CN105607276A - Novel ideal aspheric collimation system of semiconductor laser - Google Patents
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Abstract
本发明属于光通信技术领域,具体为一种半导体激光器的新型理想非球面准直系统。该光学系统由理想非球面准直平凸透镜和三棱镜组两部分构成,设计方法基于三维矢量折射理论。理想非球面准直平凸透镜将半导体激光器出射的非对称发散角特性的激光束准直为高精度准直激光束,理论上可突破衍射极限。应用于半导体激光器发射源有象散的情况,所产生的发散角明显优于传统的旋转双曲面准直平凸透镜的准直效果。再利用三棱镜组将椭圆横截面的高精度准直光束整形为横截面为圆形的高精度准直光束。本发明有助于在半导体激光器发射源有象散的情况下提高光通信系统中的发射精度。
The invention belongs to the technical field of optical communication, in particular to a novel ideal aspheric collimation system of a semiconductor laser. The optical system is composed of ideal aspheric collimating plano-convex lens and triangular prism group, and the design method is based on three-dimensional vector refraction theory. The ideal aspheric collimating plano-convex lens collimates the laser beam with asymmetric divergence angle characteristics emitted by the semiconductor laser into a high-precision collimated laser beam, which can theoretically break through the diffraction limit. Applied to the situation where the semiconductor laser emission source has astigmatism, the divergence angle produced is obviously better than the collimation effect of the traditional rotating hyperboloid collimating plano-convex lens. Then the triangular prism group is used to shape the high-precision collimated light beam with an elliptical cross-section into a high-precision collimated light beam with a circular cross-section. The invention helps to improve the emission accuracy in the optical communication system under the condition that the semiconductor laser emission source has astigmatism.
Description
技术领域technical field
本发明属于光通信技术领域,具体为一种半导体激光器出射光束的新型理想非球面准直光学系统,产生高精度准直激光束。The invention belongs to the technical field of optical communication, in particular to a novel ideal aspheric collimating optical system for emitting light beams from semiconductor lasers, which can generate high-precision collimating laser beams.
背景技术Background technique
随着科学技术的发展,人们对通信容量的需求越来越高。光通信具有微小的光束发散角和高的方向性(因而具有较高的军事保密性)、速率高、传输容量大(比微波通信高3~5个数量级)、重量轻等优点,已逐渐成为国际化的研究热点。光学天线作为光通信技术领域的关键性发射部件存在高精度准直与整形两个关键技术问题。因此高精度预准直与整形技术是确保实现远距离空间激光通信的关键技术,也是提高捕获、对准与跟踪(APT)精度的重要保证。With the development of science and technology, people's demand for communication capacity is getting higher and higher. Optical communication has the advantages of small beam divergence angle and high directivity (thus having high military confidentiality), high speed, large transmission capacity (3 to 5 orders of magnitude higher than microwave communication), light weight, etc., and has gradually become a International research hotspots. As a key transmitting component in the field of optical communication technology, the optical antenna has two key technical problems of high-precision collimation and shaping. Therefore, high-precision pre-collimation and shaping technology is the key technology to ensure the realization of long-distance space laser communication, and it is also an important guarantee to improve the accuracy of acquisition, alignment and tracking (APT).
半导体激光器是光通信系统普遍使用的激光源,其有源区类似于一个矩形平面介质波导,在传播时容易发散,其出射光束横截面具有椭圆形状,如图1(a)所示。半导体激光器在垂直于结平面(即子午平面)的典型发散角(半角)一般在0~30度范围内变化,平行于结平面(弧矢平面)方向上的发散角在0~10度范围内变化。发散角越小,方向性越好。另外,半导体激光器在子午平面内的发光源与弧矢平面内的发光源并不重合,在光轴方向存在一定的距离(Δl),称为象散。非对称发散角特性和象散的存在势必对半导体激光器出射光束的质量与光学系统的传输效率产生影响。为了使半导体激光器输出的高斯光束能够高质量、高效率地传输进入光学天线,需要对半导体激光器的输出光束进行准直与整形,压缩光束发散角以改善远场对称性和光斑形状,减小象散对光束质量的影响,提高光通信系统中发射天线的发射精度。因此对半导体激光器出射光束进行高精度准直与整形对于远距离激光通信系统具有重要的意义。Semiconductor laser is a laser source commonly used in optical communication systems. Its active region is similar to a rectangular planar dielectric waveguide, and it is easy to diverge during propagation. The cross-section of its outgoing beam has an elliptical shape, as shown in Figure 1(a). The typical divergence angle (half angle) of semiconductor lasers perpendicular to the junction plane (ie, the meridian plane) generally varies in the range of 0 to 30 degrees, and the divergence angle in the direction parallel to the junction plane (sagittal plane) is in the range of 0 to 10 degrees. Variety. The smaller the divergence angle, the better the directionality. In addition, the light source of the semiconductor laser in the meridian plane does not coincide with the light source in the sagittal plane, and there is a certain distance (Δl) in the direction of the optical axis, which is called astigmatism. The existence of asymmetrical divergence angle characteristics and astigmatism will inevitably affect the quality of the outgoing beam of the semiconductor laser and the transmission efficiency of the optical system. In order to transmit the Gaussian beam output by the semiconductor laser into the optical antenna with high quality and high efficiency, it is necessary to collimate and shape the output beam of the semiconductor laser, compress the beam divergence angle to improve the far-field symmetry and spot shape, and reduce image distortion. The effect of dispersion on the beam quality can be improved, and the transmission accuracy of the transmitting antenna in the optical communication system can be improved. Therefore, high-precision collimation and shaping of the beam emitted by the semiconductor laser is of great significance for long-distance laser communication systems.
2000年牛津大学在“Nature”杂志上报到了用三维全息法制作可见光的光子晶体,其自准直特性可以突破光的衍射极限。2012年,中科院半导体所郑婉华研究组在传统半导体激光器谐振腔结构中引入光子晶体,调控激光振荡模式,从芯片层次改善激光的输出光束质量,首次在国际上研制出905nm波段的高光束质量光子晶体激光器,激光输出远场呈近圆斑分布,垂直(快轴)发散角6.5°,水平(慢轴)发散角7.1°。2013年,济南大学的师生在“OpticsLetter”上发表了在光纤端面制作双轴双曲面微透镜将半导体激光器的快、慢轴发散角分别压缩至6.9°和32.3mrad,耦合至光纤中,耦合效率提高至80%。上述半导体激光器预准直方法所采用的光学系统,任不能从根本上改变半导体激光器非对称发散角特性与象散对光传输的影响,从而一定程度限制了光学天线的发射精度和传输效率。In 2000, Oxford University reported in the "Nature" magazine that it used three-dimensional holography to make visible light photonic crystals, and its self-collimation characteristics can break through the diffraction limit of light. In 2012, Zheng Wanhua's research group at the Institute of Semiconductors, Chinese Academy of Sciences introduced photonic crystals into the traditional semiconductor laser resonator structure to regulate the laser oscillation mode and improve the output beam quality of the laser from the chip level. For the first time, a photonic crystal with high beam quality in the 905nm band was developed internationally. Laser, the laser output far field is distributed in a near circular spot, the vertical (fast axis) divergence angle is 6.5°, and the horizontal (slow axis) divergence angle is 7.1°. In 2013, the teachers and students of Jinan University published on "Optics Letter" that a biaxial hyperboloid microlens was fabricated on the fiber end face to compress the fast and slow axis divergence angles of the semiconductor laser to 6.9° and 32.3 mrad respectively, and couple them into the fiber. Efficiency increased to 80%. The optical system used in the above semiconductor laser pre-collimation method cannot fundamentally change the influence of semiconductor laser asymmetric divergence angle characteristics and astigmatism on optical transmission, thus limiting the emission accuracy and transmission efficiency of the optical antenna to a certain extent.
发明内容Contents of the invention
本发明针对现有技术存在的不足,提出一种产生高精度准直的激光束的新方法,利用理想非球面准直平凸透镜将半导体出射的非对称发散角激光束准直为高精度准直激光束,再利用三棱镜组对椭圆截面准直光束进行整形,实现半导体激光束到光学天线的高效耦合。准直发散角接近衍射极限的激光传输,有效确保远距离空间光通信的实现。Aiming at the deficiencies in the prior art, the present invention proposes a new method for producing high-precision collimated laser beams, using an ideal aspheric collimator plano-convex lens to collimate the asymmetric divergence angle laser beams emitted by the semiconductor into high-precision collimation The laser beam is then shaped by a triangular prism group to shape the collimated beam with an elliptical cross-section to realize efficient coupling of the semiconductor laser beam to the optical antenna. The transmission of laser beams with collimated divergence angles close to the diffraction limit effectively ensures the realization of long-distance space optical communication.
本发明采用的技术方案可分如下两方面概括:一方面,理想非球面准直平凸透镜对半导体激光器出射的非对称发散角高斯光束的高精度准直;另一方面,三棱镜组将光束进一步整形为圆形截面高斯光束。该系统应用于光通信系统中的卡塞格伦天线,可有效提高光通信系统中发射天线的发射精度和传输效率。The technical scheme adopted by the present invention can be summarized in the following two aspects: on the one hand, the ideal aspheric collimating plano-convex lens can collimate the asymmetric divergence angle Gaussian beam emitted by the semiconductor laser with high precision; on the other hand, the triangular prism group can further shape the beam is a Gaussian beam of circular cross-section. The system is applied to the Cassegrain antenna in the optical communication system, which can effectively improve the emission accuracy and transmission efficiency of the transmitting antenna in the optical communication system.
本发明中的理想非球面准直平凸透镜,位于其左方焦点处的点光源所发出的光经过该透镜后,出射光束与光轴之间的发散角接近于零度,为高精度准直的平行光束,该平行光束理论上可突破衍射极限。In the ideal aspheric collimating plano-convex lens in the present invention, after the light emitted by the point light source at its left focal point passes through the lens, the divergence angle between the outgoing beam and the optical axis is close to zero, which is a high-precision collimation Parallel beams, which can theoretically break through the diffraction limit.
本发明中的理想非球面准直平凸透镜,偏离其左方焦点一定距离处的点光源(象散光源)所发出的光经过该透镜后,出射光束与光轴之间的发散角优于相同参数(焦距、中心厚度、折射率)情况下的旋转双曲面平凸透镜的准直发散角。因此本发明中的理想非球面准直平凸透镜对具有一定象散的半导体激光器出射光束具有较好的准直效果。In the ideal aspheric collimating plano-convex lens in the present invention, after the light emitted by the point light source (astigmatic light source) at a certain distance away from its left focus passes through the lens, the divergence angle between the outgoing light beam and the optical axis is better than the same The collimating divergence angle of a hyperbolic plano-convex lens of revolution for the parameters (focal length, central thickness, refractive index). Therefore, the ideal aspheric collimating plano-convex lens in the present invention has a better collimating effect on the outgoing beam of the semiconductor laser with certain astigmatism.
本发明中的三棱镜组对经理想非球面准直平凸透镜准直后的椭圆截面的平行光束的短轴进行扩束或对长轴进行压缩,通过改变三棱镜的顶角对光束的压缩(或放大)倍数进行控制,即可实现各种需要的压缩倍数,从而实现椭圆截面的准直光束整形为圆形截面的准直光束。The triangular prism group in the present invention expands the short axis of the parallel light beam of the elliptical cross-section after the ideal aspherical collimating plano-convex lens collimates or compresses the long axis, and compresses (or enlarges) the light beam by changing the apex angle of the triangular prism ) multiples can be controlled to achieve various required compression multiples, so that the collimated beam with an elliptical cross-section can be shaped into a collimated beam with a circular cross-section.
本发明中的光学准直与整形光学系统的设计是基于矢量折射定理,建立三维折射面与矢量光线模型,利用MATLAB程序对光学系统结构进行最优设计,对光线在天线中的空间传输进行三维追迹,获得像质评价参数。具体包括:1)出射光束发散角,即光束发散角与光束空间位置的三维分布;2)点列图,即接收平面的光斑分布;3)能量均匀度,即接收平面的三维能量分布曲面等。The design of optical collimation and shaping optical system in the present invention is based on vector refraction theorem, establishes three-dimensional refraction surface and vector light model, utilizes MATLAB program to carry out optimal design to optical system structure, carries out three-dimensional to the space transmission of light in antenna Tracing to obtain image quality evaluation parameters. It specifically includes: 1) the divergence angle of the outgoing beam, that is, the three-dimensional distribution of the beam divergence angle and the spatial position of the beam; 2) the spot diagram, that is, the spot distribution on the receiving plane; 3) the energy uniformity, that is, the three-dimensional energy distribution surface on the receiving plane, etc. .
附图说明Description of drawings
图1为半导体激光器的出射光束发散特性与象散特性示意图。FIG. 1 is a schematic diagram of the divergence and astigmatism characteristics of an outgoing beam of a semiconductor laser.
图2为本发明一种实施例的半导体激光器的理想非球面准直平凸透镜和三棱镜组的结构框图。Fig. 2 is a structural block diagram of an ideal aspheric collimating plano-convex lens and a triangular prism group of a semiconductor laser according to an embodiment of the present invention.
图3为本发明一种实施例的半导体激光器的理想非球面准直平凸透镜和三棱镜组的装配示意图。Fig. 3 is an assembly diagram of an ideal aspheric collimating plano-convex lens and a triangular prism group of a semiconductor laser according to an embodiment of the present invention.
图4为本发明一种实施例的点源出射光束经理想非球面准直平凸透镜的光路图。Fig. 4 is an optical path diagram of an ideal aspheric collimating plano-convex lens for a point source outgoing light beam according to an embodiment of the present invention.
图5为本发明一种实施例的象散光源出射光束经理想非球面准直平凸透镜的光路图。Fig. 5 is an optical path diagram of an ideal aspheric collimating plano-convex lens for the output beam of an astigmatic light source according to an embodiment of the present invention.
图6为本发明一种实施例中作为对比的旋转双曲面准直平凸透镜对象散光准直的光路图。Fig. 6 is an optical path diagram of astigmatism collimation of a rotating hyperboloid collimating plano-convex lens object as a comparison in an embodiment of the present invention.
图7为本发明一种实施例中象散光源情况下的理想非球面准直平凸透镜发散角与旋转双曲面准直平凸透镜发散角对比的仿真图。Fig. 7 is a simulation diagram comparing the divergence angle of the ideal aspheric collimating plano-convex lens and the divergence angle of the rotating hyperboloid collimating plano-convex lens under the condition of an astigmatic light source in an embodiment of the present invention.
图8为本发明一种实施例的三棱镜组整形光路图。Fig. 8 is an optical path diagram of a triangular prism group shaping according to an embodiment of the present invention.
具体实施方式detailed description
下面结合附图和实施例进一步阐述和说明本发明。The present invention will be further elaborated and illustrated below in conjunction with the accompanying drawings and embodiments.
图1所示,为半导体激光器的出射光束发散特性与象散特性示意图。半导体激光器出射光束具有非对称发散角特性,在子午平面内的发散角(半角)一般在0°~30°范围内变化,在弧矢平面内的发散角在0°~10°范围内变化。并且在子午平面内的发光源与弧矢平面内的发光源并不相交于同一点,在光轴方向存在一定的象散Δl),势必影响半导体激光束在光学系统中的传输效率,需要对其进行高精度的准直与整形。FIG. 1 is a schematic diagram of the divergence characteristics and astigmatism characteristics of an outgoing beam of a semiconductor laser. The output beam of a semiconductor laser has an asymmetric divergence angle characteristic. The divergence angle (half angle) in the meridian plane generally changes in the range of 0° to 30°, and the divergence angle in the sagittal plane changes in the range of 0° to 10°. Moreover, the light source in the meridian plane and the light source in the sagittal plane do not intersect at the same point, and there is a certain astigmatism Δl) in the direction of the optical axis, which will inevitably affect the transmission efficiency of the semiconductor laser beam in the optical system. It performs high-precision collimation and shaping.
图2所示,为本发明一种实施例的半导体激光器的理想非球面准直平凸透镜和三棱镜组的结构框图。主要由一个理想非球面准直平凸透镜和三棱镜组构成。理想非球面准直平凸透镜对半导体激光器出射的非对称发散角高斯光束的高精度准直;三棱镜组将椭圆截面的准直光束进一步整形为圆形截面的准直光束。其中理想非球面准直平凸透镜和三棱镜组是本发明具体设计的内容。FIG. 2 is a structural block diagram of an ideal aspheric collimating plano-convex lens and a triangular prism group of a semiconductor laser according to an embodiment of the present invention. It is mainly composed of an ideal aspheric collimating plano-convex lens and a triangular prism group. The ideal aspheric collimating plano-convex lens can collimate the asymmetric divergence angle Gaussian beam emitted by the semiconductor laser with high precision; the triangular prism group further shapes the collimated beam with an elliptical cross-section into a collimated beam with a circular cross-section. Among them, the ideal aspheric collimating plano-convex lens and the triangular prism group are the content of the specific design of the present invention.
图3所示,为本发明一种实施例的半导体激光器的理想非球面准直平凸透镜和三棱镜组的装配示意图。理想非球面准直平凸透镜与半导体激光器出射端面集成在一起,将半导体激光器出射的非对称发散角高斯光束准直为椭圆截面的准直高斯光束。在光路中加入三棱镜组,对椭圆截面的平行光束的长轴进行压缩,使出射光束为圆形截面的高精度准直高斯光束。FIG. 3 is a schematic diagram of the assembly of an ideal aspheric collimating plano-convex lens and a triangular prism group of a semiconductor laser according to an embodiment of the present invention. The ideal aspheric collimating plano-convex lens is integrated with the exit end face of the semiconductor laser to collimate the Gaussian beam with asymmetric divergence angle emitted by the semiconductor laser into a collimated Gaussian beam with an elliptical cross-section. A triangular prism group is added to the optical path to compress the long axis of the parallel beam with elliptical cross section, so that the outgoing beam is a high-precision collimated Gaussian beam with circular cross section.
图4所示,为本发明一种实施例的点源出射光束经理想非球面准直平凸透镜的光路图。其中n为材料的折射率,焦距为l,平凸透镜的中心厚度为d。α为点源出射的任意光线与主光轴的夹角,β为光线经第一折射平面的折射角,θ为第二折射曲面出射光束与折射点法线之间的夹角。γ为第二折射曲面出射光束与光轴之间的夹角,即出射光束准直发散角。对于第二折射面需要设计使得任意的折射角β所对应的出射光线均平行于光轴,则对任意入射光线所对应的光束发散角γ=0。由推导可得到随着点N的变化,第二折射曲面坐标x随折射角β的变化函数x(β),以及y随折射角β的变化函数y(β)表示为:FIG. 4 is an optical path diagram of an ideal aspheric collimating plano-convex lens for a point source outgoing beam according to an embodiment of the present invention. Where n is the refractive index of the material, the focal length is l, and the central thickness of the plano-convex lens is d. α is the angle between any light emitted from the point source and the principal optical axis, β is the refraction angle of the light passing through the first refraction plane, and θ is the angle between the light emitted by the second refraction surface and the normal line of the refraction point. γ is the angle between the outgoing beam of the second refraction curved surface and the optical axis, that is, the collimation and divergence angle of the outgoing beam. The second refraction surface needs to be designed so that the outgoing rays corresponding to any refraction angle β are parallel to the optical axis, and the beam divergence angle γ=0 corresponding to any incident light. From the derivation, it can be obtained that as the point N changes, the change function x(β) of the coordinate x of the second refraction surface with the refraction angle β, and the change function y(β) of y with the refraction angle β are expressed as:
利用上述参数方程,制作绕光轴旋转对称的理想非球面准直平凸透镜,即可实现对左焦点处点光源出射光束的高精度准直。Using the above parametric equations, an ideal aspheric collimating plano-convex lens with rotational symmetry around the optical axis can be fabricated to achieve high-precision collimation of the beam emitted by the point light source at the left focal point.
图5所示,为本发明一种实施例的象散光源出射光束经理想非球面准直平凸透镜的光路图。在给定透镜折射率n,焦距l,中心厚度d的情况下,点光源位置沿光轴负的方向移动距离Δl,将对理想非球面准直平凸透镜的出射光束发散角具有一定的影响。FIG. 5 is an optical path diagram of an ideal aspheric collimating plano-convex lens for the output beam of an astigmatic light source according to an embodiment of the present invention. In the case of a given lens refractive index n, focal length l, and center thickness d, the position of the point light source moving along the negative direction of the optical axis by a distance Δl will have a certain influence on the divergence angle of the outgoing beam of the ideal aspheric collimated plano-convex lens.
图6所示,为本发明一种实施例中作为对比的旋转双曲面准直平凸透镜对象散光准直的光路图。旋转双曲面准直平凸透镜对点光源具有良好的准直效果。而点光源偏离焦点的距离Δl(即光源象散)将对旋转双曲面准直平凸透镜的出射光束发散角具有一定的影响。FIG. 6 is an optical path diagram of astigmatism collimation of a rotating hyperboloid collimating plano-convex lens object as a comparison in an embodiment of the present invention. The rotating hyperboloid collimating plano-convex lens has a good collimating effect on point light sources. The distance Δl of the point light source away from the focal point (ie, the astigmatism of the light source) will have a certain influence on the divergence angle of the outgoing beam of the rotating hyperboloid collimating plano-convex lens.
图7所示,为本发明一种实施例中象散光源情况下的理想非球面准直平凸透镜发散角与旋转双曲面准直平凸透镜发散角对比的仿真图。在给定透镜折射率n,焦距l,中心厚度d的情况下,对于不同的象散距离Δl,理想非球面准直平凸透镜的准直发散角明显优于旋转双曲面准直平凸透镜的准直效果。表明理想非球面准直平凸透镜比旋转双曲面准直平凸透镜更适用于具有一定象散的半导体激光器发射源。As shown in FIG. 7 , it is a simulated diagram comparing the divergence angle of the ideal aspheric collimating plano-convex lens and the divergence angle of the rotating hyperboloid collimating plano-convex lens in the case of an astigmatic light source in an embodiment of the present invention. In the case of a given lens refractive index n, focal length l, and center thickness d, for different astigmatism distances Δl, the collimation divergence angle of an ideal aspheric collimating plano-convex lens is significantly better than that of a rotating hyperboloid collimating plano-convex lens Collimation effect. It shows that the ideal aspherical collimating plano-convex lens is more suitable for the semiconductor laser source with certain astigmatism than the rotating hyperboloid collimating plano-convex lens.
图8所示,为本发明一种实施例的三棱镜组整形光路图。利用三棱镜组实现对椭圆截状的平行光束的短轴的扩束或对长轴的压缩,使得椭圆截面光束整形为圆形截面准直光束。两个直角棱镜具有相同形状,其顶角均为δ。第一个三棱镜的放大倍数为:FIG. 8 is a schematic diagram of the shaping optical path of the triangular prism group according to an embodiment of the present invention. A triangular prism group is used to expand the short axis of the elliptical truncated parallel beam or to compress the long axis, so that the elliptical cross-section beam is shaped into a circular cross-section collimated beam. Two right-angle prisms have the same shape, and their apex angles are both δ. The magnification of the first prism is:
由于两个三棱镜相同,且使光束也垂直入射于第二透镜的第一面,则同样有:Since the two triangular prisms are the same, and the light beam is also vertically incident on the first surface of the second lens, then also:
因此得到总的放大(或压缩)倍数:So get the total magnification (or compression) factor:
通过仿真可得三棱镜的顶角对光束的压缩(或放大)倍数M的影响,即可实现各种需要的压缩倍数,从而实现将椭圆截面准直光束整形为圆截面准直光束。By simulating the effect of the vertex angle of the prism on the compression (or amplification) multiple M of the beam, various required compression multiples can be achieved, thereby realizing the shaping of the collimated beam with an elliptical cross-section into a collimated beam with a circular cross-section.
本发明中的理想非球面准直平凸透镜和三棱镜组的设计基于矢量折射定理,建立三维光学系统各折射面与矢量光线模型,利用MATLAB程序对光线在光学系统中的空间传输进行三维追迹,获得出射发散角与光束空间位置之间的关系,以及光束横截面能量分布。具体步骤为:1)建立各折射面的三维参数方程,根据实际需求确定各折射面的大小和显示区域。利用MATLAB程序绘制各曲面参数方程所对应的三维曲面;2)根据入射光线的方向余弦,绘制入射光线,并建立入射光线矢量方程,与第一折射面的方程联合求解,获得该折射面上各折射点的坐标,绘制三维入射光线。再求出折射点处的折射面法线方向余弦,基于矢量折射定理,求出折射光线的方向余弦;再以改折射光线作为第二折射面的入射光线,求得第二折射面的折射光线的方向余弦,并绘制出折射光线,以此类推;3)根据最后一个折射面的折射光线的方向余弦求得出射光线与主轴的夹角,绘制出空间发散角与光线位置之间的关系;4)利用出射光线与观察平面交点的坐标绘制出光斑点列图,根据高斯光束能量计算公式获得观察平面内的能量分布;5)根据各像差的定义绘制出观察平面内的光束像差曲线。The design of ideal aspheric collimating plano-convex lens and triangular prism group in the present invention is based on vector refraction theorem, establishes each refraction surface of three-dimensional optical system and vector light model, utilizes MATLAB program to carry out three-dimensional tracing to the space transmission of light in optical system, Obtain the relationship between the exit divergence angle and the spatial position of the beam, as well as the beam cross-sectional energy distribution. The specific steps are: 1) establishing three-dimensional parameter equations of each refraction surface, and determining the size and display area of each refraction surface according to actual needs. Use the MATLAB program to draw the three-dimensional surface corresponding to the parameter equation of each surface; 2) draw the incident light according to the direction cosine of the incident light, and establish the vector equation of the incident light, and solve it jointly with the equation of the first refraction surface to obtain each surface on the refraction surface The coordinates of the refraction point, plotting the incident ray in 3D. Then find the cosine of the normal direction of the refraction surface at the refraction point, and obtain the direction cosine of the refracted light based on the vector refraction theorem; then take the refracted light as the incident light of the second refraction surface, and obtain the refracted light of the second refraction surface , and draw the refracted ray, and so on; 3) Calculate the angle between the outgoing ray and the main axis according to the direction cosine of the refracted ray on the last refracting surface, and draw the relationship between the spatial divergence angle and the position of the light; 4) Use the coordinates of the intersection of the outgoing light and the observation plane to draw the spot diagram, and obtain the energy distribution in the observation plane according to the Gaussian beam energy calculation formula; 5) Draw the beam aberration curve in the observation plane according to the definition of each aberration.
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