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摘要:
本文提出了采用连续镜面变形反射镜的本征模法构建了完备正交基，通过需要调控的涡旋光场信息，来求解变形反射镜各个驱动器的电压。调控生成了拓扑荷数绝对值在5以内的整数阶、分数阶、多分数阶和叠加态的螺旋波前，实现了对涡旋光束的动态调控。生成结果与理想螺旋波前结果基本一致。显示了连续镜面变形反射镜拟合螺旋波前的能力，得到了较好的结果。该方法在高功率涡旋激光的动态调控上具有很好的应用前景。
Abstract:A complete orthogonal basis was constructed by using the eigen-mode method of continuous surface deformation mirror, and the voltage of each driver of the deformation mirror can be obtained according to the spiral wavefront information which needs to be manipulated. The spiral wavefront of integral order, fractional order, multi-fractional order, and superposition state with the absolute value of topological charge less than 5 was generated, and the dynamic manipulation of the vortex beam was realized. The results obtained were the same as those obtained by the ideal spiral wavefront. The ability of the continuous surface deformation mirror to fit the spiral wavefront was demonstrated and good results were obtained. This method has a good application prospect in the dynamic manipulation of high-power vortex laser.
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Key words:
- voretex beam /
- deformation mirror /
- eigen-mode /
- mode purity /
- dynamic manipulation
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Overview: In recent years, vortex beams have become the focus of research, and their orbital angular momentum makes them have many important applications, like optical communication, particle manipulation, and optical measurement. At the same time, researchers are paying attention to more abundant generation methods. In previous studies, vortex beam generation methods are usually divided into two categories. The first category is the outcavity, such as spiral phase plate method, spatial light modulator method, mode conversion method, metasurface method, and corner array method, and the second category is the incavity, such as point-loss method, off-axis pumping method, and spatial light modulator method. However, these methods can not tolerate high power laser output and adjust topological charges flexibly. Therefore, how to generate a vortex beam that can tolerate high power laser output and adjust the topological charges flexibly is an important problem to be solved. Continuous surface deformation mirror is a key component of adaptive optical system. In the study of wavefront fitting for continuous surface deformation mirrors, there are usually two kinds of methods. The first type is model-free method, such as genetic algorithm, simulated annealing algorithm, stochastic parallel gradient descent (SPGD) algorithm, etc. These methods generally require many iterations and slow convergence, and it is difficult to change the topological charge flexibly. The second type is pattern method, such as Zernike mode method, Lukosz mode method, and enginmode method. This method first defines a set of complete orthogonal modes, calculates the mode coefficients, and completes the fitting of the target wavefront by linear superposition of each mode. Zernike mode is orthogonal in the circular domain, Lukosz mode is orthogonal in the circular domain derivative. However, usually the configuretion of deformation mirror is not circular domain. For example, the deformation mirror driver used in this paper is arranged in circular domain. In this case, the orthogonal basis needs to be rebuilt to use these two methods. The eigenmode of the deformed mirror is directly and precisely derived from the influence function of the deformed mirror drivers, so it can not only avoid the influence of fitting error, improve the fitting accuracy, but also adapt to the different configuration of the deformed mirror. Combined with the eigenmode method, continuous surface deformation mirror can fit all kinds of vortex beams with high precision and fast fitting speed, and can be applied to all kinds of deformation mirrors with different configurations. In this paper, the eigenmode method of continuous surface deformation mirror is used to simulate and analyze the fitting of the spiral wavefront of integer order with topological charge is −5 to 5, fractional order, multi-fractional order, and superposition state with the absolute value of topological charge less than 5. Various vortex light fields are generated by dynamic manipulation. The results show that the continuous surface deformation mirror will have a good application prospect in the field of high-power vortex field manipulation.
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图 1 连续镜面变形反射镜生成涡旋光束的示意图
Figure 1. Schematic diagram of the vortex beam generated by continuous mirror deformation mirror
图 2 使用变形镜生成涡旋光束的示意图。L1、L2、L3：凸透镜；T：孔径光阑；DM：变形镜；f：焦距
Figure 2. Schematic diagram of using DM to generate vortex beams.L1, L2, L3: convex lens; T: aperture; DM: deformation mirror; f: focal length
图 3 整数阶螺旋波前的拟合。(a)~(e) 拓扑荷数为l=1~5的整数阶目标波前; (f)~(j) 拓扑荷数为l=1~5的整数阶拟合波前
Figure 3. Fitting of the integer order spiral wavefront. (a)~(e) Target wavefront with the integer order l =1~5; (f)~(j) Fitting wavefront of the integer order l=1~5
图 4 拓扑荷数为2的涡旋光束的拟合。(a) u2处未滤波的光强; (b) u4处经过滤波的光强; (c) u2处未滤波的相位; (d) u4处经过滤波的相位
Figure 4. Fitting of integer order vortex beams with topological charge is 2. (a) Unfiltered intensity at u2; (b) Filtered intensity at u4; (c) Unfiltered phase at u2; (d) Filtered phase at u4
图 5 整数阶拟合波前在经过滤波处理后的光场及相位。(a)~(d) 拓扑荷数为1、3、4、5的光强；(e)~(h) 拓扑荷数为1、3、4、5的相位
Figure 5. The light field and phase of the integer order vortex beam after focusing and filtering. (a)~(d) Intensity with topological charges l=1, 3, 4, and 5; (e)~(h) Phase with topological charges l=1, 3, 4, and 5
图 6 分数阶螺旋波前的拟合。(a)~(e) 拓扑荷数为l=0.5、1.5、2.5、3.5、4.5的目标波前；(f)~(j) 拓扑荷数为l=0.5、1.5、2.5、3.5、4.5的拟合波前
Figure 6. Fitting of the fractional order spiral wavefront. (a)~(e) Target wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5; (f)~(j) Fitting wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5
图 7 分数阶涡旋光束的滤波结果。(a)~(e) 拓扑荷数为l=0.5、1.5、2.5、3.5、4.5的目标波前在u4处的光强; (f)~(j) 拓扑荷数为l=0.5、1.5、2.5、3.5、4.5的拟合波前在u4处的光强
Figure 7. Filtering results of the fractional order vortex beam. (a)~(e) Intensity of target wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u4; (f)~(j) Intensity of fitting wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u4
图 8 分数阶涡旋光束的滤波结果。(a)~(e) 拓扑荷数为l=0.5、1.5、2.5、3.5、4.5的目标波前在u4处的相位; (f)~(j) 拓扑荷数为l=0.5、1.5、2.5、3.5、4.5的拟合波前在u4处的相位
Figure 8. Filtering results of the fractional order vortex beam. (a)~(e) Phase of target wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u4; (f)~(j) Phase of fitting wavefront with topological charges l=0.5, 1.5, 2.5, 3.5, and 4.5 at u4
图 9 多分数阶螺旋波前的拟合。(a), (b) 目标波前；(c), (d) 拟合波前
Figure 9. Fitting of multi-fractional spiral wavefront. (a), (b) Target wavefront; (c), (d) Fitting wavefront
图 10 多分数阶目标波前及拟合波前在滤波处理后的光场及相位。(a), (b) 多分数阶目标波前在u4处的光强; (c), (d) 多分数阶拟合波前在u4处的光强; (e), (f) 多分数阶目标波前在u4处的相位; (g), (h) 多分数阶拟合波前在u4处的相位
Figure 10. The light field and phase of the multi-fractional order target wavefront and the fitting wavefront after filtering. (a), (b) Intensity of multi-fractional order target wavefront at u4; (c), (d) Intensity of multi-fractional order fitting wavefront at u4; (e), (f) Phase of multi-fractional order target wavefront at u4; (g), (h) Phase of multi-fractional order fitting wavefront at u4
图 11 叠加态目标波前及拟合波前。(a)~(d) 拓扑荷数分别为l=±1、±2、±3、±4的目标波前; (e)~(h) 拓扑荷数分别为l=±1、±2、±3、±4的拟合波前
Figure 11. Superposition target wavefront and fitting wavefront. (a)~(d) Target wavefront with topological charges l=±1, ±2, ±3, and ±4; (e)~(h) Fitting wavefront with topological charges l=±1, ±2, ±3, and ±4
图 12 叠加态拟合波前在滤波处理后的光场及相位。(a)~(d) 拓扑荷数分别为l=±1、±2、±3、±4的拟合波前在u4处的光强; (e)~(h) 拓扑荷数分别为l=±1、±2、±3、±4的拟合波前在u4处的相位
Figure 12. The light field and phase of the superposition fitting wavefront after filtering. (a)~(d) Intensity of fitting wavefront at with topological chrages l=±1，±2，±3, and ±4 at u4; (e)~(h) Phase of fitting wavefront at with topological chrages l=±1，±2，±3, and ±4 at u4
图 13 叠加态拟合波前在滤波处理后的模式纯度。(a) l=±1；(b) l=±2；(c) l=±3；(d) l=±4
Figure 13. The mode purity of the superposition fitting wavefront after filtering. (a) l=±1; (b) l=±2; (c) l=±3; (d) l=±4
图 14 整数阶涡旋光束的动态调控。(a1)~(a6) 拓扑荷数为2的光强；(b1)~(b6) 拓扑荷数为2的螺旋相位；(c1)~(c6) 拓扑荷数为3的光强；(d1)~(d6) 拓扑荷数为3的螺旋相位
Figure 14. Dynamic manipulation of integer order vortex beams. (a1)~(a6) Intensity with topological charge l=2; (b1)~(b6) Spiral phase with topological charge l= 2; (c1)~(c6) Intensity with topological charge l=3; (d1)~(d6) Spiral phase with topological charge l= 3
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