WO2023279424A1 - 一种多边形部分相干涡旋光束产生系统及方法 - Google Patents
一种多边形部分相干涡旋光束产生系统及方法 Download PDFInfo
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- the invention relates to the field of optical technology, in particular to a system and method for generating a polygonal partially coherent vortex beam.
- Vortex beams are special beams with a dark hollow structure. In recent years, they have important application values in the fields of particle manipulation, optical tweezers, optical communication, optical measurement and super-resolution imaging because of their orbital angular momentum. Therefore, it has gradually attracted extensive attention of researchers. With the increasing development of science and technology, researchers need to build a variety of vortex beams to meet the special needs of these application fields.
- the control parameters of vortex beam mainly include amplitude, phase, polarization, frequency and coherence.
- One of the characteristics of laser is its high coherence. However, after passing through atmospheric turbulence, random phase, or rotating scatterers, the coherence of the beam will be reduced to a certain extent.
- partially coherent beams can improve transmission efficiency in nonlinear optical processes, enhance signal-to-noise ratio, reduce bit error rate, enable particle trapping, and ghost imaging applications.
- Partially coherent vortex beams were first proposed by Gori et al., and can be represented by an incoherent superposition of a series of coherent Laguerre-Gaussian modes. Since then, the research on vortex beams has been extended from the field of complete coherence to the field of partial coherence. Unlike the completely coherent vortex beam, which has a phase singularity at the center, resulting in zero intensity at the center, for a partially coherent vortex beam, its intensity distribution gradually evolves into a Gaussian distribution as the coherence decreases. In addition, due to the disappearance of the intensity zero point, there is no visible phase singularity in the partially coherent vortex beam, but there is a coherence singularity, that is, the point where the cross spectral density is zero.
- the phase singularity in the fully coherent vortex beam can be transformed into the coherence singularity in the partially coherent vortex beam.
- the value of the reference point in the cross spectral density function determines the coherence singularity. Location.
- Partially coherent vortex beams have some advantages over fully coherent vortex beams. For example, by adjusting the size of the coherence, the light intensity distribution can be shaped from hollow to solid, so that the hollow light intensity can be used to capture low refractive index particles. Solid light High-refractive-index particles are strongly trapped, and partially coherent vortex beams can overcome the flickering and beam expansion effects caused by transmission in the field of free-space optical communications, and their unique correlation functions have strong self-repairing capabilities. Therefore, constructing novel partially coherent vortex beams is very important in basic scientific research and practical applications.
- the first method is to adjust the phase of the vortex beam to generate a fractional partially coherent vortex beam (Zeng, J., et al. (2016).” Partially coherent fractional vortex beam.”
- the second method regulates the spatial correlation function of partially coherent beams to construct special correlated partially coherent vortex beams, such as Laguerre-Gaussian correlated partially coherent vortex Beams (ChenY.H., et al. (2014). "Experimental demonstration of a Laguerre-Gaussian correlated Shell-model vortex beam” Optics Express 22(5):5826-5838).
- the first one for the traditional integer-order partially coherent vortex beam with Gaussian correlation function structure, the amount of change of its helical phase in one cycle is an integer multiple of 2 ⁇ , that is, its topological charge is an integer, and the resulting light intensity distribution In the case of high coherence, it is a ring, and as the degree of coherence decreases, it becomes a spot of Gaussian distribution.
- the topological charge is not an integer, a partially coherent fractional vortex beam with a gap can be generated, and the light intensity distribution can be shaped.
- the correlation function of the partially coherent vortex beam is Laguerre-Gaussian correlation, its light intensity distribution is determined by the joint control of the vortex phase, initial coherence and correlation structure function.
- the light beam is mainly regulated by the correlation function, so its light intensity has a dark hollow light intensity distribution; as the coherence increases, the control effect of the correlation function decreases, and the light intensity gradually becomes a Gaussian distribution; when the coherence When the intensity increases to a large value, the correlation function no longer plays a modulating role, and at this time it is mainly regulated by the vortex phase, so the light intensity returns to the dark hollow structure.
- the existing fractional vortex phase schemes can only realize partially coherent vortex beams with gaps, and the control degree of freedom of light intensity distribution is not high.
- the method of controlling the correlation structure requires the use of a spatial light modulator in front of the dynamic scatterer to control the correlation function, resulting in excessive energy loss, making it difficult to apply to optical tweezers and other fields that require high-energy beams.
- the technical problem to be solved by the present invention is to provide a polygonal partially coherent vortex beam generation system with simple structure and good stability.
- the present invention provides a polygonal partially coherent vortex beam generation system, including a computer and a laser arranged in sequence along the optical path, a collimating beam expander, a first lens, a beam breaking element, a second lens, a Gaussian A filter, a spatial light modulator, and a third lens, the spatial light modulator is connected to a computer, and the computer is used to load the hologram of the abnormal power index vortex beam to the spatial light modulator;
- the laser generates a fully coherent beam
- the collimating and expanding element collimates and expands the fully coherent beam
- the first lens focuses the collimated and expanding fully coherent beam on the beam breaking element
- the 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 performs Fourier transform on the completely incoherent beam Filtering is performed to obtain a partially coherent beam with a Gaussian light intensity distribution
- the spatial light modulator modulates the partially coherent beam
- the third lens focuses the modulated beam to obtain a partially coherent vortex beam with a polygonal structure.
- the complex transmittance function of the hologram of the abnormal power exponent vortex beam is expressed as:
- angle(.) is the function to calculate the phase of the abnormal power exponent vortex
- P is the phase expression of the blazed grating
- the square of the modulus of the complex transmittance function t can be obtained to generate the abnormal power exponent vortex beam Hologram
- D represents the phase period of the blazed grating
- x represents the x-axis coordinate of the Cartesian coordinate system
- the blazed grating is used to separate the generated polygonal partially coherent vortex beam from the zero-order spot.
- the cross spectral density function of a partially coherent vortex beam with a polygonal structure is expressed as:
- ⁇ > represents an ensemble average operation
- "*" represents a complex conjugate operation
- E(r, ⁇ ) represents the electric field of the abnormal power exponent vortex beam when it is completely coherent
- r represents the radial factor
- ⁇ represents the angular factor
- its electric field can be expressed as:
- w 0 represents the initial beam waist radius of the beam
- i is the imaginary number unit
- rem(.) is the remainder function
- m is the spiral factor
- n is the power exponent factor, by adjusting the spiral factor m and the power exponent factor n
- the light intensity distribution of the partially coherent vortex beam can be adjusted;
- ⁇ represents the initial coherence length of the beam
- the second term in the formula is the traditional Gaussian correlation function
- a camera is also included, and the camera images the generated partially coherent vortex beam with a polygonal structure.
- 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 present invention also provides a method for generating a polygonal partially coherent vortex beam, which includes:
- the modulated beam is focused to obtain a partially coherent vortex beam with a polygonal structure.
- the fully coherent light beam is broken up by rotating ground glass and a completely incoherent light beam is generated.
- a second lens is used to perform Fourier transform on the completely incoherent light beam.
- a Gaussian filter is used to filter the completely incoherent light beam after Fourier transform.
- the system and method for generating polygonal partially coherent vortex beams of the present invention can flexibly adjust the geometric structure of partially coherent vortex beams in real time.
- the present invention can simply and conveniently generate such polygonal partially coherent vortex beams, so it has important applications in the field of particle manipulation value.
- the light intensity distribution of ellipse, triangle, quadrilateral, and pentagram can be realized by adjusting the value of power exponent factor and spiral factor. Compared with the traditional partially coherent vortex beam, its light intensity distribution has a higher degree of control freedom and retains higher energy.
- Fig. 1 is a schematic diagram of a polygonal partially coherent vortex beam generating system in a preferred embodiment of the present invention
- Fig. 2 is the hologram of the abnormal power exponent vortex beam in the preferred embodiment of the present invention
- Fig. 3 is a light intensity distribution diagram of a partially coherent vortex beam with a polygonal structure at the focal plane of a third lens obtained in a preferred embodiment of the present invention.
- Marking description 1. Laser; 2. Collimator beam expander; 3. First lens; 4. Beam breaking element; 5. Second lens; 6. Gaussian filter; 7. Spatial light modulator; 8. Three lenses; 9, camera.
- the system includes a computer and a laser 1, a collimating beam expander element 2, a first lens 3, and a laser beam that are sequentially arranged along the optical path.
- Scatter element 4, second lens 5, Gaussian filter 6, spatial light modulator 7, third lens 8, described spatial light modulator 7 is connected with computer, and described computer is used for the holography of abnormal power exponent vortex light beam
- the map is loaded into the spatial light modulator 7 .
- the computer obtains the required hologram through MATLAB calculation.
- the laser 1 generates a fully coherent beam
- the collimating and expanding element 2 collimates and expands the fully coherent beam
- the first lens 3 focuses the collimated and expanding fully coherent beam on the beam breaking element 4
- the beam breaking element 4 breaks up the completely coherent beam and generates a completely incoherent beam
- the second lens 5 performs Fourier transform on the completely incoherent beam
- the Gaussian filter 6 performs Fourier transform on the completely incoherent beam.
- the transformed completely incoherent beam is filtered to obtain a partially coherent beam with a Gaussian light intensity distribution
- the spatial light modulator 7 modulates the partially coherent beam
- the third lens 8 focuses the modulated beam to obtain a beam with Partially coherent vortex beams in polygonal structures.
- the cross spectral density function of a partially coherent vortex beam with a polygonal structure can be expressed as:
- ⁇ > represents an ensemble average operation
- "*" represents a complex conjugate operation
- E(r, ⁇ ) represents the electric field of the abnormal power exponent vortex beam when it is completely coherent
- r represents the radial factor
- ⁇ represents the angular factor
- its electric field can be expressed as:
- w 0 represents the initial beam waist radius of the beam
- i is the imaginary number unit
- rem(.) is the remainder function
- m is the spiral factor
- n is the power exponent factor, by adjusting the spiral factor m and the power exponent factor n
- the light intensity distribution of the partially coherent vortex beam can be adjusted;
- ⁇ represents the initial coherence length of the beam
- the second term in the formula is the traditional Gaussian correlation function
- the system further includes a camera 9 for imaging the generated partially coherent vortex beam with a polygonal structure.
- the beam-dispersing element 4 is a rotating ground glass, and the surface of the rotating ground glass has tiny particles obeying a Gaussian statistical distribution.
- the collimating beam expanding element 2 is a beam expander.
- the complex transmittance function of the hologram of the abnormal power exponent vortex beam can be expressed as:
- angle(.) is the function to calculate the phase of the abnormal power exponent vortex
- P is the phase expression of the blazed grating
- the square of the modulus of the complex transmittance function t can be obtained to generate the abnormal power exponent vortex beam Hologram
- D represents the phase period of the blazed grating
- x represents the x-axis coordinate of the Cartesian coordinate system
- the blazed grating is used to separate the generated polygonal partially coherent vortex beam from the zero-order spot.
- the preferred embodiment of the present invention also discloses a method for generating a polygonal partially coherent vortex beam, which includes the following steps:
- the devices and principles involved in this method are the same as those in the above-mentioned system embodiments, and will not be repeated here.
- the selected laser is a continuous wave solid-state laser with a wavelength of 532nm and a power of 300mW.
- the focal length of lens 1 and lens 2 is 100mm
- the focal length of lens 3 is 300mm
- the roughness of the rotating frosted glass is 400
- its speed is controlled by a 3-volt regulated power supply.
- the rotated ground glass needs to be placed on the back focal plane of lens 1 and the front focal plane of lens 2.
- the spatial light modulator is a transmissive spatial light modulator: HOLOEYE LC 2012, with a size of 1024*768 pixels and a pixel size of 36 ⁇ 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.
- Figure 2 is a hologram of the anomalous power exponent vortex beam used in the experiment.
- the power exponent factor n is selected as 2
- the helical factor m is selected as 2, 3, 4, and 5 respectively.
- the hologram of the abnormal power exponent vortex beam can be obtained.
- Holograms of such anomalous power-exponent vortex beams can be produced by the HOLOEYE LC 2012 spatial light modulator described above.
- FIG. 3 is an experimentally obtained light intensity distribution diagram of a partially coherent vortex beam with a polygonal structure on the focal plane of the lens 3 .
- the initial beam waist radius of the beam in the experiment is 1 mm, and the coherence length is 0.5 mm. It can be seen from the figure that when the power exponent factor n is equal to 2, by changing the value of the spiral factor m, the light intensity distribution of ellipse, triangle, quadrilateral and pentagram can be generated. It can be seen that the invention realizes the diversified shaping of partially coherent vortex beams, which will provide potential applications in the field of particle manipulation.
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Abstract
一种多边形部分相干涡旋光束产生系统及方法，包括计算机以及沿光路依次设置的激光器（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）、空间光调制器（7）、第三透镜（8），空间光调制器（7）与计算机连接，计算机用于将反常幂指数涡旋光束的全息图加载至空间光调制器（7）。多边形部分相干涡旋光束产生系统及方法可以实时灵活调控部分相干涡旋光束的几何结构，简单方便的产生这种多边形部分相干涡旋光束，在微粒操纵领域具有重要的应用价值。进一步可通过调控幂指数因子和螺旋因子的数值来实现椭圆形、三角形、四边形、五角星形的光强分布。光强分布比传统部分相干涡旋光束具有较高的调控自由度，且保留了较高的能量。
Description
本发明涉及光学技术领域，特别涉及一种多边形部分相干涡旋光束产生系统及方法。
涡旋光束是一种具有暗中空结构的特殊光束，近年来由于其携带轨道角动量，并在微粒操纵，光镊，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。因此逐渐吸引了科研人员的广泛关注。随着科学技术的日益发展，科研人员需要构建多种多样的涡旋光束，满足这些应用领域的特殊需求。涡旋光束的调控参量主要有振幅，相位，偏振，频率和相干性。激光的一大特点就是其具有高相干性，但是，在通过大气湍流，随机相位，或者旋转散射体之后，光束的相干性会得到一定的降低，我们把这种具有较低相干度的光束称之为部分相干光束。与完全相干光束相比，部分相干光束的更在广泛的存在与自然界，并且在实际的应用中具有一些独特的优势。例如，部分相干光束可以提高非线性光学过程中的传输效率，增强信噪比，降低误码率，实现微粒捕获，和鬼成像等应用。
部分相干涡旋光束是由Gori等人首次提出，可以用一系列相干的拉盖尔高斯模的非相干叠加来表示。此后，对于涡旋光束的研究从完全相干领域扩展到部分相干领域。不同于完全相干涡旋光束中心具有一个相位奇点导致其中心光强为零，对于部分相干涡旋光束，随着相干性的降低，其光强分布逐渐演化为高斯分布。此外，由于光强零点消失，部分相干涡旋光束不存在可见的相位奇点，但是其存在相干奇点，即交叉谱密度为零的点。并且，通过调控其相干性大小，完全相干涡旋光束中的相位奇点可以与部分相干涡旋光束中的相干奇点互相转化，交叉谱密度函数中参考点的取值决定了相干奇点的位置。部分相干涡旋光束相比完全相干涡旋光束具有一些优势，例如，通过调控相干性的大小可以实现光强分布从空心到实心的整形，从而可以利用空心光强捕获低折射率 粒子，实心光强捕获高折射率粒子，并且部分相干涡旋光束在自由空间光通讯领域中，可以克服传输引起的光强闪烁和光束扩展效应，以及其特有的关联函数具有较强的自修复能力。因此，构建新型的部分相干涡旋光束在基础科学研究和实际应用中是非常重要的。
目前对构建新型的部分相干涡旋光束的方法主要有两种，第一种对涡旋光束的相位进行调控产生分数阶部分相干涡旋光束(Zeng,J.,et al.(2018)."Partially coherent fractional vortex beam."Optics Express 26(21):26830)，第二种对部分相干光束的空间关联函数进行调控构建特殊关联部分相干涡旋光束，例如拉盖尔-高斯关联部分相干涡旋光束(ChenY.H.,et al.(2014).“Experimental demonstration of a Laguerre-Gaussian correlated Shell-model vortex beam”Optics Express 22(5):5826-5838)。
第一种，对于传统的具有高斯关联函数结构的整数阶部分相干涡旋光束，其螺旋相位在一个周期内的改变量是2π的整数倍，即其拓扑荷数为整数，产生的光强分布在高相干情况下为圆环，随着相干度降低变为高斯分布的光斑。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。第二种，当部分相干涡旋光束的关联函数为拉盖尔-高斯关联时，其光强分布分别由涡旋相位，初始相干度和关联结构函数三者进行联合调控决定。当相干度很低时，光束主要由关联函数调控，因此其光强具有暗中空光强分布；随着相干度的升高，关联函数的调控效果降低，光强逐渐变为高斯分布；当相干度增加到很大时，关联函数不再起调制作用，此时主要由涡旋相位调控，因此光强又回到了暗中空结构。
综上所述，现有分数阶涡旋相位的方案只能实现带有缺口的部分相干涡旋光束，其光强分布的调控自由度不高。而调控关联结构的方法，需要在动态散射体前面利用空间光调制器调控关联函数，导致能量损耗过大，难以应用于光镊等需要光束具有较高能量的领域。
发明内容
本发明要解决的技术问题的是提供一种结构简单、稳定性好的多边形部分相干涡旋光束产生系统。
为了解决上述问题，本发明提供了一种多边形部分相干涡旋光束产生系统， 包括计算机以及沿光路依次设置的激光器、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、空间光调制器、第三透镜，所述空间光调制器与计算机连接，所述计算机用于将反常幂指数涡旋光束的全息图加载至空间光调制器；
所述激光器产生完全相干光束，所述准直扩束元件对完全相干光束进行准直扩束，所述第一透镜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滤波得到具有高斯光强分布的部分相干光束，所述空间光调制器对部分相干光束进行调制，所述第三透镜将调制后的光束进行聚焦并得到具有多边形结构的部分相干涡旋光束。
作为本发明的进一步改进，所述反常幂指数涡旋光束的全息图的复透过率函数表示为：
t＝exp[i·(angle(E(r,θ))+P)]
其中，angle(.)为对该反常幂指数涡旋求相位的函数，P为闪耀光栅的相位表达式，对该复透过率函数t的模求平方可得到产生反常幂指数涡旋光束的全息图；
其中，P的表达式为：
P＝2πx/D
其中，D表示该闪耀光栅的相位周期，x表示笛卡尔坐标系的x轴坐标，所述闪耀光栅用于将产生的多边形部分相干涡旋光束与零级光斑分离开。
作为本发明的进一步改进，具有多边形结构的部分相干涡旋光束的交叉谱密度函数表示为：
W(r
1,θ
1,r
2,θ
2)＝<E
*(r
1,θ
1)E(r
2,θ
2)> (1)
其中，<>表示求系综平均运算，“*”表示求复共轭运算。E(r,θ)表示完全相干时，反常幂指数涡旋光束电场，r表示径向因子，θ表示角向因子，其电场可以表示为：
其中，w
0表示光束初始的束腰半径，i为虚数单位，rem(.)为求余函数，m为螺旋因子，n为幂指数因子，通过调控螺旋因子m和幂指数因子n的大小，可以调控该部分相干涡旋光束的光强分布；将公式(2)代入公式(1)，即得到在空间-频率域中该多边形部分相干涡旋光束的交叉谱密度表达式：
其中，σ表示光束的初始相干长度，式中第二项即为传统的高斯关联函数。
作为本发明的进一步改进，还包括相机，所述相机对产生的具有多边形结构的部分相干涡旋光束进行成像。
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。
本发明还提供了一种多边形部分相干涡旋光束产生方法，其包括：
产生完全相干光束；
对完全相干光束进行准直扩束；
将完全相干光束打散并生成完全非相干光束；
对完全非相干光束进行傅里叶变换；
对经过傅里叶变换后的完全非相干光束进行滤波得到具有高斯光强分布的部分相干光束；
利用加载了反常幂指数涡旋光束的全息图的空间光调制器对部分相干光束进行调制；
将调制后的光束进行聚焦并得到具有多边形结构的部分相干涡旋光束。
作为本发明的进一步改进，利用旋转毛玻璃将完全相干光束打散并生成完 全非相干光束。
作为本发明的进一步改进，利用第二透镜对完全非相干光束进行傅里叶变换。
作为本发明的进一步改进，利用高斯滤波片对经过傅里叶变换后的完全非相干光束进行滤波。
本发明的有益效果：
本发明多边形部分相干涡旋光束产生系统及方法可以实时灵活调控部分相干涡旋光束的几何结构，本发明可以简单方便的产生这种多边形部分相干涡旋光束，因而在微粒操纵领域具有重要的应用价值。进一步可通过调控幂指数因子和螺旋因子的数值来实现椭圆形、三角形、四边形、五角星形的光强分布。其光强分布相比传统部分相干涡旋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。
图1是本发明优选实施例中多边形部分相干涡旋光束产生系统的示意图；
图2是本发明优选实施例中的反常幂指数涡旋光束的全息图；
图3是本发明优选实施例中得到的具有多边形结构的部分相干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、空间光调制器；8、第三透镜；9、相机。
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多边形部分相干涡旋光束产生系统，该系统包括计算机以及沿光路依次设置的激光器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、空间光调制器7、第三透镜8，所述空间光调制器7与计算机连接，所述计算机用于将反常幂指数涡旋光束的全息图加载至空间光调制器7。可选的，计算机通过MATLAB计算得到所需的全息图。
所述激光器1产生完全相干光束，所述准直扩束元件2对完全相干光束进行准直扩束，所述第一透镜3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滤波得到具有高斯光强分布的部分相干光束，所述空间光调制器7对部分相干光束进行调制，所述第三透镜8将调制后的光束进行聚焦并得到具有多边形结构的部分相干涡旋光束。
在本发明中，具有多边形结构的部分相干涡旋光束的交叉谱密度函数可以表示为：
W(r
1,θ
1,r
2,θ
2)＝<E
*(r
1,θ
1)E(r
2,θ
2)> (1)
其中，<>表示求系综平均运算，“*”表示求复共轭运算。E(r,θ)表示完全相干时，反常幂指数涡旋光束电场，r表示径向因子，θ表示角向因子，其电场可以表示为：
其中，w
0表示光束初始的束腰半径，i为虚数单位，rem(.)为求余函数，m为螺旋因子，n为幂指数因子，通过调控螺旋因子m和幂指数因子n的大小，可以调控部分相干涡旋光束的光强分布；将公式(2)代入公式(1)，即得到在空间-频率域中该多边形部分相干涡旋光束的交叉谱密度表达式：
其中，σ表示光束的初始相干长度，式中第二项即为传统的高斯关联函数。
在本实施例中，该系统还包括相机9，所述相机9对产生的具有多边形结构的部分相干涡旋光束进行成像。
可选的，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。
可选的，所述准直扩束元件2为扩束器。
在本发明中，所述反常幂指数涡旋光束的全息图的复透过率函数可以表示为：
t＝exp[i·(angle(E(r,θ))+P)] (4)
其中，angle(.)为对该反常幂指数涡旋求相位的函数，P为闪耀光栅的相位表达式，对该复透过率函数t的模求平方可得到产生反常幂指数涡旋光束的全息图；
其中，P的表达式为：
P＝2πx/D (5)
其中，D表示该闪耀光栅的相位周期，x表示笛卡尔坐标系的x轴坐标，所述闪耀光栅用于将产生的多边形部分相干涡旋光束与零级光斑分离开。
本发明优选实施例还公开了一种多边形部分相干涡旋光束产生方法，其包括以下步骤：
A、产生完全相干光束；
B、对完全相干光束进行准直扩束；
C、将完全相干光束打散并生成完全非相干光束；
D、对完全非相干光束进行傅里叶变换；
E、对经过傅里叶变换后的完全非相干光束进行滤波得到具有高斯光强分布的部分相干光束；
F、利用加载了反常幂指数涡旋光束的全息图的空间光调制器对部分相干光束进行调制；
G、将调制后的光束进行聚焦并得到具有多边形结构的部分相干涡旋光束。
可选的，利用旋转毛玻璃将完全相干光束打散并生成完全非相干光束；利用第二透镜对完全非相干光束进行傅里叶变换；利用高斯滤波片对经过傅里叶变换后的完全非相干光束进行滤波。该方法中涉及的器件及原理与上述系统实施例中相同，在此不多赘述。
在实验中，选用的激光器为波长为532nm的连续波固体激光器，功率为300mW。透镜1和透镜2的焦距为100mm，透镜3的焦距为300mm，旋转毛玻璃的粗糙度为400，通过3伏稳压电源控制其转速。旋转的毛玻璃需要放置在透镜1的后焦平面和透镜2的前焦平面上。空间光调制器为透射式空间光调制器：HOLOEYE LC 2012，尺寸大小为1024*768像素，像素大小为36μm，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。
图2为实验中所使用的反常幂指数涡旋光束的全息图。选取幂指数因子n为2，选取螺旋因子m分别为2，3，4，5，根据上述全息图透过率函数即可得到反常幂指数涡旋光束的全息图。这种反常幂指数涡旋光束的全息图可以通过上述的HOLOEYE LC 2012空间光调制器来产生。
图3为实验得到的具有多边形结构的部分相干涡旋光束在透镜3的焦平面上的光强分布图。实验中光束的初始束腰半径为1mm，相干长度为0.5mm。从图中可以看出，当幂指数因子n等于2不变时，通过改变螺旋因子m的值，可以产生椭圆形、三角形、四边形、五角星形的光强分布。可见，本发明实现了部分相干涡旋光束的多样化整形，这将为微粒操纵领域提供潜在的应用。
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)
- 一种多边形部分相干涡旋光束产生系统，其特征在于，包括计算机以及沿光路依次设置的激光器、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、空间光调制器、第三透镜，所述空间光调制器与计算机连接，所述计算机用于将反常幂指数涡旋光束的全息图加载至空间光调制器；所述激光器产生完全相干光束，所述准直扩束元件对完全相干光束进行准直扩束，所述第一透镜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滤波得到具有高斯光强分布的部分相干光束，所述空间光调制器对部分相干光束进行调制，所述第三透镜将调制后的光束进行聚焦并得到具有多边形结构的部分相干涡旋光束。
- 如权利要求1所述的多边形部分相干涡旋光束产生系统，其特征在于，所述反常幂指数涡旋光束的全息图的复透过率函数表示为：t＝exp[i·(angle(E(r,θ))+P)]其中，angle(.)为对该反常幂指数涡旋求相位的函数，P为闪耀光栅的相位表达式，对该复透过率函数t的模求平方可得到产生反常幂指数涡旋光束的全息图；其中，P的表达式为：P＝2πx/D其中，D表示该闪耀光栅的相位周期，x表示笛卡尔坐标系的x轴坐标，所述闪耀光栅用于将产生的多边形部分相干涡旋光束与零级光斑分离开。
- 如权利要求1所述的多边形部分相干涡旋光束产生系统，其特征在于，具有多边形结构的部分相干涡旋光束的交叉谱密度函数表示为：W(r 1,θ 1,r 2,θ 2)＝<E *(r 1,θ 1)E(r 2,θ 2)> (1)其中，<>表示求系综平均运算，“*”表示求复共轭运算。E(r,θ)表示完全相干时，反常幂指数涡旋光束电场，r表示径向因子，θ表示角向因子，其电场可以表示为：
其中，w 0表示光束初始的束腰半径，i为虚数单位，rem(.)为求余函数，m为螺旋因子，n为幂指数因子，通过调控螺旋因子m和幂指数因子n的大小，可以调控部分相干涡旋光束的光强分布；将公式(2)代入公式(1)，即得到在空间-频率域中该多边形部分相干涡旋光束的交叉谱密度表达式：
其中，σ表示光束的初始相干长度，式中第二项即为传统的高斯关联函数。 - 如权利要求1所述的多边形部分相干涡旋光束产生系统，其特征在于，还包括相机，所述相机对产生的具有多边形结构的部分相干涡旋光束进行成像。
- 如权利要求1所述的多边形部分相干涡旋光束产生系统，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。
- 如权利要求1所述的多边形部分相干涡旋光束产生系统，其特征在于，所述准直扩束元件为扩束器。
- 一种多边形部分相干涡旋光束产生方法，其特征在于，包括：产生完全相干光束；对完全相干光束进行准直扩束；将完全相干光束打散并生成完全非相干光束；对完全非相干光束进行傅里叶变换；对经过傅里叶变换后的完全非相干光束进行滤波得到具有高斯光强分布的部分相干光束；利用加载了反常幂指数涡旋光束的全息图的空间光调制器对部分相干光束进行调制；将调制后的光束进行聚焦并得到具有多边形结构的部分相干涡旋光束。
- 如权利要求7所述的多边形部分相干涡旋光束产生方法，其特征在于，利用旋转毛玻璃将完全相干光束打散并生成完全非相干光束。
- 如权利要求7所述的多边形部分相干涡旋光束产生方法，其特征在于，利用第二透镜对完全非相干光束进行傅里叶变换。
- 如权利要求7所述的多边形部分相干涡旋光束产生方法，其特征在于，利用高斯滤波片对经过傅里叶变换后的完全非相干光束进行滤波。
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