WO2023060781A1 - 基于模式分解快速产生动态扭曲部分相干光的系统及方法 - Google Patents
基于模式分解快速产生动态扭曲部分相干光的系统及方法 Download PDFInfo
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- the invention relates to the field of optical technology, in particular to a system and method for quickly generating dynamically twisted partially coherent light based on mode decomposition.
- the phase is an important control parameter of the light field. Since the twisted phase was proposed by Simon et al. in 1993, people have done a lot of research on twisted partially coherent light by means of mode decomposition, Wigner distribution and tensor representation. It has new statistical properties in properties such as degree and orbital angular momentum, and has broad application prospects in beam shaping, particle trapping, imaging resolution improvement, and free-space optical communication. The ability to actually generate twisted partially coherent light is the basic premise to meet the application requirements, so the actual generation method of twisted partially coherent light has been explored to a certain extent.
- Twisted partially coherent light is different from a beam with a general phase. Its phase is inseparable. Therefore, twisted partially coherent light cannot be obtained by directly generating an electric field, but needs to be obtained by converting or superimposing other easily generated beams. .
- the principle of converting light beams into twisted partially coherent light is to generate a light source first, and then convert it into twisted partially coherent light through an optical system.
- a typical experiment is that Wang Haiyun and others designed a 3-cylindrical mirror conversion system based on Williamson's theorem, which converts the anisotropic Gaussian Schell mode beam generated in advance by means of a spatial light modulator into a twisted Gaussian Schell mode beam.
- the principle of the mode superposition method is to generate the corresponding fundamental mode and perform weighted superposition to obtain distorted partially coherent light.
- the fundamental mode it can be divided into superposition methods such as eigenmode, pseudo mode, and random mode.
- a typical experiment is Tian's pseudo mode superposition method experiment. They decompose the distorted Gaussian Schell mode beam into a weighted superposition form in which the fundamental mode is a pseudo mode.
- the spatial light modulator is loaded with the corresponding hologram, and the distorted Gaussian Schell mode beam is obtained through superposition, and the random phase plays the role of eliminating the unnecessary mode correlation term.
- the method of pseudo-mode superposition has the advantage that dynamic beams can be generated without changing the optical system.
- the first two methods are based on Williamson's theorem, and the appropriate variance matrix and transmission matrix are designed in advance, and then the corresponding initial light field and transmission system are experimentally generated to obtain the required light field; the third method is based on mode decomposition, and the weighted fundamental mode is synthesized , to get the light field.
- Friberg et al. first produced an anisotropic Gaussian Schell model beam through an acousto-optic deflector and a filter system, and then passed through an optical beam consisting of 6 cylindrical mirrors placed in a designed special position. conversion system, and finally converted into a distorted Gaussian Schell model beam; then Wang Haiyun and others improved the method on the basis of this theory and experiment, and irradiated the expanded collimated light on the spatial light modulator loaded with a hologram, directly Anisotropic Gaussian Schell mode beams are produced with better results, and a 3-cylindrical mirror system is designed to replace the original 6-cylindrical mirror system equivalently.
- the technical problem to be solved by the present invention is to provide a system and method for quickly generating dynamically distorted partially coherent light based on mode decomposition, which is simple and feasible, requires a small number of modes, and takes a short time to generate light beams.
- the present invention provides a system for rapidly generating dynamically distorted partially coherent light based on mode decomposition, which includes:
- the first computer is used to decompose the twisted partially coherent light beam into a superposition form of a weighted orthogonal and complete intrinsic fundamental mode;
- the spatial light modulator is used to receive laser light and modulate the laser light to obtain dynamically twisted partially coherent light.
- an amplitude filtering system is also included, which is used to filter the dynamically twisted partially coherent light emitted from the spatial light modulator, and only keep the first diffraction order.
- the amplitude filtering system is a 4f system, including a first lens, a diaphragm, and a second lens arranged in sequence, and the dynamically distorted partially coherent light emitted from the spatial light modulator passes through the first lens sequentially.
- the individual holograms of each intrinsic fundamental mode are arranged in sequence, and the display time is proportional to the corresponding weight, the required intrinsic fundamental mode and the corresponding weight ratio It is determined according to the specific parameters of the twisted partially coherent light to be generated.
- the present invention also includes a charge-coupled device CCD and a second computer, the charge-coupled device CCD is connected to the second computer, the charge-coupled device CCD is used to receive the dynamically twisted partially coherent light, and the first Two computers are used to calculate and verify whether the dynamically distorted partially coherent light is consistent with the theory.
- a beam expander is also included, disposed between the laser and the spatial light modulator, for converting the laser light generated by the laser into beam expanded collimated light.
- a reflection plane mirror is also included, and the reflection plane mirror is arranged between the laser and the beam expander to lengthen the optical path.
- the present invention also provides a method for quickly generating dynamically distorted partially coherent light based on mode decomposition, which is applied to any system for rapidly generating dynamically distorted partially coherent light based on mode decomposition as described above, which includes the following steps:
- the first computer decomposes the twisted partially coherent light beam into a superposition form of weighted orthogonal complete intrinsic fundamental modes
- the first computer determines the mode of the required intrinsic fundamental mode and its requirements according to the superposition form of the intrinsic fundamental mode of the twisted partial coherent light decomposition, the specific parameter size of the twisted partial coherent light to be generated, and the accuracy requirements. weight size;
- the spatial light modulator receives the laser light generated by the laser, the first computer loads a dynamic hologram containing each intrinsic fundamental mode to the spatial light modulator, and uses the spatial light modulator to modulate the laser light, Get dynamically distorted partially coherent light.
- step S1 includes:
- the cross-spectral density of any beam that satisfies the non-negative positive definiteness can be expressed as the non-negative weight function ⁇ ( ⁇ ) and the mode function ⁇ ( ⁇ , ⁇ ) on the parameter ⁇ Integral form:
- n represents the order of the mode
- ⁇ ( ⁇ , ⁇ n ) is the mode function
- ⁇ ( ⁇ n ) is the corresponding weight function
- ⁇ , ⁇ and ⁇ represent the beam waist width, coherence length and twist factor respectively, and f( ⁇ , ⁇ , ⁇ , ⁇ ′) represents the specific correlation structure of the corresponding twisted partially coherent light;
- step S2 includes:
- the system and method for rapidly generating dynamically distorted partially coherent light based on mode decomposition in the present invention select modes based on proportionally determined weights, which requires fewer modes and takes less time to generate light beams; only need to change the hologram loaded in the spatial light modulator , the dynamic control of twisted partially coherent beams can be realized; the modes are orthogonal to each other, and no additional cross terms will be generated.
- Fig. 1 is a schematic diagram 1 of a system for rapidly generating dynamically distorted partially coherent light based on mode decomposition in a preferred embodiment of the present invention
- Fig. 2 is a schematic diagram 2 of a system for rapidly generating dynamically distorted partially coherent light based on mode decomposition in a preferred embodiment of the present invention
- Fig. 3 is a diagram of the intensity, coherence distribution and fitting situation of the dynamically distorted partially coherent light generated in theory and experiment by the system for quickly generating dynamically distorted partially coherent light based on mode decomposition in a preferred embodiment of the present invention
- Fig. 4 is a diagram of the transmission rotation of different distances of dynamically twisted partially coherent light generated in theory and experiments by the system for rapidly generating dynamically twisted partially coherent light based on mode decomposition in a preferred embodiment of the present invention.
- Marking description 1. Laser; 2. Reflecting plane mirror; 3. Beam expander; 4. Spatial light modulator; 5. First lens; 6. Aperture; 7. Second lens; 8. Charge-coupled device CCD; 9 1. The first computer; 10. The second computer; 11. The cylindrical lens; 12. The third lens.
- FIG. 1 a schematic diagram of a system for rapidly generating dynamically distorted partially coherent light based on mode decomposition in a preferred embodiment of the present invention, the system includes:
- the laser 1 is used to generate laser light; optionally, the laser 1 is a helium-neon laser.
- the first computer 9 is used to decompose the twisted partially coherent light beam into a superposition form of a weighted orthogonal and complete intrinsic fundamental mode;
- the specific parameter size and accuracy requirements of the light are used to determine the required intrinsic fundamental mode mode and its weight; and load the dynamic hologram containing each intrinsic fundamental mode to the spatial light modulator;
- the spatial light modulator 4 (SLM) is used to receive and modulate the laser light to obtain dynamically twisted partially coherent light.
- an amplitude filtering system is also included, which is used to filter the dynamically twisted partially coherent light emitted from the spatial light modulator, and only keep the first diffraction order.
- the amplitude filtering system is a 4f system, including a first lens 5, a diaphragm 6 and a second lens 7 arranged in sequence, and the dynamically distorted partially coherent light emitted from the spatial light modulator 4 passes through the first lens in sequence.
- a beam expander 3 is also included, disposed between the laser 1 and the spatial light modulator 4, for converting the laser light generated by the laser 1 into expanded beam collimated light.
- a reflective plane mirror 2 is also included, and the reflective plane mirror 2 is arranged between the laser 1 and the beam expander 3 to lengthen the optical path.
- the individual holograms of each intrinsic fundamental mode are arranged in sequence, and the display time is proportional to the corresponding weight, and the required intrinsic fundamental mode and the corresponding weight ratio are partially coherent according to the distortion to be generated
- the specific parameters of the light are determined. Such as beam waist, coherence length, twisted phase, etc.
- it also includes a charge-coupled device CCD8 and a second computer 10, the charge-coupled device CCD8 is connected to the second computer 10, the charge-coupled device CCD8 is used to receive the dynamically twisted partially coherent light, the The second computer 10 is used to calculate and verify whether the dynamically distorted partially coherent light is consistent with the theory.
- the preferred embodiment of the present invention also discloses a method for rapidly generating dynamically distorted partially coherent light based on mode decomposition, which is applied to the above-mentioned system for rapidly generating dynamically distorted partially coherent light based on mode decomposition, which includes the following steps:
- the first computer decomposes the twisted partially coherent light beam into a superposition form of weighted orthogonal complete intrinsic fundamental modes
- the first computer determines the mode of the required intrinsic fundamental mode and its requirements according to the superposition form of the intrinsic fundamental mode of the twisted partial coherent light decomposition, the specific parameter size of the twisted partial coherent light to be generated, and the accuracy requirements. weight size;
- the spatial light modulator receives the laser light generated by the laser, the first computer loads a dynamic hologram containing each intrinsic fundamental mode to the spatial light modulator, and uses the spatial light modulator to modulate the laser light, Get dynamically distorted partially coherent light.
- step S1 includes:
- the cross spectral density (CSD) of any beam that satisfies the nonnegative positive definiteness can be expressed as a nonnegative weight function ⁇ ( ⁇ ) and a mode function ⁇ ( ⁇ , ⁇ ) to the integral form of the parameter ⁇ :
- n represents the order of the mode
- ⁇ ( ⁇ , ⁇ n ) is the mode function
- ⁇ ( ⁇ n ) is the corresponding weight function
- ⁇ , ⁇ and ⁇ represent the beam waist width, coherence length and twist factor respectively, and f( ⁇ , ⁇ , ⁇ , ⁇ ′) represents the specific correlation structure of the corresponding twisted partially coherent light;
- step S2 includes:
- the CSD of the generated beam during the duration of a hologram of order n is The same is true for other modes.
- the CSD of the obtained beam can be expressed as:
- the method only needs to expand or reduce the mode range (increase or decrease the superposition mode) to realize the precise adjustment of the generated distorted partially coherent light. And because this method selects the mode according to the weight in the orthogonal complete base, the required mode is less, the experiment is generated faster, and it is only limited by the refresh frequency of the SLM; and there is no crossover between the pseudo mode and the random mode mode Associative term, experimentally generated beam stabilization.
- the second schematic diagram of the system for rapidly generating dynamically twisted partially coherent light based on mode decomposition in the preferred embodiment of the present invention which generates twisted Gaussian Schell mode (TGSM) beams based on eigenmode decomposition.
- TGSM twisted Gaussian Schell mode
- TGSM can be expressed as the weighted superposition of Laguerre Gaussian beams for the intrinsic fundamental mode, namely
- ⁇ , t, and w are parameters jointly determined by ⁇ , ⁇ , and ⁇ , respectively:
- the SLM model used is BQ-SLM1024, the number of pixels is 1024 ⁇ 768, and the pixel size is 18 ⁇ m ⁇ 18 ⁇ m.
- the beam expander with a wavelength of 632nm
- the direct light is incident on the SLM, and after passing through the amplitude filtering system composed of two lenses with a focal length of 15cm, different modes of Laguerre-Gauss Shell mode beams are generated on the rear focal plane of the amplitude filtering system.
- the Laguerre Gaussian of each mode generated by the experiment was received at the rear focal plane of the 4f system using a charge-coupled device CCD8
- the photo of the intensity of the light beam is used to verify whether the beam waist width and coherence length are consistent with the theoretical design; this embodiment adds a cylindrical mirror 11 with a focal length of 15 cm and a third lens with a focal length of 20 cm on the basis of the above embodiment 12. Verify twist factor against transmission rotation.
- the CCD model used is GS3-U3-28S5M-C with a pixel size of 1920 ⁇ 1440 and a pixel size of 4.54 ⁇ m.
- the beam waist width can be verified by the beam intensity. According to formula (7), the theoretical intensity distribution is uniquely determined by the beam waist width:
- the intensity distribution of the experiment is the weighted superposition of the intensity of each mode, that is, the superposition of the photo intensity received by the CCD:
- the coherence length can be represented by the weight spectrum, the intensity distribution of multiple photos, and the intensity of a certain point (the center point is selected), and the process is as follows:
- the coherence degree of the experimentally synthesized twisted partially coherent beam can be expressed as:
- the coherence length can be represented by weight spectrum, intensity distribution and central point intensity.
- the twisted phase is the only factor that causes the rotation of the beam transmission. Therefore, when the wavelength is constant, the twist factor corresponds to the transmission rotation.
- the twist factor corresponds to the transmission rotation.
- Fig. 3 is a diagram of the intensity, coherence distribution and fitting situation of the dynamically distorted partially coherent light generated in the theory and experiment of the system for quickly generating dynamically distorted partially coherent light based on mode decomposition in the preferred embodiment of the present invention; wherein, the first row and the second row are the intensity fitting and the coherence model fitting respectively, which verify that the beam waist width and coherence length of the experimentally generated beam are consistent with the theoretical design.
- Fig. 4 is a diagram of the transmission rotation of different distances of dynamically twisted partially coherent light generated in theory and experiments by the system for rapidly generating dynamically twisted partially coherent light based on mode decomposition in a preferred embodiment of the present invention.
- the first row and the second row are the theoretical and experimental results respectively, which verify that the distortion factor of the experimentally generated beam is consistent with the theoretical design.
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Abstract
本发明公开了一种基于模式分解快速产生动态扭曲部分相干光的系统及方法，该系统包括：激光器，用于产生激光；第一计算机，用于将扭曲部分相干光束分解为含权的正交完备的本征基模的叠加形式；并根据扭曲部分相干光分解的本征基模叠加形式、要产生的扭曲部分相干光的具体参数大小以及精确度的要求来确定所需要的本征基模的模式及其权重大小；并加载包含各个本征基模的动态全息图至空间光调制器；空间光调制器，用于接收激光并对激光进行调制，得到动态扭曲部分相干光。本发明需要的模式数少，产生光束耗时更短；只需要更改加载在空间光调制器中的全息图即可实现扭曲部分相干光束的动态调控；模式之间相互正交，不会产生额外的交叉项。
Description
本发明涉及光学技术领域，特别涉及一种基于模式分解快速产生动态扭曲部分相干光的系统及方法。
众所周知，相位是光场的一个重要调控参量。自1993年Simon等人提出扭曲相位后，人们通过模式分解、维格纳分布和张量表示等方法对扭曲部分相干光进行了大量的研究，证实了扭曲部分相干光在强度、相干度、偏振度和轨道角动量等性质上具有全新的统计特性，在光束整形、粒子捕获、提高成像分辨率和自由空间光通信等方面有广阔的应用前景。能够实际产生扭曲部分相干光是满足应用要求的基础前提，因此扭曲部分相干光的实际产生方法得到了一定程度的探索。
扭曲部分相干光不同于带有一般相位的光束，它的相位具有不可分离性，因此不能通过直接产生电场的方法来获得扭曲部分相干光，而需要通过获得其他易产生的光束进行转化或者叠加得到。光束转化为扭曲部分相干光的原理即先产生一个光源，然后经过一个光学系统将之转化为扭曲部分相干光。比较典型的一个实验是王海云等人根据Williamson定理，设计出了一个3柱面镜转化系统，将借助空间光调制器提前产生的各向异性高斯谢尔模光束转化为了扭曲高斯谢尔模光束，若需要产生不同参数的光，则需要调整对应的光源和转化系统。模式叠加方法的原理则是产生对应基模并进行含权叠加得到扭曲部分相干光，根据基模的形式可以分为本征模、伪模、随机模等叠加方法。比较典型的一个实验是Tian的伪模叠加方法实验，他们将扭曲高斯谢尔模光束分解为基模为伪模的含权叠加形式。实验中，空间光调制器加载对应全息图，通过叠加得到扭曲高斯谢尔模光束，随机相位起消除不需要的模式关联项的作用。相比于光束转化的方法，伪模叠加的方法优点在于不需要改变光学系统就能产生动态光束。
扭曲部分相干光已有的产生方法具有的耗时且不可调性等缺点，给光束的产生带来了较大的限制，很难满足扭曲部分相干光的实际使用要求，因此拥有一种能够快速产生动态可调的扭曲部分相干光的方法显得尤为重要。
目前，一共有三种产生扭曲部分相干光束的实验得到了报道。前两种方法基于Williamson定理，提前设计好合适的方差矩阵和传输矩阵，然后实验产生对应的初始光场和传输系统，得到所需光场；第三种方法基于模式分解，合成含权基模，得到光场。
第一种方法，是Friberg等人先通过一个声光偏转器以及滤波系统产生了各向异性高斯谢尔模型光束，再经过一个设计好的特殊位置摆放的由6个柱面镜组成的光学转换系统，最后转换为扭曲高斯谢尔模型光束；而后王海云等人在此理论和实验基础上进行了方法的改进，将扩束准直光照射在加载了全息图的空间光调制器上，直接产生各项异性高斯谢尔模光束且产生效果更好，并且设计了一个3柱面镜系统等效替代了原本的6柱面镜系统，最后实验产生了一个严格精确的扭曲高斯谢尔模型光束；第三种方法是Tian等人将扭曲高斯谢尔模型光束分解成了含权伪模的采样叠加形式，并通过给各模式引入随机相位的方法降低因模式之间的相关性所产生的额外的统计关联项，最终叠加得到了近似的扭曲高斯谢尔模型光束。
综上所述，基于Williamson定理的两种方法中，一组初始光源和光学转化系统只能产生对应参数的扭曲部分相干光，不满足产生光束动态可调的实际使用要求。基于模式分解的方法中则需要大量引入随机相位的全息图，无法较快产生所需的图片。
发明内容
本发明要解决的技术问题是提供一种简单可行、需要模式数少、产生光束耗时短的基于模式分解快速产生动态扭曲部分相干光的系统及方法。
为了解决上述问题，本发明提供了一种基于模式分解快速产生动态扭曲部分相干光的系统，其包括：
激光器，用于产生激光；
第一计算机，用于将扭曲部分相干光束分解为含权的正交完备的本征基模 的叠加形式；并根据扭曲部分相干光分解的本征基模叠加形式、要产生的扭曲部分相干光的具体参数大小以及精确度的要求来确定所需要的本征基模的模式及其权重大小；并加载包含各个本征基模的动态全息图至空间光调制器；
空间光调制器，用于接收激光并对激光进行调制，得到动态扭曲部分相干光。
作为本发明的进一步改进，还包括振幅过滤系统，用于对从所述空间光调制器出射的动态扭曲部分相干光进行过滤，只保留第一衍射级。
作为本发明的进一步改进，所述振幅过滤系统为4f系统，包括依次设置的第一透镜、光阑和第二透镜，从所述空间光调制器出射的动态扭曲部分相干光依次经过所述第一透镜、光阑和第二透镜。
作为本发明的进一步改进，在所述动态全息图中，各个本征基模的单个全息图按序排列，且显示时间与对应的权重成比例，所需要的本征基模及对应的权重比根据要产生的扭曲部分相干光的具体参数来确定。
作为本发明的进一步改进，还包括电荷耦合元件CCD和第二计算机，所述电荷耦合元件CCD和第二计算机连接，所述电荷耦合元件CCD用于接收所述动态扭曲部分相干光，所述第二计算机用于计算并验证所述动态扭曲部分相干光是否与理论一致。
作为本发明的进一步改进，还包括扩束镜，设置于所述激光器和空间光调制器之间，用于将所述激光器产生的激光变成扩束准直光。
作为本发明的进一步改进，还包括反射平面镜，所述反射平面镜设置于所述激光器和扩束镜之间，用于加长光路。
本发明还提供了一种基于模式分解快速产生动态扭曲部分相干光的方法，应用于如上述任一所述的基于模式分解快速产生动态扭曲部分相干光的系统，其包括以下步骤：
S1、所述第一计算机将扭曲部分相干光束分解为含权的正交完备的本征基模的叠加形式；
S2、所述第一计算机根据扭曲部分相干光分解的本征基模叠加形式、要产生的扭曲部分相干光的具体参数大小以及精确度的要求来确定所需要的本征基 模的模式及其权重大小；
S2、所述空间光调制器接收所述激光器产生的激光，所述第一计算机加载包含各个本征基模的动态全息图至空间光调制器，利用所述空间光调制器对激光进行调制，得到动态扭曲部分相干光。
作为本发明的进一步改进，步骤S1包括：
S11、根据模式分解理论以及交叉谱密度函数构建方法，任意满足非负正定性的光束的交叉谱密度可以表示为非负权重函数λ(ν)和模式函数Φ(ρ,ν)对参量ν的积分形式：
W(ρ,ρ′)＝∫λ(ν)Φ*(ρ,ν)Φ(ρ′,ν)d
2v (1)
S12、将λ(ν)视为一组由带有正系数的狄拉克函数组成，即：
将式(2)的连续积分形式表示为模式的离散叠加形式：
其中，n代表模式的阶数，Φ(ρ,ν
n)是模式函数，λ(ν
n)是对应的权重函数；
S13、将扭曲部分相干光的交叉谱密度表示为：
W(ρ,ρ′)＝Aexp[f(σ,δ,ρ,ρ′)-ikμ(ρ×ρ′)
⊥] (4)
其中，σ、δ和μ分别表示束腰宽度、相干长度和扭曲因子，f(σ,δ,ρ,ρ′)表示对应扭曲部分相干光的具体关联结构；
S14、当f(σ,δ,ρ,ρ′)确定时，结合式(3)和式(4)，确定满足正交完备性的模式函数Φ(ρ,ν
n)及其权重函数λ(ν
n)的具体形式，将对应的扭曲部分相干光进行本征模式分解，表示为：
作为本发明的进一步改进，步骤S2包括：
S21、给定一个模式范围；
S22、在给定的范围中根据式(5)中确定的权重函数计算各本征基模的权重值，同时进行归一化得到归一化权重值分布，按从大到小的顺序排列作为选取模式的优先级；
S23、根据精度要求确定一个归一化权重值的标准，与上一步确定的优先级结合，选取归一化权重值在该标准上的本征基模，由此确定具体需要的本征基模及其权重。
本发明的有益效果：
本发明基于模式分解快速产生动态扭曲部分相干光的系统及方法基于比例确定的权重大小选取模式，需要的模式数少，产生光束耗时更短；只需要更改加载在空间光调制器中的全息图，就可以实现扭曲部分相干光束的动态调控；模式之间相互正交，不会产生额外的交叉项。
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基于模式分解快速产生动态扭曲部分相干光的系统的示意图一；
图2是本发明优选实施例中基于模式分解快速产生动态扭曲部分相干光的系统的示意图二；
图3是本发明优选实施例中基于模式分解快速产生动态扭曲部分相干光的系统在理论和实验中产生的动态扭曲部分相干光的强度、相干度分布及拟合情况图；
图4是本发明优选实施例中基于模式分解快速产生动态扭曲部分相干光的系统在理论和实验中产生的动态扭曲部分相干光的不同距离的传输旋转情况图。
标记说明：1、激光器；2、反射平面镜；3、扩束镜；4、空间光调制器；5、第一透镜；6、光阑；7、第二透镜；8、电荷耦合器件CCD；9、第一计算机； 10、第二计算机；11、柱透镜；12、第三透镜。
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，本发明优选实施例中的基于模式分解快速产生动态扭曲部分相干光的系统的示意图一，该系统包括：
激光器1，用于产生激光；可选的，激光器1为氦氖激光器。
第一计算机9，用于将扭曲部分相干光束分解为含权的正交完备的本征基模的叠加形式；并根据扭曲部分相干光分解的本征基模叠加形式、要产生的扭曲部分相干光的具体参数大小以及精确度的要求来确定所需要的本征基模的模式及其权重大小；并加载包含各个本征基模的动态全息图至空间光调制器；
空间光调制器4(SLM)，用于接收激光并对激光进行调制，得到动态扭曲部分相干光。
进一步地，还包括振幅过滤系统，用于对从所述空间光调制器出射的动态扭曲部分相干光进行过滤，只保留第一衍射级。
具体地，所述振幅过滤系统为4f系统，包括依次设置的第一透镜5、光阑6和第二透镜7，从所述空间光调制器4出射的动态扭曲部分相干光依次经过所述第一透镜5、光阑6和第二透镜7。光束经过4f系统后得到翻转平移的本征模光束，经过叠加合成得到所需的扭曲部分相干光。
在一些实施例中，还包括扩束镜3，设置于激光器1和空间光调制器4之间，用于将激光器1产生的激光变成扩束准直光。
可选地，还包括反射平面镜2，反射平面镜2设置于激光器1和扩束镜3之间，用于加长光路。
在所述动态全息图中，各个本征基模的单个全息图按序排列，且显示时间与对应的权重成比例，所需要的本征基模及对应的权重比根据要产生的扭曲部分相干光的具体参数来确定。如束腰、相干长度、扭曲相位等。
在一些实施例中，还包括电荷耦合元件CCD8和第二计算机10，所述电荷 耦合元件CCD8和第二计算机10连接，所述电荷耦合元件CCD8用于接收所述动态扭曲部分相干光，所述第二计算机10用于计算并验证所述动态扭曲部分相干光是否与理论一致。
本发明优选实施例还公开了一种基于模式分解快速产生动态扭曲部分相干光的方法，应用于上述基于模式分解快速产生动态扭曲部分相干光的系统，其包括以下步骤：
S1、所述第一计算机将扭曲部分相干光束分解为含权的正交完备的本征基模的叠加形式；
S2、所述第一计算机根据扭曲部分相干光分解的本征基模叠加形式、要产生的扭曲部分相干光的具体参数大小以及精确度的要求来确定所需要的本征基模的模式及其权重大小；
S2、所述空间光调制器接收所述激光器产生的激光，所述第一计算机加载包含各个本征基模的动态全息图至空间光调制器，利用所述空间光调制器对激光进行调制，得到动态扭曲部分相干光。
进一步地，步骤S1包括：
S11、根据模式分解理论以及Gori等人提出的交叉谱密度函数构建方法，任意满足非负正定性的光束的交叉谱密度(CSD)可以表示为非负权重函数λ(ν)和模式函数Φ(ρ,ν)对参量ν的积分形式：
W(ρ,ρ′)＝∫λ(ν)Φ*(ρ,ν)Φ(ρ′,ν)d
2v (1)
S12、将λ(ν)视为一组由带有正系数的狄拉克函数组成，即：
将式(2)的连续积分形式表示为模式的离散叠加形式：
其中，n代表模式的阶数，Φ(ρ,ν
n)是模式函数，λ(ν
n)是对应的权重函数；
S13、将扭曲部分相干光的交叉谱密度表示为：
W(ρ,ρ′)＝Aexp[f(σ,δ,ρ,ρ′)-ikμ(ρ×ρ′)
⊥] (4)
其中，σ、δ和μ分别表示束腰宽度、相干长度和扭曲因子，f(σ,δ,ρ,ρ′)表示对应扭曲部分相干光的具体关联结构；
S14、当f(σ,δ,ρ,ρ′)确定时，结合式(3)和式(4)，确定满足正交完备性的模式函数Φ(ρ,ν
n)及其权重函数λ(ν
n)的具体形式，将对应的扭曲部分相干光进行本征模式分解，表示为：
进一步地，步骤S2包括：
S21、给定一个模式范围；其中，虽然无法取遍所有的模式，但是可以给定一个的模式范围，若继续扩大该范围，强度几乎不会发生变化，则可以认为已经取到所需要的模式。
S22、在给定的范围中根据式(5)中确定的权重函数计算各本征基模的权重值，同时进行归一化得到归一化权重值分布，按从大到小的顺序排列作为选取模式的优先级；使得只需要更少的模式数就能产生同等精确度的扭曲部分相干光。
S23、根据精度要求确定一个归一化权重值的标准，与上一步确定的优先级结合，选取归一化权重值在该标准上的本征基模，由此确定具体需要的本征基模及其权重。
由于扭曲部分相干光束的交叉谱密度可以表示式(5)，激光经过空间光调制器4后同时刻产生了加载的全息图对应的本征基模Φ
n
*(ρ)Φ
n(ρ′)，由于其播放时间与权重成比例，故在阶数n的全息图的持续时间段内，产生的光束的CSD为
其他模式同理，当整个动态全息图播放一轮，得到的光束的CSD可以表示为：
即为所需要的扭曲部分相干光束的近似。
如果需要产生不同参数的扭曲部分相干光束，如束腰宽度、相干长度和扭曲因子等，只要通过计算好所需的模式及其权重，就能在仅仅改变加载的动态 全息图而不改变光学系统的情况下实现扭曲部分相干光束的动态产生。同时该方法只需要扩大或缩小模式范围(增加或减少叠加模式)就能对产生的扭曲部分相干光实现精确度的调整。且由于该方法是在正交完备基中按照权重大小来选取模式的，需要的模式少，实验产生更快速，仅仅受限于SLM的刷新频率；且没有伪模及随机模模式之间的交叉关联项，实验产生的光束稳定。
如图2所示，本发明优选实施例中的基于模式分解快速产生动态扭曲部分相干光的系统的示意图二，其基于本征模分解形式产生扭曲高斯谢尔模(TGSM)光束。
根据上式(6)以及扭曲TGSM的CSD解析式：
可以将TGSM表示为本征基模为拉盖尔高斯光束的含权叠加，即
其中ξ、t、w分别是由σ、δ和μ共同确定的参数：
且a＝1/(4σ
2),b＝1/(2δ
2),u＝kμ。
根据式(8)、(9)、(10)可知，可以用不同含权的拉盖尔模式组叠加产生不同参数的TGSM光束，我们选取要产生的TGSM光束参数为：σ＝0.5mm,δ＝0.28mm,μ＝0.001mm
-1。根据式(9)中的
和式(10)，可以得到各模式的归一化本征值谱
选取了一个标准值为0.01。归一化本征值大于该标准的模式选用，小于该标准的模式忽略，最终确定的模式为：阶数n＝0，拓扑核数为m＝-2～25；n＝1，m＝0～11，一共40个模式。
根据确定的模式及其权重使用Matlab运行出动态全息图，动态全息图中各模式全息图按照n＝0，m＝-2～25；n＝1，m＝0～11的顺序排列，且播放时间与权重成比例，将动态全息图加载到SLM上，使用的SLM型号是BQ-SLM1024，像素数为1024×768，像素大小为18μm×18μm，在图2中将波长为632nm的扩束准直光入射到SLM上，再经过两个焦距为15cm的透镜组成的振幅过滤系统后，在振幅过滤系统后焦面产生不同模式的拉盖尔高斯谢尔模光束。
为了验证实验产生的光束是σ＝0.5mm,δ＝0.28mm,μ＝0.001mm
-1的TGSM光束，使用电荷耦合器件CCD8在4f系统后焦面接收了实验产生的各模式的拉盖尔高斯光束的强度照片，用于验证束腰宽度和相干长度和理论设计是否一致；该实施例在上述实施例的基础上加上了一个焦距为15cm的柱面镜11和焦距为20cm的第三透镜12，根据传输旋转情况验证扭曲因子。使用的CCD型号是GS3-U3-28S5M-C，像素为1920×1440，像素大小为4.54μm。
其中束腰宽度可以由光束的强度来验证，根据式(7)，理论的强度分布均由束腰宽度唯一确定：
根据式(8)，实验的强度分布为各个模式强度的含权叠加，亦即CCD接收照片强度的叠加：
相干长度可以由权重谱、多张照片的强度分布以及某一点强度(选取了中心点)来表示，其过程如下：
根据式(7)可得，中心点与其他点的理论相干度分布可以由相干长度唯一确 定：
而根据式(8)，实验合成的扭曲部分相干光束的相干度可以表示为：
而由于本征模式之间相互正交，故可以简化为：
即相干长度可以由权重谱、强度分布以及中心点强度来表示。
扭曲相位是造成光束传输旋转的唯一因素，因此在波长一定的情况下，扭曲因子和传输旋转情况一一对应，根据TGSM光束的张量传输定律，我们用Matlab模拟了TGSM光束在图二中的理论传输旋转情况，并和实验旋转结果进行了拟合。
图3是本发明优选实施例中基于模式分解快速产生动态扭曲部分相干光的系统在理论和实验中产生的动态扭曲部分相干光的强度、相干度分布及拟合情况图；其中，第一行及第二行分别是强度拟合和相干度的模方拟合，验证了实验产生光束的束腰宽度及相干长度和理论设计一致。
图4是本发明优选实施例中基于模式分解快速产生动态扭曲部分相干光的系统在理论和实验中产生的动态扭曲部分相干光的不同距离的传输旋转情况图。其中，第一行和第二行分别是理论和实验的结果，验证了实验产生光束的扭曲因子和理论设计一致。
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)
- 基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，包括：激光器，用于产生激光；第一计算机，用于将扭曲部分相干光束分解为含权的正交完备的本征基模的叠加形式；并根据扭曲部分相干光分解的本征基模叠加形式、要产生的扭曲部分相干光的具体参数大小以及精确度的要求来确定所需要的本征基模的模式及其权重大小；并加载包含各个本征基模的动态全息图至空间光调制器；空间光调制器，用于接收激光并对激光进行调制，得到动态扭曲部分相干光。
- 如权利要求1所述的基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，还包括振幅过滤系统，用于对从所述空间光调制器出射的动态扭曲部分相干光进行过滤，只保留第一衍射级。
- 如权利要求2所述的基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，所述振幅过滤系统为4f系统，包括依次设置的第一透镜、光阑和第二透镜，从所述空间光调制器出射的动态扭曲部分相干光依次经过所述第一透镜、光阑和第二透镜。
- 如权利要求1所述的基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，在所述动态全息图中，各个本征基模的单个全息图按序排列，且显示时间与对应的权重成比例，所需要的本征基模及对应的权重比根据要产生的扭曲部分相干光的具体参数来确定。
- 如权利要求1所述的基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，还包括电荷耦合元件CCD和第二计算机，所述电荷耦合元件CCD和第二计算机连接，所述电荷耦合元件CCD用于接收所述动态扭曲部分相干光，所述第二计算机用于计算并验证所述动态扭曲部分相干光是否与理论一致。
- 如权利要求1所述的基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，还包括扩束镜，设置于所述激光器和空间光调制器之间，用于将所述激光器产生的激光变成扩束准直光。
- 如权利要求6所述的基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，还包括反射平面镜，所述反射平面镜设置于所述激光器和扩束镜之间，用于加长光路。
- 基于模式分解快速产生动态扭曲部分相干光的方法，应用于如权利要求1-7任一所述的基于模式分解快速产生动态扭曲部分相干光的系统，其特征在于，包括以下步骤：S1、所述第一计算机将扭曲部分相干光束分解为含权的正交完备的本征基模的叠加形式；S2、所述第一计算机根据扭曲部分相干光分解的本征基模叠加形式、要产生的扭曲部分相干光的具体参数大小以及精确度的要求来确定所需要的本征基模的模式及其权重大小；S2、所述空间光调制器接收所述激光器产生的激光，所述第一计算机加载包含各个本征基模的动态全息图至空间光调制器，利用所述空间光调制器对激光进行调制，得到动态扭曲部分相干光。
- 如权利要求8所述的基于模式分解快速产生动态扭曲部分相干光的方法，其特征在于，步骤S1包括：S11、根据模式分解理论以及交叉谱密度函数构建方法，任意满足非负正定性的光束的交叉谱密度可以表示为非负权重函数λ(ν)和模式函数Φ(ρ,ν)对参量ν的积分形式：W(ρ,ρ′)＝∫λ(ν)Φ *(ρ,ν)Φ(ρ′,ν)d 2v (1)S12、将λ(ν)视为一组由带有正系数的狄拉克函数组成，即：
将式(2)的连续积分形式表示为模式的离散叠加形式：
其中，n代表模式的阶数，Φ(ρ,ν n)是模式函数，λ(ν n)是对应的权重函数；S13、将扭曲部分相干光的交叉谱密度表示为：W(ρ,ρ′)＝Aexp[f(σ,δ,ρ,ρ′)-ikμ(ρ×ρ′) ⊥] (4)其中，σ、δ和μ分别表示束腰宽度、相干长度和扭曲因子，f(σ,δ,ρ,ρ′)表示对应扭曲部分相干光的具体关联结构；S14、当f(σ,δ,ρ,ρ′)确定时，结合式(3)和式(4)，确定满足正交完备性的模式函数Φ(ρ,ν n)及其权重函数λ(ν n)的具体形式，将对应的扭曲部分相干光进行本征模式分解，表示为：
- 如权利要求9所述的基于模式分解快速产生动态扭曲部分相干光的方法，其特征在于，步骤S2包括：S21、给定一个模式范围；S22、在给定的范围中根据式(5)中确定的权重函数计算各本征基模的权重值，同时进行归一化得到归一化权重值分布，按从大到小的顺序排列作为选取模式的优先级；S23、根据精度要求确定一个归一化权重值的标准，与上一步确定的优先级结合，选取归一化权重值在该标准上的本征基模，由此确定具体需要的本征基模及其权重。
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