WO2023155237A1 - 一种部分相干矢量幂指数涡旋光束的产生系统及方法 - Google Patents

一种部分相干矢量幂指数涡旋光束的产生系统及方法 Download PDF

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WO2023155237A1
WO2023155237A1 PCT/CN2022/078312 CN2022078312W WO2023155237A1 WO 2023155237 A1 WO2023155237 A1 WO 2023155237A1 CN 2022078312 W CN2022078312 W CN 2022078312W WO 2023155237 A1 WO2023155237 A1 WO 2023155237A1
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partially coherent
vortex
exponent
power
vector
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张�浩
赵承良
杭奕亦
卢兴园
王卓异
蔡阳健
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苏州大学
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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
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0927—Systems for changing the beam intensity distribution, e.g. Gaussian to top-hat
    • 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
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0938—Using specific optical elements

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  • the invention relates to the field of optical technology, in particular to a system and method for generating a partial coherence vector power exponent vortex beam.
  • vortex beams have gradually become a research hotspot in the field of optical field manipulation. Its central light intensity is zero, and has a spiral wavefront, and carries orbital angular momentum. It has important application value in the fields of micro-nano processing, particle manipulation, optical communication, optical measurement and super-resolution imaging.
  • researchers need to construct some special vortex beams to meet the requirements of complex applications.
  • laser light is a highly coherent light beam.
  • the coherence of the beam will decrease.
  • Such reduced coherence beams are called partially coherent beams.
  • Gori first proposed the concept of partially coherent vortex beams.
  • partially coherent vortex beams can be represented by a series of incoherent superposition of Laguerre-Gaussian beams.
  • the light intensity at the center of the vortex beam is no longer zero, and its dark space structure gradually becomes Gaussian distribution, so the beam shaping from dark space to Gaussian distribution can be realized.
  • the phase singularity at its center disappears and transforms into a coherent singularity, the point where the cross-spectral density is zero.
  • Coherence singularity and phase singularity can be transformed into each other by adjusting the size of coherence.
  • Polarization is an essential characteristic of light beams.
  • light beams can be divided into two types, scalar light beams and vector light beams.
  • the polarization states of scalar beams mainly include spatially invariant linear polarization, left-handed circular polarization, and right-handed circular polarization; distributed.
  • radially polarized light can be focused into a smaller focused spot than scalar beams.
  • Wolf gave a unified theory of coherence and polarization of beams. Guo et al.
  • the first method regulates the phase of partially coherent vector beams and introduces an integer-order vortex phase to generate integer-order partially coherent vortex beams (Guo, L.N., et al.(2016). "Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam.” Optics Express 24(13):13714), the second topological charge for partially coherent vector vortex beams Controlling and constructing a partially coherent vector fractional vortex beam with fractional vortex phase, (Zeng J, et al.(2020). "Partially coherent radially polarized fractional vortex beam” Optics Express 28(8):11493).
  • the first one for the traditional integer-order partially coherent vector vortex beam, the topological charge is an integer, and the change of the vortex phase in one cycle is an integer multiple of 2 ⁇ .
  • the light intensity distribution is circular, and the polarization state distribution is handed polarization; as the coherence decreases, the light intensity becomes a Gaussian distribution spot, and the polarization state becomes circular polarization.
  • the second type when the topological charge is not an integer, can generate a partially coherent fractional vortex beam with a gap, realizing the shaping of its light intensity distribution.
  • changing the fractional-order topological charge value can tune the distribution of the polarization state.
  • the scheme of integer order vortex phase can only form the light intensity distribution of circular partially coherent vector beams, while the scheme of fractional order vortex phase can only produce a variety of polarization state distributions, but it can only be used at high When coherent, a partially coherent vortex beam with a gap is realized, and when low coherence is achieved, a similar circular light intensity distribution is achieved.
  • the degree of freedom of regulation of the light intensity distribution is not high, and it cannot be stably transmitted in free space.
  • the technical problem to be solved by the present invention is to provide a generation system of a partial coherence vector exponent vortex beam with high feasibility, high control degree of freedom, and high energy retention.
  • the present invention provides a system for generating a partial coherence vector power index vortex beam, which includes a computer, a spatial light modulator, a half-wave plate, a radial polarizer, and a third lens;
  • the computer is connected to the spatial light modulator, and the computer is used to load the hologram of the power exponential spiral phase to the spatial light modulator;
  • the spatial light modulator is used to receive a partially coherent beam, and modulate the partially coherent beam to obtain a partially coherent beam with a power exponential spiral phase;
  • the half-wave plate is used to modulate the polarization direction of the partially coherent light beam having a power exponential spiral phase to a vertical polarization
  • the radial polarizer is used to modulate the polarization direction of the vertically polarized partially coherent light beam with a power exponential spiral phase to radial polarization;
  • the third lens is used to focus the radially polarized partially coherent light beam having a power exponent spiral phase to obtain a partially coherent vector power exponent vortex light beam with a spatially varying polarization state.
  • a partially coherent beam generating system is also included, and the partially coherent beam generating system includes a laser, a collimating beam expanding element, a first lens, a beam breaking element, a second lens, and a Gaussian filter;
  • the laser is used to generate a fully coherent beam
  • the collimating and expanding element is used to collimate and expand the fully coherent beam
  • the first lens is used to focus the collimated and expanded fully coherent beam on
  • the beam breaking element breaks up the completely coherent beam and generates a completely incoherent beam
  • the second lens performs Fourier transform on the completely incoherent beam
  • the Gaussian filter pair passes the Fourier Amplitude filtering is performed on the completely incoherent beam after leaf transformation to obtain a partially coherent beam with Gaussian intensity distribution.
  • the beam breaking element is a rotating frosted glass, and the surface of the rotating ground glass has tiny particles obeying a Gaussian statistical distribution.
  • the collimating beam expanding element is a beam expander.
  • the spatial light modulator is a transmissive spatial light modulator or a reflective spatial light modulator; when the spatial light modulator is a reflective spatial light modulator, the partial coherence vector power
  • the generation system of the exponential vortex beam also includes a beam splitting cube, the partially coherent beam is transmitted from the beam splitting cube to the reflective spatial light modulator, and is reflected back to the beam splitting cube by the reflective spatial light modulator , and then reflected by the beam-splitting cube to the half-wave plate.
  • the cross spectral density matrix of the partial coherence vector power exponent vortex beam is expressed as:
  • ⁇ > represents the ensemble average operation
  • "*" represents the complex conjugate operation
  • Ex(r) and Ey(r) represent the horizontal polarization component and Vertical polarization component
  • r 1 and r 2 represent the radial coordinate vectors of any two points
  • x, y represent the horizontal axis and vertical axis of the Cartesian coordinate system respectively
  • its electric field can be expressed as:
  • w 0 represents the initial beam waist radius of the beam
  • ⁇ represents the angular coordinate vector
  • i is the imaginary unit
  • rem(.) is the remainder function
  • l is the topological charge number
  • n is the exponential phase gradient factor; by adjusting the topological charge
  • the magnitude of the number and the exponential phase gradient factor can regulate the light intensity distribution of the partial coherence power exponential vortex beam
  • ⁇ ⁇ represents the initial coherence length of the beam
  • ⁇ 1 and ⁇ 2 represent the angular coordinate vectors of any two points.
  • a camera is also included, and the camera images the generated partial coherence vector exponent vortex beam.
  • the computer obtains the exponential spiral phase loaded on the spatial light modulator through MATLAB calculation.
  • the present invention also provides a method for generating a partial coherence vector exponent vortex beam.
  • the method for generating a partial coherence vector exponent vortex beam includes:
  • a spatial light modulator loaded with a power exponential spiral phase to receive a partially coherent beam, and modulate the partially coherent beam to obtain a partially coherent beam with a power exponential spiral phase;
  • a radially polarized partially coherent beam with a power spiral phase is focused to obtain a partially coherent vector power vortex beam with a spatially varying polarization state.
  • a half-wave plate is used to modulate the polarization direction of a partially coherent beam with a power exponential spiral phase to a vertical polarization
  • the polarization direction of a vertically polarized partially coherent beam with a power exponential spiral phase is modulated into a radial polarization using a radial polarizer.
  • the generation system and method of the partial coherence vector power exponent vortex beam of the present invention is by adding a spiral phase distribution of space index change to the traditional partial coherence vector beam, and by adjusting the size of the coherence, the value of the exponential phase gradient factor and the topological charge can be Realize triangular, quadrangular, five-pointed star-shaped light intensity distribution, and spatially varying polarization states, and because the polarization state distribution has vector characteristics, there is a dark core in the center light intensity, and its light intensity distribution has a higher intensity than traditional partially coherent vector beams High degree of control freedom, and retain high energy.
  • Fig. 1 is the schematic diagram of the generation system of partial coherence vector power exponent vortex beam in the preferred embodiment of the present invention
  • Fig. 2 is a light intensity distribution diagram of the partial coherence vector power exponent vortex beam at the focal plane of the third lens obtained in the preferred embodiment of the present invention.
  • Marking description 1. Laser; 2. Collimating beam expanding element; 3. First lens; 4. Beam breaking element; 5. Second lens; 6. Gaussian filter; 7. Beam splitting cube; 8. Spatial light Modulator; 9, half-wave plate; 10, radial polarizer; 11, third lens; 12, camera.
  • FIG. 1 it is the generation system of the partial coherence vector exponent index vortex beam in the preferred embodiment of the present invention, and this system comprises computer, spatial light modulator 8, half-wave plate 9, radial polarizer 10, the third Lens 11.
  • the computer is connected to the spatial light modulator 8, and the computer is used to load the hologram of the power exponent spiral phase to the spatial light modulator 8;
  • the beam is modulated to obtain a partially coherent beam with a power exponential spiral phase;
  • the half-wave plate 9 is used to modulate the polarization direction of the partially coherent beam with a power exponential spiral phase to vertical polarization;
  • the radial polarizer 10 is used to The polarization direction of the vertically polarized partially coherent light beam with the power exponential spiral phase is modulated into radial polarization;
  • the third lens 11 is used to focus the radially polarized partially coherent light beam with the power exponential spiral phase to obtain the spatial variation of the polarization state
  • the partial coherence vector exponent of the vortex beam is connected to the spatial light modulator 8, and the computer is used to load the hologram of the power exponent spiral phase to the spatial light modulator 8;
  • the system for generating the partially coherent vector exponent vortex beam further includes a partially coherent beam generating system, and the partially coherent beam generating system includes a laser 1, a collimating beam expanding element 2, a first lens 3, A beam breaking element 4 , a second lens 5 , and a Gaussian filter 6 .
  • the laser 1 is used to generate a fully coherent beam
  • the collimating and expanding element 2 is used to collimate and expand the fully coherent beam
  • the first lens 3 is used to collimate and expand the fully coherent beam.
  • the beam is focused on the beam breaking element 4, the beam breaking element 4 breaks the completely coherent beam and generates a completely incoherent beam, the second lens 5 performs Fourier transform on the completely incoherent beam, and the Gaussian
  • the filter 6 performs amplitude filtering on the fully incoherent light beam after Fourier transform to obtain a partially coherent light beam with a Gaussian light intensity distribution.
  • the beam breaking element 4 is a rotating ground glass, and the surface of the rotating ground glass has tiny particles obeying a Gaussian statistical distribution.
  • the rotating ground glass is arranged on the rear focal plane of the first lens 3 and the front focal plane of the second lens 5 .
  • the collimating beam expanding element 2 is a beam expander.
  • the spatial light modulator 8 is a transmissive spatial light modulator 8 or a reflective spatial light modulator 8; when the spatial light modulator 8 is a reflective spatial light modulator 8, the partially coherent
  • the generation system of the vector power exponent vortex beam also includes a beam splitting cube 7, the partially coherent beam is transmitted to the reflective spatial light modulator 8 by the beam splitting cube 7, and is reflected by the reflective spatial light modulator 8 back to the beam-splitting cube 7, and then reflected by the beam-splitting cube 7 to the half-wave plate 9.
  • the generation system of the partial coherence vector exponent vortex beam also includes a camera 12, the camera 12 is arranged on the back focal plane of the third lens 12, and the partial coherence vector exponent index generated by the camera 12 is Vortex beam for imaging.
  • the computer obtains the exponential spiral phase loaded on the spatial light modulator 8 through MATLAB calculation.
  • the cross spectral density matrix of the partial coherence vector power exponent vortex beam is expressed as:
  • ⁇ > represents the ensemble average operation
  • "*" represents the complex conjugate operation
  • Ex(r) and Ey(r) represent the horizontal polarization component and Vertical polarization component
  • r 1 and r 2 represent the radial coordinate vectors of any two points
  • x, y represent the horizontal axis and vertical axis of the Cartesian coordinate system respectively
  • its electric field can be expressed as:
  • w 0 represents the initial beam waist radius of the beam
  • ⁇ represents the angular coordinate vector
  • i is the imaginary unit
  • rem(.) is the remainder function
  • l is the topological charge number
  • n is the exponential phase gradient factor; by adjusting the topological charge
  • the magnitude of the number and the exponential phase gradient factor can regulate the light intensity distribution of the partial coherence power exponential vortex beam
  • ⁇ ⁇ represents the initial coherence length of the beam
  • ⁇ 1 and ⁇ 2 represent the angular coordinate vectors of any two points.
  • Formula (5) is the traditional Gaussian correlation function.
  • the present invention uses rotating ground glass to generate a partially coherent beam with a Gaussian correlation structure, and then loads a hologram of the power exponent spiral phase through a spatial light modulator.
  • a partially coherent power-exponent vortex beam with a polygonal structure can be generated, and finally the polarization state distribution can be adjusted by a radial polarizer, thereby generating a partially coherent vector power-exponent vortex beam with the desired spatial variation of the polarization state.
  • the preferred embodiment of the present invention also discloses a method for generating a partial coherence vector exponent vortex beam.
  • the method for generating a partial coherence vector exponent vortex beam includes the following steps:
  • the half-wave plate 9 is used to modulate the polarization direction of the partially coherent light beam with the power exponential spiral phase to be vertically polarized;
  • a radial polarizer 10 is used to modulate the polarization direction of a vertically polarized partially coherent light beam with a power exponential spiral phase into a radial polarization.
  • the generation method of the partial coherence vector exponent vortex beam in this embodiment is based on the generation system of the aforementioned partial coherence vector exponent vortex beam, so the specific implementation of the method can be seen in the generation of the partial coherence vector exponent vortex beam mentioned above
  • the embodiment part of the system for the specific implementation manner, reference may be made to the description of the corresponding embodiments of each part, and no further introduction will be made here.
  • the selected laser is a continuous wave solid-state laser with a wavelength of 532nm and a power of 100mW.
  • the focal lengths of the first lens 3 and the second lens 5 are both 100 mm, and the focal length of the third lens 11 is 500 mm.
  • the rotating ground glass is on the rear focal plane of the first lens 3 and the front focal plane of the second lens 5 .
  • the roughness of the rotating frosted glass is 400, and its speed is controlled by a 3-volt regulated power supply.
  • the spatial light modulator is a reflective spatial light modulator: HOLOEYE PLUTO-VIS-016, with a size of 1920*1080 pixels and a pixel size of 8 ⁇ m.
  • the generated hologram is input into the spatial light modulator through a personal computer.
  • the camera is a professional CCD camera ECO655MVGE, the specific parameters are 2448*2050 pixels in size and 3.45 ⁇ m in pixel size.
  • FIG. 2 it is the simulated light intensity distribution of the partial coherence vector power exponent vortex beam on the focal plane of the third lens 11 with a focal length of 500 mm.
  • the initial beam waist radius w 0 of the beam is 1 mm
  • the coherence length ⁇ ⁇ ⁇ is 1 mm
  • the exponential phase gradient factor n is 2.
  • the partial coherence vector exponent vortex beam has a spatially varying polarization state distribution, and its center has a polarization singularity, the beam center does not become a Gaussian distribution due to the reduced coherence, but has a weaker light intensity distribution.
  • the invention realizes the light intensity structure regulation and polarization regulation of the partially coherent beam, which will provide potential applications in the field of particle manipulation.
  • the generation system and method of the partial coherence vector power exponent vortex beam of the present invention is by adding a spiral phase distribution of space index change to the traditional partial coherence vector beam, and by adjusting the size of the coherence, the value of the exponential phase gradient factor and the topological charge can be Realize triangular, quadrangular, five-pointed star-shaped light intensity distribution, and spatially varying polarization states, and because the polarization state distribution has vector characteristics, there is a dark core in the center light intensity, and its light intensity distribution has a higher intensity than traditional partially coherent vector beams High degree of control freedom, and retain high energy.

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Abstract

一种部分相干矢量幂指数涡旋光束的产生系统及方法，产生系统包括计算机、空间光调制器（8）、半波片（9）、径向偏振器（10）、第三透镜（11）；计算机与空间光调制器（8）连接，计算机用于将幂指数螺旋相位的全息图加载至空间光调制器（8）。部分相干矢量幂指数涡旋光束的产生系统及方法通过给传统的部分相干矢量光束附加一个空间指数变化的螺旋相位分布，通过调控相干度的大小，指数相位梯度因子和拓扑荷的数值可以实现三角形、四边形、五角星形的光强分布，以及空间变化的偏振态，并且由于偏振态分布具有矢量特性，其中心光强存在一个暗核，其光强分布相比传统部分相干矢量光束具有较高的调控自由度，且保留了较高的能量。

Description

一种部分相干矢量幂指数涡旋光束的产生系统及方法 技术领域
本发明涉及光学技术领域，特别涉及一种部分相干矢量幂指数涡旋光束的产生系统及方法。
背景技术
近年来，涡旋光束逐渐成为光场调控领域的一大研究热点。其中心光强为零，且具有螺旋型波前，并且携带轨道角动量。在微纳加工，微粒操纵，光通信，光学测量和超分辨成像等领域具有重要的应用价值。为了应对日益复杂的应用需求，科研人员需要构建一些特殊的涡旋光束来满足复杂应用的需求。此外，激光是一种具有高相干性的光束。然而，在实际的应用中，例如光束通过大气湍流，或者旋转散射体之后，光束的相干性会降低。这种相干性降低的光束被称之为部分相干光束。Gori首先提出了部分相干涡旋光束这一概念，他表示部分相干涡旋光束可以用一系列的拉盖尔高斯光束的非相干叠加来表示。随着相干性的降低，涡旋光束中心光强不再为零，其暗中空结构逐渐变为高斯分布，因此可以实现暗中空到高斯分布的光束整形。对于部分相干涡旋光束，其中心的相位奇点消失，并转化为相干奇点，即交叉谱密度为零的点。相干奇点和相位奇点可以通过调控相干性的大小来实现它们之间的相互转化。
偏振是光束的一大本质特性，根据光束的偏振特性可以把光束分为两类，分别是标量光束和矢量光束。其中标量光束的偏振态主要有空间不变的线偏振，左旋圆偏振和右旋圆偏振；矢量光束主要有径向偏振、旋向偏振和高阶偏振等，其特点是具有空间变化的偏振态分布。在紧聚焦的条件下，径向偏振光可以被聚焦成比标量光束更小的聚焦光斑。Wolf给出了光束的相干性和偏振的统一理论，Guo等人证明了当涡旋相位引入部分相干径向偏振光束时，其携带的涡旋相位具有抵抗相干引起的光强分布退化和相干诱导的退偏振的效应。Zeng等人证明了将分数阶涡旋相位引入部分相干径向偏振光束，可以实现对高折射率和低折射率的粒子的复杂操纵，并且通过调控相位分布实现对偏振态的调控，因 此可以用于相位物体的测量。随后的研究证明了携带有涡旋相位的部分相干矢量光束对光束整形、鬼成像，进一步降低湍流的影响都有帮助。因此，构建独特的的部分相干矢量涡旋光束在基础科学研究和实际应用中是非常重要的。
目前，构建部分相干矢量涡旋光束的方法主要有两种，第一种对部分相干矢量光束的相位进行调控，引入一个整数阶的涡旋相位，从而产生整数阶部分相干涡旋光束(Guo,L.N.,et al.(2016)."Vortex phase-induced changes of the statistical properties ofa partially coherent radially polarized beam."Optics Express 24(13):13714)，第二种对部分相干矢量涡旋光束的拓扑荷进行调控构建具有分数阶涡旋相位的部分相干矢量分数阶涡旋光束，(Zeng J,et al.(2020).“Partially coherent radially polarized fractional vortex beam”Optics Express 28(8):11493)。
第一种，对于传统整数阶部分相干矢量涡旋光束，拓扑荷数为整数，其涡旋相位在一个周期内的改变量是2π的整数倍。高相干情况下光强分布在为圆环，偏振态分布为旋向偏振；随着相干度降低变，光强为高斯分布的光斑，偏振态变为圆偏振。
第二种，当拓扑荷数不为整数时，可以产生具有缺口的部分相干分数阶涡旋光束，实现了对其光强分布的整形。此外，由于分数阶相位非对称的相位分布，改变分数阶拓扑荷值可以调控偏振态的分布。
综上所述，整数阶涡旋相位的方案只能构成圆形的部分相干矢量光束的光强分布，而分数阶涡旋相位的方案尽管产生了多样的偏振态分布，但是其只能在高相干时实现带有缺口的部分相干涡旋光束，低相干时实现类似圆形的光强分布，其光强分布的调控自由度不高，且不能在自由空间稳定传输。
发明内容
本发明要解决的技术问题的是提供一种可行性高、调控自由度高、保留了较高能量的部分相干矢量幂指数涡旋光束的产生系统。
为了解决上述问题，本发明提供了一种部分相干矢量幂指数涡旋光束的产生系统，其包括计算机、空间光调制器、半波片、径向偏振器、第三透镜；
所述计算机与空间光调制器连接，所述计算机用于将幂指数螺旋相位的全 息图加载至空间光调制器；
所述空间光调制器用于接收部分相干光束，并对部分相干光束进行调制得到具有幂指数螺旋相位的部分相干光束；
所述半波片用于将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
所述径向偏振器用于将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振；
所述第三透镜用于将径向偏振的具有幂指数螺旋相位的部分相干光束聚焦以得到偏振态空间变化的部分相干矢量幂指数涡旋光束。
作为本发明的进一步改进，还包括部分相干光束产生系统，所述部分相干光束产生系统包括激光器、准直扩束元件、第一透镜、光束打散元件、第二透镜、高斯滤波片；
所述激光器用于产生完全相干光束，所述准直扩束元件用于对所述完全相干光束进行准直扩束，所述第一透镜用于将准直扩束后的完全相干光束聚焦在光束打散元件上，所述光束打散元件将完全相干光束打散并生成完全非相干光束，所述第二透镜对完全非相干光束进行傅里叶变换，所述高斯滤波片对经过傅里叶变换后的完全非相干光束进行振幅滤波得到具有高斯光强分布的部分相干光束。
作为本发明的进一步改进，所述光束打散元件为旋转毛玻璃，所述旋转毛玻璃的表面具有服从高斯统计分布的微小颗粒。
作为本发明的进一步改进，所述准直扩束元件为扩束器。
作为本发明的进一步改进，所述空间光调制器为透射式空间光调制器或反射式空间光调制器；当所述空间光调制器为反射式空间光调制器时，所述部分相干矢量幂指数涡旋光束的产生系统还包括分束立方体，部分相干光束由所述分束立方体透射至所述反射式空间光调制器，并由所述反射式空间光调制器反射回所述分束立方体，再由所述分束立方体反射至所述半波片。
作为本发明的进一步改进，所述部分相干矢量幂指数涡旋光束的交叉谱密度矩阵表示为：
Figure PCTCN2022078312-appb-000001
其中，<>表示求系综平均运算；“*”表示求复共轭运算；Ex(r)和Ey(r)分别表示完全相干时，径向偏振幂指数涡旋光束电场的水平偏振分量和垂直偏振分量；r 1和r 2表示任意两点的径向坐标矢量；x，y分别表示直角坐标系的水平轴和垂直轴；其电场可以表示为：
Figure PCTCN2022078312-appb-000002
Figure PCTCN2022078312-appb-000003
其中，w 0表示光束初始的束腰半径，θ表示角向坐标矢量，i为虚数单位，rem(.)为求余函数，l为拓扑荷数，n为指数相位梯度因子；通过调控拓扑荷数和指数相位梯度因子的大小，可以调控该部分相干幂指数涡旋光束的光强分布；将公式(2)和(3)代入公式(1)，即得到在空间-频率域中该部分相干矢量幂指数涡旋光束的交叉谱密度表达式：
Figure PCTCN2022078312-appb-000004
其中：
Figure PCTCN2022078312-appb-000005
其中，σ αβ表示光束的初始相干长度；θ 1和θ 2表示任意两点的角向坐标矢量。
作为本发明的进一步改进，还包括相机，所述相机对产生的部分相干矢量幂指数涡旋光束进行成像。
作为本发明的进一步改进，所述计算机通过MATLAB计算得到加载在所述空间光调制器上的幂指数螺旋相位。
为了解决上述问题，本发明还提供了一种部分相干矢量幂指数涡旋光束的产生方法，所述部分相干矢量幂指数涡旋光束的产生方法包括：
利用加载了幂指数螺旋相位的空间光调制器接收部分相干光束，并对部分 相干光束进行调制得到具有幂指数螺旋相位的部分相干光束；
将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振；
将径向偏振的具有幂指数螺旋相位的部分相干光束聚焦以得到偏振态空间变化的部分相干矢量幂指数涡旋光束。
作为本发明的进一步改进，利用半波片将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
利用径向偏振器将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振。
本发明的有益效果：
本发明部分相干矢量幂指数涡旋光束的产生系统及方法通过给传统的部分相干矢量光束附加一个空间指数变化的螺旋相位分布，通过调控相干度的大小，指数相位梯度因子和拓扑荷的数值可以实现三角形、四边形、五角星形的光强分布，以及空间变化的偏振态，并且由于偏振态分布具有矢量特性，其中心光强存在一个暗核，其光强分布相比传统部分相干矢量光束具有较高的调控自由度，且保留了较高的能量。
上述说明仅是本发明技术方案的概述，为了能够更清楚了解本发明的技术手段，而可依照说明书的内容予以实施，并且为了让本发明的上述和其他目的、特征和优点能够更明显易懂，以下特举较佳实施例，并配合附图，详细说明如下。
附图说明
图1是本发明优选实施例中部分相干矢量幂指数涡旋光束的产生系统的示意图；
图2是本发明优选实施例中得到的部分相干矢量幂指数涡旋光束在第三透镜焦平面的光强分布图。
标记说明：1、激光器；2、准直扩束元件；3、第一透镜；4、光束打散元 件；5、第二透镜；6、高斯滤波片；7、分束立方体；8、空间光调制器；9、半波片；10、径向偏振器；11、第三透镜；12、相机。
具体实施方式
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人员可以更好地理解本发明并能予以实施，但所举实施例不作为对本发明的限定。
如图1所示，为本发明优选实施例中的部分相干矢量幂指数涡旋光束的产生系统，该系统包括计算机、空间光调制器8、半波片9、径向偏振器10、第三透镜11。
所述计算机与空间光调制器8连接，所述计算机用于将幂指数螺旋相位的全息图加载至空间光调制器8；所述空间光调制器8用于接收部分相干光束，并对部分相干光束进行调制得到具有幂指数螺旋相位的部分相干光束；所述半波片9用于将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；所述径向偏振器10用于将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振；所述第三透镜11用于将径向偏振的具有幂指数螺旋相位的部分相干光束聚焦以得到偏振态空间变化的部分相干矢量幂指数涡旋光束。
在一些实施例中，所述部分相干矢量幂指数涡旋光束的产生系统还包括部分相干光束产生系统，所述部分相干光束产生系统包括激光器1、准直扩束元件2、第一透镜3、光束打散元件4、第二透镜5、高斯滤波片6。
所述激光器1用于产生完全相干光束，所述准直扩束元件2用于对所述完全相干光束进行准直扩束，所述第一透镜3用于将准直扩束后的完全相干光束聚焦在光束打散元件4上，所述光束打散元件4将完全相干光束打散并生成完全非相干光束，所述第二透镜5对完全非相干光束进行傅里叶变换，所述高斯滤波片6对经过傅里叶变换后的完全非相干光束进行振幅滤波得到具有高斯光强分布的部分相干光束。
可选地，所述光束打散元件4为旋转毛玻璃，所述旋转毛玻璃的表面具有服从高斯统计分布的微小颗粒。具体地，旋转毛玻璃设置于第一透镜3的后焦平面和第二透镜5的前焦平面上。
可选地，所述准直扩束元件2为扩束器。
可选地，所述空间光调制器8为透射式空间光调制器8或反射式空间光调制器8；当所述空间光调制器8为反射式空间光调制器8时，所述部分相干矢量幂指数涡旋光束的产生系统还包括分束立方体7，部分相干光束由所述分束立方体7透射至所述反射式空间光调制器8，并由所述反射式空间光调制器8反射回所述分束立方体7，再由所述分束立方体7反射至所述半波片9。
在一些实施例中，所述部分相干矢量幂指数涡旋光束的产生系统还包括相机12，相机12设置于第三透镜12的后焦平面上，所述相机12对产生的部分相干矢量幂指数涡旋光束进行成像。
可选地，所述计算机通过MATLAB计算得到加载在所述空间光调制器8上的幂指数螺旋相位。
本发明的原理如下：
所述部分相干矢量幂指数涡旋光束的交叉谱密度矩阵表示为：
Figure PCTCN2022078312-appb-000006
其中，<>表示求系综平均运算；“*”表示求复共轭运算；Ex(r)和Ey(r)分别表示完全相干时，径向偏振幂指数涡旋光束电场的水平偏振分量和垂直偏振分量；r 1和r 2表示任意两点的径向坐标矢量；x，y分别表示直角坐标系的水平轴和垂直轴；其电场可以表示为：
Figure PCTCN2022078312-appb-000007
Figure PCTCN2022078312-appb-000008
其中，w 0表示光束初始的束腰半径，θ表示角向坐标矢量，i为虚数单位，rem(.)为求余函数，l为拓扑荷数，n为指数相位梯度因子；通过调控拓扑荷数和指数相位梯度因子的大小，可以调控该部分相干幂指数涡旋光束的光强分布；将公式(2)和(3)代入公式(1)，即得到在空间-频率域中该部分相干矢量幂指数涡旋光束的交叉谱密度表达式：
Figure PCTCN2022078312-appb-000009
其中：
Figure PCTCN2022078312-appb-000010
其中，σ αβ表示光束的初始相干长度；θ 1和θ 2表示任意两点的角向坐标矢量。
公式(5)即为传统的高斯关联函数。为了实现这样的部分相干矢量幂指数涡旋光束，本发明利用旋转毛玻璃产生具有高斯关联结构的部分相干光束，再通过空间光调制器加载幂指数螺旋相位的全息图，当部分相干光束通过空间光调制器后即可产生具有多边形结构的部分相干幂指数涡旋光束，最后经过一个径向偏振器调控其偏振态分布，从而产生所需的偏振态空间变化的部分相干矢量幂指数涡旋光束。
本发明优选实施例还公开了一种部分相干矢量幂指数涡旋光束的产生方法，所述部分相干矢量幂指数涡旋光束的产生方法包括以下步骤：
S1、利用加载了幂指数螺旋相位的空间光调制器8接收部分相干光束，并对部分相干光束进行调制得到具有幂指数螺旋相位的部分相干光束；
S2、将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
S3、将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振；
S4、将径向偏振的具有幂指数螺旋相位的部分相干光束聚焦以得到偏振态空间变化的部分相干矢量幂指数涡旋光束。
可选地，利用半波片9将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
利用径向偏振器10将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振。
本实施例中部分相干矢量幂指数涡旋光束的产生方法基于前述部分相干矢量幂指数涡旋光束的产生系统，因此该方法的具体实施方式可见前文中的部分 相干矢量幂指数涡旋光束的产生系统的实施例部分，所以，其具体实施方式可以参照相应的各个部分实施例的描述，在此不再展开介绍。
为了验证本发明的有效性，在一具体实施例中，选用的激光器为连续波固体激光器，波长为532nm，功率为100mW。第一透镜3和第二透镜5的焦距均为100mm，第三透镜11的焦距为500mm。旋转毛玻璃在第一透镜3的后焦平面和第二透镜5的前焦平面上。旋转毛玻璃的粗糙度为400，通过3伏稳压电源控制其转速。空间光调制器为反射式空间光调制器：HOLOEYE PLUTO-VIS-016，尺寸大小为1920*1080像素，像素大小为8μm，通过个人计算机将产生的全息图输入空间光调制器。相机为专业CCD相机ECO655MVGE，具体参数为尺寸大小为2448*2050像素，像素大小为3.45μm。
如图2所示，为模拟得到的这种部分相干矢量幂指数涡旋光束在焦距为500mm的第三透镜11的焦平面上的光强分布。光束的初始束腰半径w 0为1mm，相干长度σ αβ为1mm，指数相位梯度因子n为2。从图2中可以看出，当指数相位梯度因子n等于2不变时，通过改变拓扑荷数l的值，其中，图(a)中l＝3；图(b)中l＝4，图(c)中l＝3；分别可以产生三角形、四边形、五角星形的光强分布。此外，由于该部分相干矢量幂指数涡旋光束具有空间变化的偏振态分布，其中心具有一个偏振奇点，因此光束中心并未没有因为相干度降低而变成高斯分布，而是具有一个较弱的光强分布。相比于传统的部分相干矢量涡旋光束只具有圆形光强分布，该发明实现了部分相干光束的光强结构调控以及偏振调控，这将为微粒操纵领域提供潜在的应用。
本发明部分相干矢量幂指数涡旋光束的产生系统及方法通过给传统的部分相干矢量光束附加一个空间指数变化的螺旋相位分布，通过调控相干度的大小，指数相位梯度因子和拓扑荷的数值可以实现三角形、四边形、五角星形的光强分布，以及空间变化的偏振态，并且由于偏振态分布具有矢量特性，其中心光强存在一个暗核，其光强分布相比传统部分相干矢量光束具有较高的调控自由度，且保留了较高的能量。
以上实施例仅是为充分说明本发明而所举的较佳的实施例，本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换，均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。

Claims (10)

  1. 一种部分相干矢量幂指数涡旋光束的产生系统，其特征在于，包括计算机、空间光调制器、半波片、径向偏振器、第三透镜；
    所述计算机与空间光调制器连接，所述计算机用于将幂指数螺旋相位的全息图加载至空间光调制器；
    所述空间光调制器用于接收部分相干光束，并对部分相干光束进行调制得到具有幂指数螺旋相位的部分相干光束；
    所述半波片用于将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
    所述径向偏振器用于将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振；
    所述第三透镜用于将径向偏振的具有幂指数螺旋相位的部分相干光束聚焦以得到偏振态空间变化的部分相干矢量幂指数涡旋光束。
  2. 如权利要求1所述的部分相干矢量幂指数涡旋光束的产生系统，其特征在于，还包括部分相干光束产生系统，所述部分相干光束产生系统包括激光器、准直扩束元件、第一透镜、光束打散元件、第二透镜、高斯滤波片；
    所述激光器用于产生完全相干光束，所述准直扩束元件用于对所述完全相干光束进行准直扩束，所述第一透镜用于将准直扩束后的完全相干光束聚焦在光束打散元件上，所述光束打散元件将完全相干光束打散并生成完全非相干光束，所述第二透镜对完全非相干光束进行傅里叶变换，所述高斯滤波片对经过傅里叶变换后的完全非相干光束进行振幅滤波得到具有高斯光强分布的部分相干光束。
  3. 如权利要求2所述的部分相干矢量幂指数涡旋光束的产生系统，其特征在于，所述光束打散元件为旋转毛玻璃，所述旋转毛玻璃的表面具有服从高斯统计分布的微小颗粒。
  4. 如权利要求2所述的部分相干矢量幂指数涡旋光束的产生系统，其特征在于，所述准直扩束元件为扩束器。
  5. 如权利要求1所述的部分相干矢量幂指数涡旋光束的产生系统，其特征 在于，所述空间光调制器为透射式空间光调制器或反射式空间光调制器；当所述空间光调制器为反射式空间光调制器时，所述部分相干矢量幂指数涡旋光束的产生系统还包括分束立方体，部分相干光束由所述分束立方体透射至所述反射式空间光调制器，并由所述反射式空间光调制器反射回所述分束立方体，再由所述分束立方体反射至所述半波片。
  6. 如权利要求1所述的部分相干矢量幂指数涡旋光束的产生系统，其特征在于，所述部分相干矢量幂指数涡旋光束的交叉谱密度矩阵表示为：
    Figure PCTCN2022078312-appb-100001
    其中，<>表示求系综平均运算；“*”表示求复共轭运算；Ex(r)和Ey(r)分别表示完全相干时，径向偏振幂指数涡旋光束电场的水平偏振分量和垂直偏振分量；r 1和r 2表示任意两点的径向坐标矢量；x，y分别表示直角坐标系的水平轴和垂直轴；其电场可以表示为：
    Figure PCTCN2022078312-appb-100002
    Figure PCTCN2022078312-appb-100003
    其中，w 0表示光束初始的束腰半径，θ表示角向坐标矢量，i为虚数单位，rem(.)为求余函数，l为拓扑荷数，n为指数相位梯度因子；通过调控拓扑荷数和指数相位梯度因子的大小，可以调控该部分相干幂指数涡旋光束的光强分布；将公式(2)和(3)代入公式(1)，即得到在空间-频率域中该部分相干矢量幂指数涡旋光束的交叉谱密度表达式：
    Figure PCTCN2022078312-appb-100004
    其中：
    Figure PCTCN2022078312-appb-100005
    其中，σ αβ表示光束的初始相干长度；θ 1和θ 2表示任意两点的角向坐标矢量。
  7. 如权利要求1所述的部分相干矢量幂指数涡旋光束的产生系统，其特征在于，还包括相机，所述相机对产生的部分相干矢量幂指数涡旋光束进行成像。
  8. 如权利要求1所述的部分相干矢量幂指数涡旋光束的产生系统，其特征在于，所述计算机通过MATLAB计算得到加载在所述空间光调制器上的幂指数螺旋相位。
  9. 一种部分相干矢量幂指数涡旋光束的产生方法，其特征在于，包括：
    利用加载了幂指数螺旋相位的空间光调制器接收部分相干光束，并对部分相干光束进行调制得到具有幂指数螺旋相位的部分相干光束；
    将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
    将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振；
    将径向偏振的具有幂指数螺旋相位的部分相干光束聚焦以得到偏振态空间变化的部分相干矢量幂指数涡旋光束。
  10. 如权利要求9所述的部分相干矢量幂指数涡旋光束的产生方法，其特征在于，利用半波片将具有幂指数螺旋相位的部分相干光束的偏振方向调制为垂直偏振；
    利用径向偏振器将垂直偏振的具有幂指数螺旋相位的部分相干光束的偏振方向调制为径向偏振。
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