的光信息，在光通信领域有巨大的应用潜力，同时其在光操控、光加工、量子信息和超分辨显微成像等方面也有广泛的应用，至今仍吸引众多科研学者的关注。
近年来学者们研究发现光子的轨道角动量并非只沿着光轴的传播方向。2020年Chong A等人首次从理论到实验展示了具有时空涡旋相位并携带光子横向轨道角动量的新型超快脉冲波包，证实时空涡旋光场中横向轨道角动量的存在；同年，Chen J等人报道一种脉冲光在经过预处理之后，经高数值孔径物镜紧聚焦可在共焦区形成携带横向轨道角动量的时空波包；2022年Chen J等人报道高数值孔径物镜紧聚焦时空波包中自旋和轨道角动量耦合的相关研究。上述报道携带横向OAM的涡旋场主要是在动态的脉冲光场实现。2022年Meng X等人报道一种利用偶极子立体阵列的辐射场，该偶极子立体阵列的馈电须经严格优化设计，之后反向聚焦该辐射场，得到OAM指向可调整的涡旋场。经分析，该方法虽能控制OAM的指向，然而其所采用的理论模型庞大复杂，且需要经过繁琐的优化设计，计算工作量巨大。
针对上述问题，本发明提供了一种产生携带任意指向轨道角动量涡旋焦场的方法，该方法只利用一只偶极子的辐射场，并在其上叠加空间螺旋位相，并结合时间反演技术和Debye量衍射积分理论，产生携带任意指向OAM的涡旋焦场。
为解决上述技术问题，本发明所采用的技术方案是：一种产生携带任意指向轨道角动量涡旋焦场的方法，该方法包括以下步骤：
步骤1、由两个具有共焦区的物镜建立
光学聚焦系统；
步骤2、在所述
光学聚焦系统的共焦区放置偶极子；
步骤3、计算偶极子的辐射场，并在此基础上叠加相同空间指向的螺旋位相因子，以获得叠加辐射场；
步骤4、所述
光学聚焦系统将所述叠加辐射场收集并准直到
光学聚焦系统的入瞳面，并根据透镜对光线的弯折效应以求得入瞳面的辐射场；
步骤5、基于时间反演技术，反转此时入瞳面的辐射场，并用相对180度相移从
光学聚焦系统的入瞳面两侧向两物镜共焦区方向传播，可在共焦区形成携带指定拓扑荷数的轨道角动量的定向涡旋焦场。
进一步的，在步骤1中，所述
光学聚焦系统由两个外形尺寸和光学参数完全相同的高数值孔径物镜构成，两个物镜的光轴处在同一直线上且共焦放置；
在所述
光学聚焦系统中建立参考直角坐标系；其中，所述参考直角坐标系的原点O为两个物镜的公共焦点；以光轴所在方向为Z轴，且Z轴垂直于XOY平面；Y轴方向竖直向上，X轴垂直于YOZ平面。
进一步的，在步骤2中，所述偶极子的中心位于参考直角坐标系的原点O，所述偶极子的振荡方向参数为
，其中
为偶极子的振荡方向与参考直角坐标系Z轴的夹角，
为偶极子的振荡方向在XOY平面的投影与X轴正方向的夹角。
进一步的，在步骤3中，偶极子产生的辐射场是基于电磁辐射理论求得，该计算方式具体如下：
（1）
（2）
（3）
（4）
其中，C为辐射场的常系数，
为辐射场
分量的系数，
为辐射场
分量的系数，
为虚数单位，
为偶极子振荡角频率，
为真空中的导磁率，
为偶极子振荡电流的大小，
为偶极子的长度，
为辐射场的空间球坐标，
和
为球坐标的单位矢量。
进一步的，在步骤3中，
方向的螺旋位相因子的计算方式具体如下：
在参考直角坐标系下，沿Z轴方向的螺旋位相因子为：
（5）
其中
为拓扑荷数，
为参考直角坐标系中沿Z轴方向的方位角，其计算公式为
；
沿空间任意方向
的螺旋位相因子的计算过程如下：1) 以XYZ参考直角坐标系为旋转整体，以参考直角坐标系的原点O为旋转点，Z轴沿着偶极子振荡方向与OZ所在平面一步旋转至
方向，形成旋转后的
轴；2）参考直角坐标系的X轴和Y轴同步旋转至
和
轴，
、
和
为旋转后新坐标系的三个主轴；3）推导得空间方向
的螺旋位相因子为：
（6）
为新坐标系中沿
轴方向的方位角，其计算公式为
。
进一步的，在步骤3中，所述叠加辐射场是采用在偶极子的辐射场的基础上叠加相同空间指向的螺旋位相因子而得到，具体包括如下：
将计算所得的位于坐标原点且空间指向
的偶极子的辐射场叠加计算所得相同空间指向的螺旋位相因子，得到叠加后辐射场表达式如式所示：
（7）
其中，
为偶极子产生的辐射场，
为螺旋位相因子。
进一步的，在步骤4中，所述入瞳面的辐射场的计算方式具体如下：
在参考直角坐标系的Z轴方向平行放置两个相同的高数值孔径物镜，以原点O为它们的共焦点，XOY平面为它们的共焦平面，计算所得叠加后辐射场由物镜共焦区域往外辐射，经两个相同的高数值孔径物镜准直后往外侧传播，并根据透镜对光线的弯折效应以求得，若物镜的切趾函数为
，则可求得物镜入瞳面处的辐射场为：
（8）
其中，
为入瞳面的极坐标，
为入瞳面观测点与入瞳中心的距离，
为入瞳面观测点的方位角。
进一步的，在步骤5中，基于Debye矢量衍射积分公式，可计算得到共焦区焦场分布：
（9）
其中，
为焦场的柱坐标。
进一步的，在步骤5中，根据计算所得的共焦区电场，以计算共焦区电场所携带OAM的空间指向的公式如下：
基于所生成的空间焦场的数据，计算其规范动量密度
，再通过其与位置矢量
的叉乘，得到共焦区电场所携带的轨道角动量
：
（10）
其中，式中
和
为共焦场的电场矢量及其共轭矢量，
为取虚部操作；通过式（10）计算得到
沿着X、Y和Z轴的分量
、
和
，进而可以确定
与X、Y和Z轴的夹角，即方向角
。
由上述对本发明结构的描述可知，和现有技术相比，本发明具有如下优点：
本发明综合偶极子的辐射场、巧妙叠加相应的空间螺旋位相、时间反演技术和Debye矢量衍射积分理论，通过将一只偶极子置于参考直角坐标系的原点，其空间指向参数为
，其中
为偶极子轴向与Z轴的夹角，
为偶极子在XOY平面的投影与X轴的夹角；设置
可任意调整其空间指向；在偶极子辐射场的基础上，叠加相同空间指向的螺旋位相；叠加辐射场被
聚焦系统收集并准直到入瞳面；通过反转此时入瞳面的辐射场，并用相对180度相移从
聚焦系统两侧入瞳面向共焦区传播，可在共焦区形成携带指定拓扑荷数的轨道角动量的定向涡旋焦场，即利用一只偶极子的辐射场，巧妙叠加相应的空间螺旋位相，得到所需入瞳光场的解析表达式；因此，通过本发明方法无需复杂的优化过程，且构建的涡旋焦场的OAM指向可灵活定制，并且OAM的拓扑荷数亦可定制；本发明所提方法的计算模型精巧简洁，计算工作量小，依本方法所定制的涡旋场在光镊、光加工等领域具有广泛的应用潜力。
构成本申请的一部分的附图用来提供对本发明的进一步理解，本发明的示意性实施例及其说明用于解释本发明，并不构成对本发明的不当限定。在附图中：
图1为本发明
光学聚焦系统的示意图；
图2为本发明实施例一的焦场光强为最大值的二分之一时（
）的3D轮廓图；
图3为本发明实施例一的焦场Z分量在XOY平面的光强分布图；
图4为本发明实施例一的焦场Z分量在XOY平面的位相分布图；
图5为本发明实施例二的光强及偏振分布图；
图6为本发明实施例二的入瞳场
分量的位相分布图；
图7为本发明实施例二的焦场光强
的3D轮廓图；
图8为本发明实施例三的共焦区焦场光强
的3D轮廓图；
图9为本发明实施例四的焦场光强
的3D轮廓图。
为了更好地理解本发明的技术方案，下面将结合说明书附图以及具体的实施方式对本发明的技术方案进行详细的说明。
参考图1所示，产生携带任意指向轨道角动量涡旋焦场的方法，该方法包括以下步骤：由两个具有共焦区的物镜建立
光学聚焦系统；在所述
光学聚焦系统的共焦区放置偶极子；计算偶极子的辐射场，并在此基础上叠加相同空间指向的螺旋位相因子，以获得叠加辐射场；所述
光学聚焦系统将所述叠加辐射场收集并准直到
光学聚焦系统的入瞳面，并根据透镜对光线的弯折效应以求得入瞳面的辐射场；基于时间反演技术，反转此时入瞳面的辐射场，并用相对180度相移从
光学聚焦系统的入瞳面两侧向两物镜共焦区方向传播，可在共焦区形成携带指定拓扑荷数的轨道角动量的定向涡旋焦场。
本发明综合偶极子的辐射场、巧妙叠加相应的空间螺旋位相、时间反演技术和Debye矢量衍射积分理论，通过将一只偶极子置于参考直角坐标系的原点，其空间指向参数为
，其中
为偶极子轴向与Z轴的夹角，
为偶极子在XOY平面的投影与X轴的夹角；设置
可任意调整其空间指向；在偶极子辐射场的基础上，叠加相同空间指向的螺旋位相；叠加辐射场被
聚焦系统收集并准直到入瞳面；通过反转此时入瞳面的辐射场，并用相对180度相移从
聚焦系统两侧入瞳面向共焦区传播，可在共焦区形成携带指定拓扑荷数的轨道角动量的定向涡旋焦场，即利用一只偶极子的辐射场，巧妙叠加相应的空间螺旋位相，得到所需入瞳光场的解析表达式；因此，通过本发明方法无需复杂的优化过程，且构建的涡旋焦场的OAM指向可灵活定制，并且OAM的拓扑荷数亦可定制；本发明所提方法的计算模型精巧简洁，计算工作量小，依本方法所定制的涡旋场在光镊、光加工等领域具有广泛的应用潜力。
现对本发明方法的具体实施步骤进行详细介绍。
(1)设置偶极子的空间位置和空间指向
：
光学聚焦系统由两个外形尺寸和光学参数完全相同的高数值孔径物镜构成，两个物镜的光轴处在同一直线上且共焦放置；
在
光学聚焦系统中建立参考直角坐标系；其中，参考直角坐标系的原点O为两个物镜的公共焦点；以光轴所在方向为Z轴，且Z轴垂直于XOY平面；Y轴方向竖直向上，X轴垂直于YOZ平面；
将偶极子的中心位于参考直角坐标系的原点O，偶极子的振荡方向参数为
，其中
为偶极子的振荡方向与参考空间直角坐标系Z轴的夹角，
为偶极子的振荡方向在XOY平面的投影与X轴正方向的夹角；通过方向参数为
可以唯一确定偶极子在3D空间的指向。
（2）计算偶极子的辐射场：
根据电磁辐射理论，求解偶极子的辐射场：
(1)
辐射场的常系数
、辐射场
分量的系数
和辐射场
分量的系数
具体表达式分别如式（2）（3）和（4）所示：
（2）
（3）
（4）
其中，
为虚数单位，
为偶极子振荡角频率，
为真空中的导磁率，
为偶极子振荡电流的大小，
为偶极子的长度，
为辐射场的空间球坐标，
和
为球坐标的单位矢量。
（3）计算
方向的螺旋位相因子：
在参考直角坐标系下，沿Z轴方向的螺旋位相因子为：
（5）
其中
为拓扑荷数，
为参考直角坐标系中沿Z轴方向的方位角，其计算公式为
。
沿空间任意方向
的螺旋位相因子的计算过程如下：1) 以XYZ参考直角坐标系为旋转整体，以图1所示的参考直角坐标系的原点O为旋转点，Z轴沿着偶极子振荡方向与OZ所在平面一步旋转至
方向， 形成旋转后的
轴；2）参考直角坐标系的X轴和Y轴同步旋转至
和
轴，
、
和
为旋转后新坐标系的三个主轴；3）推导得空间方向
的螺旋位相因子为：
（6）
为新坐标系中沿
轴方向的方位角，其计算公式为
。
（4）偶极子的辐射场叠加空间螺旋位相因子：
为获得携带OAM的涡旋焦场所需要的入射场，将计算所得的位于坐标原点且空间指向
的偶极子的辐射场叠加计算所得相同空间指向的螺旋位相因子，得到叠加后辐射场表达式如式所示：
（7）。
（5）计算
光学聚焦系统入瞳面的辐射场：
在图1所示参考直角坐标系的Z轴方向平行放置两个相同的高数值孔径物镜，以原点O为它们的共焦点，XOY平面为它们的共焦平面；计算所得叠加后辐射场由共焦区域往外辐射，经两个相同的高数值孔径物镜准直后往外侧传播；由于透镜对辐射光线的弯折，若物镜的切趾函数为
，则可求得物镜入瞳面处的辐射场为：
（8）
其中
为入瞳面的极坐标，
为入瞳面观测点与入瞳中心的距离，
为入瞳面观测点的方位角。
（6）反向聚焦计算共焦区的光焦场分布：
将已经计算得到物镜入瞳面处辐射场的解析表达式，基于时间反演技术，假设该辐射场在两物镜的入瞳面处发生反转，并向两物镜共焦区域原点处汇聚，在共焦区域将形成期待的光焦场，
光学聚焦系统两侧入瞳面的入射场相位相差180度，共焦区焦场分布可由Debye量衍射积分公式计算得到：
（9）
其中
为焦场的柱坐标。
（7）计算共焦区电场所携带OAM的空间指向：
为定量评估共焦区电场所携带OAM的空间指向，基于所生成的空间焦场的数据，计算其规范动量密度
，再通过其与位置矢量
的叉乘，如式所示，得到共焦区电场所携带的轨道角动量
：
（10）
式中
和
为共焦区的电场矢量及其共轭矢量，
为取虚部操作；通过式（10）计算得到
沿着X、Y和Z轴的分量
、
和
，进而可以确定
与X、Y和Z轴的夹角，即方向角
。
下面举实施例来证实本发明所提方法的有效性。
为简化计算，所列举的实施例将与光焦场形状及偏振无关的参数C归一化，即取C=1；为汇聚偶极子对的反向辐射场，取高数值孔径物镜汇聚角
，即
；以满足正弦条件的物镜作为本发明实施例所用的物镜，其切趾函数为
。
实施例一：生成携带Z轴OAM的涡旋焦场：
偶极子置于参考直角坐标系的O点，设定空间指向参数
、拓扑电荷数
，利用公式计算得到共焦区的电场分布；图2为焦场光强为最大值的二分之一时（
）的3D轮廓图；由图2可以看出，所生成的焦场是沿Z轴指向的中空涡旋结构；正是由于Z轴方向OAM的缘故，导致焦场沿Z轴方向是中空的结构。进一步分析焦场的数据，发现在上述设定参数的条件下，焦场分量中以Z方向分量为主，X和Y分量的大小可忽略；焦场Z分量在XOY平面的光强分布如图3所示，相应的位相分布如图4所示。
在本实施例一所生成焦场的电场数据基础上，通过式（9）和式（10）计算得到OAM的数据如下：
，
，
，其中
为约化普朗克常数；由以上数据可知，实施例一所携带的OAM沿着Z轴指向，其大小约等于拓扑荷数
。
为生成本实施例所述携带Z轴OAM的涡旋焦场，利用式（8）计算得到所需的入瞳场，其光强及偏振分布如图5所示；由图5可以看出，入瞳场的偏振呈径向对称分布；入瞳场的光强沿径向呈规律性的变化，中心区域光强为零，沿外围光强逐渐增大；该入瞳场主要是
分量，图6为此入瞳场
分量的位相分布图，可以明显看出其在一周的范围内位相连续变化2次，与所设定的拓扑荷数一致。
实施例二：生成携带X轴OAM的涡旋焦场：
为生成携带X轴OAM的涡旋焦场，设定空间指向参数
、拓扑电荷数
；与实施例一类似的方法，利用公式计算得到共焦区焦场；图7为焦场光强
的3D轮廓图；由图7可以看出，所生成的焦场是沿X轴指向的中空涡旋结构；分析焦场的数据，发现焦场分量中以X方向分量为主，Y和Z分量的大小可忽略；焦场X分量在YOZ平面的光强分布和位相分布类似实施例一的规律。
在本实施例二所生成焦场数据基础上，通过式（9）和式（10）计算得到OAM的数据如下：
，
，
；由以上数据可知，实施例二所携带的OAM沿着X轴指向，其大小约等于拓扑荷数
。
实施例三：生成携带Y轴OAM的涡旋焦场：
为生成携带Y轴OAM的涡旋焦场，设定空间指向参数
、拓扑电荷数
；利用公式计算得到共焦区焦场；图8为共焦区焦场光强
的3D轮廓图；由图8可以看出，所生成的焦场是沿Y轴指向的中空涡旋结构；分析焦场的数据，发现焦场分量中以Y方向分量为主，X和Z分量的大小可忽略；焦场Y分量在XOZ平面的光强分布和位相分布类似实施例一的规律。
在本实施例三所生成焦场的电场数据基础上，通过式（9）和式（10）计算得到OAM的数据如下：
，
，
；由以上数据可知，实施例三所携带的OAM沿着Y轴指向，其大小约等于拓扑荷数
。
实施例四：生成携带任意空间指向OAM的涡旋焦场：
上述实施例一、二和三展示了本发明所提出的方法在实现生成携带OAM的三主轴指向涡旋焦场的有效性；为展示本方法定制其它任意空间指向OAM的涡旋焦场的有效性，在不失一般性的前提下，以指向参数
、拓扑电荷数
为例，利用公式计算得到共焦区焦场；图9为焦场光强
的3D轮廓图；由图9可以看出，所生成的焦场是沿着非主轴方向的中空涡旋结构；与图2、图7和图8对比，发现图9所示的涡旋焦场的中空部分较大，这是由于本实施例四所设置拓扑荷数4大于实施例一、实施例二和实施例三所设置拓扑荷数2的缘故。
同时，在本实施例四所生成焦场数据基础上，通过式（9）和式（10）计算得到OAM的数据如下：
，
，
；由以上数据可计算
的大小为
，略小于本实施例四所设定的拓扑荷数4；另外可计算得到
的方向角
，由本实施例四所设定的空间指向参数
，可计算得到设定的理论方向角为
，可见本实施例四所生成涡旋焦场的OAM空间指向与设定值近似相等，可见其由参数
可决定涡旋焦场携带OAM的空间指向。
由以上实施例一、实施例二和、实施例三和实施例四证明本发明所提出的方法的有效性；通过设定空间指向参数
和拓扑荷数
，可灵活生成携带指定方向和指定拓扑荷数的OAM的涡旋焦场。
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。
Claims (4)
- 一种产生携带任意指向轨道角动量涡旋焦场的方法，其特征在于，该方法包括以下步骤：步骤1、由两个具有共焦区的物镜建立 光学聚焦系统；所述 光学聚焦系统由两个外形尺寸和光学参数完全相同的高数值孔径物镜构成，两个物镜的光轴处在同一直线上且共焦放置；在所述 光学聚焦系统中建立参考直角坐标系；其中，所述参考直角坐标系的原点O为两个物镜的公共焦点；其中，以光轴所在方向为Z轴，且Z轴垂直于XOY平面；Y轴方向竖直向上，X轴垂直于YOZ平面；步骤2、在所述 光学聚焦系统的共焦区放置偶极子；其中，所述偶极子的中心位于参考直角坐标系的原点O，所述偶极子的振荡方向参数为 ， 为偶极子的振荡方向与参考直角坐标系Z轴的夹角， 为偶极子的振荡方向在XOY平面的投影与X轴正方向的夹角；步骤3、计算偶极子的辐射场，并在此基础上叠加相同空间指向的螺旋位相因子，以获得叠加辐射场；其中，偶极子产生的辐射场是基于电磁辐射理论求得，该计算方式具体如下：（1）（2）（3）（4）其中，C为辐射场的常系数， 为辐射场 分量的系数， 为辐射场 分量的系数， 为虚数单位， 为偶极子振荡角频率， 为真空中的导磁率， 为偶极子振荡电流的大小， 为偶极子的长度， 为辐射场的空间球坐标， 和 为球坐标的单位矢量，k为波数；方向的螺旋位相因子的计算方式具体如下：在参考直角坐标系下，沿Z轴方向的螺旋位相因子为：（5）其中 为拓扑荷数， 为参考直角坐标系中沿Z轴方向的方位角，其计算公式为 ，x和y分别为偶极子辐射场观测点在参考坐标系中的坐标值；沿空间任意方向 的螺旋位相因子的计算过程如下：1) 以XYZ参考直角坐标系为旋转整体，以参考直角坐标系的原点O为旋转点，Z轴沿着偶极子振荡方向与OZ所在平面一步旋转至 方向，形成旋转后的 轴；2）参考直角坐标系的X轴和Y轴同步旋转至 和 轴， 、 和 为旋转后新坐标系的三个主轴；3）推导得空间方向 的螺旋位相因子为：（6）为新坐标系中沿 轴方向的方位角，其计算公式为 ，x'和y'分别为偶极子辐射场观测点在旋转后新坐标系中的坐标值；所述叠加辐射场是采用在偶极子的辐射场的基础上叠加相同空间指向的螺旋位相因子而得到，具体包括如下：将计算所得的位于坐标原点且空间指向 的偶极子的辐射场叠加计算所得相同空间指向的螺旋位相因子，得到叠加后辐射场表达式如式所示：（7）其中， 为偶极子产生的辐射场， 为螺旋位相因子；步骤4、所述 光学聚焦系统将所述叠加辐射场收集并准直到 光学聚焦系统的入瞳面，并根据透镜对光线的弯折效应以求得入瞳面的辐射场；步骤5、基于时间反演技术，反转此时入瞳面的辐射场，并用相对180度相移从 光学聚焦系统的入瞳面两侧向两物镜共焦区方向传播，可在共焦区形成携带指定拓扑荷数的轨道角动量的定向涡旋焦场。
- 根据权利要求1所述的一种产生携带任意指向轨道角动量涡旋焦场的方法，其特征在于：在步骤4中，所述入瞳面的辐射场的计算方式具体如下：在参考直角坐标系的Z轴方向平行放置两个相同的高数值孔径物镜，以原点O为它们的共焦点，XOY平面为它们的共焦平面，计算所得叠加后辐射场由物镜共焦区域往外辐射，经两个相同的高数值孔径物镜准直后往外侧传播，并根据透镜对光线的弯折效应以求得，若物镜的切趾函数为 ，则可求得物镜入瞳面处的辐射场为：（8）其中， 为入瞳面的极坐标， 为入瞳面观测点与入瞳中心的距离， 为入瞳面观测点的方位角。
- 根据权利要求2所述的一种产生携带任意指向轨道角动量涡旋焦场的方法，其特征在于：在步骤5中，基于Debye矢量衍射积分公式，可计算得到共焦区焦场分布：（9）其中， 为焦场的柱坐标。
- 根据权利要求3所述的一种产生携带任意指向轨道角动量涡旋焦场的方法，其特征在于：在步骤5中，根据计算所得的共焦区电场，以计算共焦区电场所携带轨道角动量的空间指向的公式如下：基于所生成的空间焦场的数据，计算其规范动量密度 ，再通过其与位置矢量 的叉乘，得到共焦区电场所携带的轨道角动量 ：（10）其中，式中 和 为共焦区的电场矢量及其共轭矢量， 为取虚部操作；通过式计算得到 沿着X、Y和Z轴的分量 、 和 ，进而可以确定 与X、Y和Z轴的夹角，即方向角 。
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