新型光学涡旋的调控与应用研究
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摘要
光学涡旋是具有螺旋型波前和轨道角动量的特殊光场,此种特性使其在诸如光学微操作、原子光学、空间光信息传输等多个领域都有重要的潜在应用价值。特别是最近十几年来,光学涡旋方面的研究与应用迅速发展成为现代光学中的一个新兴领域,光学涡旋的产生、调制、探测以及应用机理等问题,成为本学科前沿的研究热点。长期以来,对光学涡旋的研究通常是以拉盖尔—高斯模的形式来描述的,2007年,Kotlyar提出了光学涡旋另一种解的形式—超几何分布模,在此理论基础上,本文对光学涡旋产生和旁瓣抑制的方法及其在实践中的相关应用进行了理论与实验研究,主要研究内容和成果如下：
1.基于纯相位型空间光调制器研究了螺旋相位结构对严格有限孔径平面波的衍射,并详细讨论了夫琅和费衍射场的特点及其影响因素。利用激光直写技术加工了拓扑荷为1的螺旋相位板并产生光学涡旋,优化了制作工艺参数,并利用原子力显微镜和光学干涉的方法验证了螺旋相位板的加工效果。
2.提出了直接由涡旋光束主亮环半径和第一旁瓣半径的比值来确定用于抑制光学涡旋旁瓣的最佳环状螺旋相位结构内外半径的方法,并推导出了环状螺旋相位结构对有限孔径平面波的夫琅和费衍射公式。证明得出了用于抑制光学涡旋旁瓣的最佳环状螺旋相位结构内外半径比值只与螺旋相位结构的拓扑荷有关,与入射光波长和螺旋相位结构尺寸大小等其他因素无关的结论。为提高最佳环状螺旋相位结构的设计奠定了理论基础。
3.提出了基于类贝塞尔振幅调制螺旋相位结构抑制光学涡旋旁瓣的方法,推导了该相位结构对有限孔径平面波的夫琅和费衍射光场公式,并给出了计算最佳振幅调制参数和主亮环半径的解析式,基于数值计算的结果讨论了n+1阶和n-1阶类贝塞尔函数做振幅调制的适用范围,并利用纯相位型空间光调制器验证了该方法的有效性。该方法的优点在于不仅可以完全消除光学涡旋的旁瓣,而且不会改变涡旋光束主亮环的大小和形状。
4.提出了基于光学涡旋主环—旁瓣关系的光学涡旋调制与探测方法,该方法在用于以光学涡旋为信息载体的自由空间光通信系统时,可以避开信息载体光束与解码器件之间所需的严格对准或相位匹配等苛刻条件,只需要接收并测量涡旋光束远场衍射图样中光强分布的半径即可进行信息解码。此种设计方法中同一拓扑荷的径向调制参数适用于其他条件下的入射光波长或螺旋相位结构尺寸。
5.提出了利用类贝塞尔振幅调制螺旋相位滤波器实现提高径向希尔伯特变换输出图像对比度的方法,并给出了该相位滤波器点扩散函数的解析式。通过计算模拟验证了该方法对提高径向希尔伯特变换输出图像对比度的有效性。
Optical vortex is a particular light field that posses helical phase wavefront and orbital angular momentum. The unique nature of vortex field is expected to lead to important potential application in many areas including optical micromanipulation, atomic optics, space optical communication and so on. Especially in the last ten years, the study on optical vortex has become a new research field in the modern optics. In this application prospect, the production, modulation, detection and application mechanism of optical vortices have become a focal issues urgently needed to research. Different from Laguerre-Gaussian mode, in 2007, Kotlyar et al proposed an other solution form of optical vortices field-Hypergeometric mode. On the basis of this theory, this thesis focuses on the generation, sidelobes suppression and application of optical vortices. The major content and result are shown as follows:
1. We proposed a simple, economical and reliable technique for fabricating a spiral phase plate (SPP) in a quartz substrate to generate optical vortex with a unit topological charge at the wavelengths of 632.8nm. The spiral phase plate is first formed in the photoresist by direct laser writing lithography and then transferred into the quartz substrate by inductively coupled plasma etching. The performance of the fabricated SPP is verified by using beam intensity distribution, which is in agreement with the theoretical calculation result. The interference measurement suggests that we have succeeded to generate optical vortex with a unit topological charge with the fabricated SPP. We also study the Fraunhofer diffraction of a plane wave of circular cross section by a spiral phase mask based on Spatial Light Modulator.
2. We proposed a simple and accurate method for calculating the optimal width of an annular spiral phase plate (SPP) to generate optical vortices with sidelobes suppression and analyzed its properties. It is shown that sidelobes can be sharply suppressed when the ratio of inner and outer radii of an annular SPP equals to that of the principal ring and the first sidelobe diffracted by a circular SPP with the same topological charge n. Moreover, the ratio of inner and outer radii of the optimal annular SPP only depends on the topological charge n, while it is not affected by the incident wavelength and size of the SPP. This proposed approach is helpful for designing or setting an optimal annular SPP in many applications. Such as designing multi-ring structure of optical vortices with same or different topological charges and angular momentum directions in dynamic multi-optical tweezers as well as improving the bandwidth of the free space optical communication.
3. We propose a generalized approach to producing optical vortices with suppressed sidelobes using a variable Bessel like function added to the conventional spiral phase plate (SPP) and establishes explicit relations between the radial modulation and the optimal sidelobes expression effect in the Bessel-like modulation technique. Experimental verifications are implemented by a phase-only spatial light modulator (SLM). Comparing with prior techniques, the proposed method has advantages in terms of wide topological charge coverage with variable Bessel like analytical functions and the unchanged primary ring size as compared to the conventional one. Furthermore, it verifies that both central and outskirt ring areas of the phase plate resulted in sidelobes in the diffraction pattern and the corresponding structural dimensions can be determined quantitatively.
4. We propose a technique for modulating and detecting optical vortices based on the principal-sidelobe ring relationship, where topological charges are determined by radius ratios of the principal ring and the modified first sidelobe. The method is immune to harassments from alignment or phase matching between the encoded beams and the decoding element. Moreover, it is demonstrated that the radius ratio and corresponding radial modulation parameters are independent to the incident wavelength and the size of spiral phase mask.
5. We proposed a novel spiral phase filter, called the Bessel-like modulated spiral phase filter to improve the output image contrast of radial Hilbert transform, and analyzed the analytical point spread function of the image processing system. The theoretical simulation shown that the Bessel-like modulated spiral phase filter possesses some advantages in comparison with the conventional spiral phase filter as for high contrast edge enhancement with high resolution.
1.基于纯相位型空间光调制器研究了螺旋相位结构对严格有限孔径平面波的衍射,并详细讨论了夫琅和费衍射场的特点及其影响因素。利用激光直写技术加工了拓扑荷为1的螺旋相位板并产生光学涡旋,优化了制作工艺参数,并利用原子力显微镜和光学干涉的方法验证了螺旋相位板的加工效果。
2.提出了直接由涡旋光束主亮环半径和第一旁瓣半径的比值来确定用于抑制光学涡旋旁瓣的最佳环状螺旋相位结构内外半径的方法,并推导出了环状螺旋相位结构对有限孔径平面波的夫琅和费衍射公式。证明得出了用于抑制光学涡旋旁瓣的最佳环状螺旋相位结构内外半径比值只与螺旋相位结构的拓扑荷有关,与入射光波长和螺旋相位结构尺寸大小等其他因素无关的结论。为提高最佳环状螺旋相位结构的设计奠定了理论基础。
3.提出了基于类贝塞尔振幅调制螺旋相位结构抑制光学涡旋旁瓣的方法,推导了该相位结构对有限孔径平面波的夫琅和费衍射光场公式,并给出了计算最佳振幅调制参数和主亮环半径的解析式,基于数值计算的结果讨论了n+1阶和n-1阶类贝塞尔函数做振幅调制的适用范围,并利用纯相位型空间光调制器验证了该方法的有效性。该方法的优点在于不仅可以完全消除光学涡旋的旁瓣,而且不会改变涡旋光束主亮环的大小和形状。
4.提出了基于光学涡旋主环—旁瓣关系的光学涡旋调制与探测方法,该方法在用于以光学涡旋为信息载体的自由空间光通信系统时,可以避开信息载体光束与解码器件之间所需的严格对准或相位匹配等苛刻条件,只需要接收并测量涡旋光束远场衍射图样中光强分布的半径即可进行信息解码。此种设计方法中同一拓扑荷的径向调制参数适用于其他条件下的入射光波长或螺旋相位结构尺寸。
5.提出了利用类贝塞尔振幅调制螺旋相位滤波器实现提高径向希尔伯特变换输出图像对比度的方法,并给出了该相位滤波器点扩散函数的解析式。通过计算模拟验证了该方法对提高径向希尔伯特变换输出图像对比度的有效性。
Optical vortex is a particular light field that posses helical phase wavefront and orbital angular momentum. The unique nature of vortex field is expected to lead to important potential application in many areas including optical micromanipulation, atomic optics, space optical communication and so on. Especially in the last ten years, the study on optical vortex has become a new research field in the modern optics. In this application prospect, the production, modulation, detection and application mechanism of optical vortices have become a focal issues urgently needed to research. Different from Laguerre-Gaussian mode, in 2007, Kotlyar et al proposed an other solution form of optical vortices field-Hypergeometric mode. On the basis of this theory, this thesis focuses on the generation, sidelobes suppression and application of optical vortices. The major content and result are shown as follows:
1. We proposed a simple, economical and reliable technique for fabricating a spiral phase plate (SPP) in a quartz substrate to generate optical vortex with a unit topological charge at the wavelengths of 632.8nm. The spiral phase plate is first formed in the photoresist by direct laser writing lithography and then transferred into the quartz substrate by inductively coupled plasma etching. The performance of the fabricated SPP is verified by using beam intensity distribution, which is in agreement with the theoretical calculation result. The interference measurement suggests that we have succeeded to generate optical vortex with a unit topological charge with the fabricated SPP. We also study the Fraunhofer diffraction of a plane wave of circular cross section by a spiral phase mask based on Spatial Light Modulator.
2. We proposed a simple and accurate method for calculating the optimal width of an annular spiral phase plate (SPP) to generate optical vortices with sidelobes suppression and analyzed its properties. It is shown that sidelobes can be sharply suppressed when the ratio of inner and outer radii of an annular SPP equals to that of the principal ring and the first sidelobe diffracted by a circular SPP with the same topological charge n. Moreover, the ratio of inner and outer radii of the optimal annular SPP only depends on the topological charge n, while it is not affected by the incident wavelength and size of the SPP. This proposed approach is helpful for designing or setting an optimal annular SPP in many applications. Such as designing multi-ring structure of optical vortices with same or different topological charges and angular momentum directions in dynamic multi-optical tweezers as well as improving the bandwidth of the free space optical communication.
3. We propose a generalized approach to producing optical vortices with suppressed sidelobes using a variable Bessel like function added to the conventional spiral phase plate (SPP) and establishes explicit relations between the radial modulation and the optimal sidelobes expression effect in the Bessel-like modulation technique. Experimental verifications are implemented by a phase-only spatial light modulator (SLM). Comparing with prior techniques, the proposed method has advantages in terms of wide topological charge coverage with variable Bessel like analytical functions and the unchanged primary ring size as compared to the conventional one. Furthermore, it verifies that both central and outskirt ring areas of the phase plate resulted in sidelobes in the diffraction pattern and the corresponding structural dimensions can be determined quantitatively.
4. We propose a technique for modulating and detecting optical vortices based on the principal-sidelobe ring relationship, where topological charges are determined by radius ratios of the principal ring and the modified first sidelobe. The method is immune to harassments from alignment or phase matching between the encoded beams and the decoding element. Moreover, it is demonstrated that the radius ratio and corresponding radial modulation parameters are independent to the incident wavelength and the size of spiral phase mask.
5. We proposed a novel spiral phase filter, called the Bessel-like modulated spiral phase filter to improve the output image contrast of radial Hilbert transform, and analyzed the analytical point spread function of the image processing system. The theoretical simulation shown that the Bessel-like modulated spiral phase filter possesses some advantages in comparison with the conventional spiral phase filter as for high contrast edge enhancement with high resolution.
引文
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