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摘要: 无衍射光束是一种能在自由空间稳定传输的光束。近来，一类具有复杂光学形态的无衍射光束被引入，比如马蒂厄光束、抛物光束、非对称贝塞尔光束等。为了产生具有复杂结构的无衍射光束，需要对光波进行复振幅调制，即同时调制光波的振幅和相位。但目前的商用光学调制元件只能调制光波的振幅或相位。本文基于二元计算全息法，编码二维复透过率函数分布，构建了具有复振幅调制功能的二元实振幅非负计算全息图。利用实验室自主研发的投影成像光刻系统，对银盐干板进行曝光处理，经显影、定影处理，将其加工为相应的振幅掩模板，用来产生精确的具有复杂结构的无衍射光束。以无衍射马蒂厄光束为例，采用罗曼型迂回相位编码方法，在全息图每个抽样单元内开一个矩形通光孔径，通过改变通光孔径的面积来对复值光波的振幅进行编码，通过改变通光孔径中心偏离抽样单元中心的距离，来对复值光波的相位进行编码。最终构建了两种产生马蒂厄光束的典型二元实振幅计算全息图，其像素数高达28000 pixel×28000 pixel。之后利用加工好的振幅掩模板，准确、方便、高效地产生了椭圆系数q=10，拓扑荷数m=0与m=1的第一种偶型马蒂厄光束，其他类型的马蒂厄光束可相应产生，这是一种光束形态多样、光束结构复杂的无衍射光束。实验结果证实，采用罗曼型迂回相位编码方法产生具有复杂结构的无衍射光束，有效避免了实验过程中分离的相位调制元件和振幅调制元件之间的对准误差，二元计算全息编码法是一种能用来调控产生复杂结构无衍射光束的新途径。Abstract:The diffraction of optical fields is a universal phenomenon that can cause beams to spread during propagation in free space. Ideal non-diffracting (spatially stable) structured beams can propagate in free space without changing their initial field distribution at any plane orthogonal to the direction of propagation. Moreover, the non-diffracting structured beams also have the ability for self-recovery after encountering obstacles. Hence generating non-diffracting beams or structured beams is a very important field of research for overcoming the diffraction behavior of beams during propagation in free space. Any non-diffracting structured beams with a certain intensity, phase distribution, and propagation properties have special applications in the field of optics. Lately, some non-diffracting beams with complex structures are introduced one after another, such as Mathieu beams, parabolic beams, Lommel beams, asymmetric Bessel beams, and so on. The complex amplitude modulation is necessary to produce the non-diffracting beams with abundant structures. At present, no commercial optical modulator can modulate the phase and amplitude of light waves simultaneously. Based on binary computer-generated holography that can encode the two-dimensional transmission function distribution, a binary real amplitude computer-generated hologram with complex amplitude modulation functionality is designed and constructed. Binary real amplitude computer-generated holograms, which are a kind of binary optical diffracting element that generate non-diffracting beams with complex optical morphology, are designed and constructed by encoding the complex optical filed information by using the Lohmann-type detour phase coding method. For the Lohmann-type detour phase coding method, the coding principle is mainly that the complex field distribution information is transformed into amplitude and phase information. The complex field distribution is sampled, and one can obtain a matrix of point sources. Here, we extract the amplitude and phase information as input information to generate two 2D real value matrices for detour phase coding. By using the homemade projection imaging lithography system, the silver salt halide plate was exposed, developed and fixed, and then a binary mask is precisely machined. The homemade projection imaging lithography system can machine holograms with an ultrahigh resolution of 79874 × 79874 dpi and a maximum output of 156 mm × 156 mm. Using the mask, the non-diffracting beams with abundant structures can be produced accurately.Taking the non-diffracting Mathieu beam as an example, two kinds of binary real amplitude computer-generated holograms for generating Mathieu beams are constructed by using the Roman type detour phase coding method. In the process of the machine, the photolithography file is firstly divided into 47 unit patterns of 600 pixel × 600 pixel, where each unit pattern is automatically inputted into a DMD (Digital Micromirror Device) in proper sequence, and then subsequently scanned line-by-line for projection exposure. When the lithography is complete, the silver halide plate is processed to obtain the mask. In this experiment, the calculated CGH is 28000 pixel × 28000 pixel, and the size of a pixel is 318 nm×318 nm. The size of the produced binary masks is 8.9 mm × 8.9 mm. The non-diffracting Mathieu beams with elliptic coefficient q=10 and topological charge number m=0, 1 are generated, which belong to the even type Mathieu beams of the first kind. Undoubtedly, the classes of non-diffracting Mathieu beams, including the even type Mathieu beams of the second kind, odd type Mathieu beams of the first kind, and odd-type Mathieu beams of the second kind can also be generated using the same encoding method and experimental setup. Since one can encode both the amplitude information and the phase information of optical field in sole spatial light modulation, the experimental system is simple in structure. The experimental results show that the coding method of binary computer-generated holography is an accurate, convenient and efficient way to generate high-quality non-diffracting beams with abundant structures.
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图 3 构建马蒂厄光束二元全息图过程
Figure 3. The process of constructing a Mathieu beam binary hologram
图 4 产生马蒂厄光束的二元计算全息图。(a) m=0, q=10; (b) m=1, q=10
Figure 4. Binary computer-generated hologram of a Mathieu beam. (a) m=0, q=10; (b) m=1, q=10
图 8 采用掩模板产生的马蒂厄光束。(a) m=0, q=10; (b) m=1, q=10
Figure 8. Mathieu beam produced by the mask. (a) m=0, q=10; (b) m=1, q=10
图 9 理论模拟产生的马蒂厄光束。 (a) m=0, q=10; (b) m=1, q=10
Figure 9. Mathieu beam generated through theoretical simulation. (a) m=0, q=10; (b) m=1, q=10
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