| 题名 | 光子筛和光传输变换 |
| 作者 | 张军勇 |
| 学位类别 | 博士 |
| 答辩日期 | 2010 |
| 授予单位 | 中国科学院上海光学精密机械研究所 |
| 导师 | 林尊琪 |
| 关键词 | 光子筛 瑞利-索末菲衍射积分 变形分数傅立叶变换 B积分 |
| 其他题名 | Reaserch on photon sieves and beam propagation |
| 中文摘要 | 本论文主要包括极紫外线和软x射线波段、以及可见光频段的光传输变换和成像理论。在电磁波谱中，相对于可见光而言，从紫外线到x射线波段的辐射研究是比较晚的。然而在这个波段里，存在着大量的原子共振线辐射，使得辐射在很短的距离内被吸收，绝大多数物质的典型吸收长度为纳米(nm)或者微米(um)量级。固体材料的强吸收特性使得不能利用普通透镜的折射特性对该波段成像，目前对这些波段的利用大多基于衍射光学元件(Diffractive Optical Elements)，通常是菲涅耳波带片(Fresnel Zone Plates)。但是，2001年Nature上报道了一种新型的极紫外线和软x射线成像元件，即光子筛(Photon Sieves)。通过把菲涅耳波带板改为光子筛，同时对小孔应用切趾技术，既保证了低级衍射的相干，又使得高阶衍射得到压缩，从而得到小于针孔最小直径的焦斑。光子筛以其独特的光学特性、材料的无选择性、以及从短波区到红外波段都可以聚焦成像，这将为高分辨率显微镜、太阳轨道极紫外线成像、生命科学等提供新的机遇。 另一方面，激光束的传输变换贯穿于任何一个完整的光学系统中，其目的是为了得到高性能的光束质量。光束质量的好坏，一方面来自元器件制造的不完善，另一方面源于光场自身的内在物理属性，主要是衍射和强光的非线性效应。激光领域常用的传输变换方法主要有矩阵光学、衍射积分、算子光学和维格纳(Wigner)分布函数法。分数傅立叶变换由维格纳(Wigner)分布函数在相空间旋转得到，这一等价的描述方法是由Namias在1980年量子力学中求解自由电子的薛定谔方程而引入的。将分数变换引入到光学领域可以说是开拓了一个全新的角度研究光的传输变换问题。 本论文在前人的研究基础上主要完成了以下几个方面的工作： 1、 首次建立了光子筛的一般性聚焦和成像理论。该部分工作分三步完成：第一、发展了圆孔光子筛的远场模型，分别建立了极坐标下旋转对称的椭圆孔光子筛模型和直角坐标系下坐标对称的方孔光子筛模型，得到了单个椭圆孔、圆环孔和方孔在远场条件下的解析表达式。第二、进一步讨论了依赖于潜在的菲涅耳环的小孔的位置对聚焦贡献的影响。最后，在前两步的基础上，建立了任意形状小孔构成的光子筛的一般性聚焦和成像理论。 2、 改进型菲涅耳波带片能够实现更高的空间分辨率，在此工作的基础上，首次证明了光子筛和改进型菲涅耳波带片在聚焦成像方面的等价性，同时进行了成像对比研究。 3、 作为衍射元件的光子筛具有强色散性，首次提出了用负衍射透镜补偿光子筛的强色差特性，探索性地解决光子筛在光学系统中的色散问题。 4、 1993年，Lohmann建立了用球面透镜实现标准分数傅立叶变换的Ⅰ型和Ⅱ型光学结构。与此对应，用非球面透镜建立了变形分数傅立叶变换系统的基本光学单元，首次在傍轴条件下得到了该光学结构的输出函数解析式，它可以用于分析、设计变形分数傅立叶变换系统。 5、 在变形分数傅立叶变换系统中，尝试性地研究了几类常见的激光束的非傍轴光束传输特性以及矢量场传输。 6、 自聚焦是限制获得高功率激光输出的主要因素，对光束进行整形和控制变换进而补偿非线性效应的技术在高功率激光工程中就显得赿来赿重要。初步研究了空间滤波器级联技术补偿非线性B积分，以及强激光束在非线性介质中的传输特性。 |
| 英文摘要 | This paper mainly includes two parts, one is the imaging theory of extreme ultraviolet and soft x-ray, and the other is light propagation in the visible wavelengths region. In the spectrum of electromagnetic wave, the research on the extreme ultraviolet and soft x-ray is relatively late compared with the visible wavelengths. Moreover, there exists a lot of atomic resonance line, so the radiation is rapidly absorbed at very short range. Generally speaking, the typical absorption length is mostly in the nanometer or micrometer range. In a word, the common convergent lens can not focus soft x-ray into image as a result of the highly absorption property of material. But this spectral region can be focused to imgae by means of diffractive optical elements (DOE), such as Fresnel Zone Plate (FZP). Fortunately, the German scientists Kipp et al. suggested the novel concept of ‘photon sieve’ in 2001 year, which consists of a great number of circular pinholes by applying apodization techniques properly distributed over the Fresnel zones. The function principle of photon sieves is as follows: those designed pinholes not only can make the lower-order diffracted field interfere constructively, but also can suppress the higher-oder diffraction. Photon sieves makes it possible to focus soft x-rays to spot sizes smaller than the diameter of the smallest pinholes; it can be used in soft x-ray microscopy, lithography, spectroscopy, and so on. Besides, beam propagation and transformation is introduced into the optical systems in order to get the high quality beam. Since the requirements for beam quality run almost through whole system, the effects of propagation on that can not therefore be avoided. On one hand, the imperfection of the optics elements and many random factors in the system arouse the difficulty in technique to control the beam quality; on the other hand, the inherent physical characteristics of electromagnetic field, such as diffraction and nonlinear optical effects, also arouse the difficulty in physics. As known, the most commonly used methods of beam propagation and transformation include Matrix Optics, Diffraction Integrals, Operator Methods and Wigner Distribution Function. The integer domain Fourier transforms is extended to non-integer domain by use of the rotation of Wigner distribution function. The concept of fractional Fourier transform was formally introduced by Namias and later developed by other scientists. In the optics community, the concept and the optical implementation of fractional Fourier transform and its relation to other transforms have been introduced. The non-integer Fourier transforms introduced into optics provides a theoretical possibility to study the beam propagation and transforms. This paper develops the existing results of other people at the following several aspects, and achieves some novel and innovative results. The corresponding works is as follows: 1、 With the help of Rayleigh-Sommerfeld diffraction integral and coordinate rotation, the general focusing and imaging theory of photon sieves is derived and described. This part of work was completed in three stages: First, based on the traditional photon sieves composed of a lot of circular pinholes, we provide individual far-field model for photon sieves composed of elliptical or square pinholes. The second step is to discuss the dependence of focusing contribution on the order m of local rings of underlying traditional Fresnel zone plate, and get the analytical expression. Finally, on the basis of the above-mentioned work, the general focusing and imaging theory of photon sieves composed of arbitrary shape pinholes is discussed. These obtained results can be used for analysis, design, and simulation of a high numerical aperture photon sieve. 2、 Most investments showed that the modified Fresnel zone plate had higher resolution. Based on our previous research, we continue to prove that as the number of pinholes increase, photon sieves have the same properties in imaging compared with the modified Fresnel zone plate. 3、 As is known to all, diffractive optical element has strong dispersion property. For the first time, the negative diffractive lens has been proposed to compensate the high dispersion of photon sieves in an optical system. Moreover, the result is relatively stasfactory. 4、 In 1993, Lohmann used spherical lens to complete the standard fractional Fourier transforms. Accordingly, the non-spherical lens (such as cylindrical lens) is the basic optical unit which can complete the anamorphic fractional Fourier transforms. The analytical expression is first given in the case of approximate axis. The mentioned-above results can be used to design and analyze the anamorphic fractional Fourier transform system. 5、 Based on the anamorphic fractional Fourier transform system, some laser beam propagations are studied in the condition of the axially symmetric paraxial and non-paraxial axis. 6、 Beam shaping and beam controlling becomes more important and practical. In order to get clear knowledge about the laser beam propagation through an optical system, we preliminarily investigate the compensation of B-integral by use of the cascaded spatial filter in the high power laser system. |
| 语种 | 中文 |
| 内容类型 | 学位论文 |
| 源URL | [http://ir.siom.ac.cn/handle/181231/15623]  |
| 专题 | 上海光学精密机械研究所_学位论文 |
| 推荐引用方式 GB/T 7714 | 张军勇. 光子筛和光传输变换[D]. 中国科学院上海光学精密机械研究所. 2010. |
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