高密度光栅中的简化模式方法
文献类型：学位论文
| 作者 | 项长铖 |
| 文献子类 | 博士 |
| 导师 | 周常河 |
| 关键词 | 简化模式方法 Simpified modal method 衍射光栅 Diffraction grating 谐振 Resonance 光学测量 Optical measurement |
| 其他题名 | Simplified modal method for high-density gratings |
| 英文摘要 | 光栅以最常见的人造周期性结构为人们所熟知。近年来随着微加工技术的不断发展，光栅制造精度与密度不断提高，光栅逐渐发展出许多新颖的功能。光栅功能的迅速发展使得光栅理论的研究不断受到关注。简化模式理论用简单清晰的物理图像来描述光栅内部的衍射过程，是指导光栅的设计工作的有力工具，已经成功用于设计矩形光栅、三角光栅、正弦光栅等。深入理解简化模式方法、进一步拓展简化模式方法在光栅设计中的作用具有重要的意义。 本博士论文内容主要是进一步研究和拓展简化模式理论，分析了光栅模式的对称性，提出基于简化模式方法的多重反射模型，设计了基于动态光栅对的器件，具体内容包括： 1. 光栅模式的色散方程和对称性及其应用 光栅模式的对称性在光栅衍射过程中起着重要的作用。在本论文中，我们首先证明了光栅模式对称性与模式有效折射率满足对称模式方程之间的等价关系，并指出模式的对称性只在布拉格角或垂直入射的情况下存在。提出采用对称模式方程求解模式折射率的新方法，通过比较证明该方法与传统的求解方法相比具有效率上的优势。布拉格角入射是大部分光栅设计适用的情形，因此运用布拉格角下入射的对称模式方程求解模式折射率，是对简化模式方法设计光栅的重要提升。 运用模式的对称性以及对称模式方程，还设计了新型的1X5分束的单脊结构光栅，在一定容差范围内具有优异的性能。由于单脊结构的光栅易于制造，该分束光栅将会引起越来越多的关注，有着巨大的应用前景。 2. 基于简化模式方法的光栅多重反射模型及其应用 提出了基于简化模式方法的光栅多重反射模型，用于分析任意角度入射下的亚波长高对比度光栅的衍射。在这一模型中，模式间的相互耦合被考虑进来，并且完全用矩阵描述了模式在光栅中的多重反射。 用该模型分析了导模谐振布儒斯特滤波光栅的衍射。在这个例子中，当仅计算了两个模式时，该模型对光栅的模拟结果就与严格耦合波方法的模拟结果非常接近。对于更一般的实例，可能计算中需要考虑更多的模式。根据这一多重反射模型，还提出了预测谐振波长的法布里-珀罗条件，与传统的方法相比，能更精确地预测谐振波长。 3. 动态调控光栅对的设计 利用动态调控光栅对衍射效率随错移量周期性变化的性质，设计并优化了一个用于位移测量的动态调控光栅对，其周期性信号对比度高且一个周期内只有一个极点，便于电子细分。这种用于位移测量的动态调控光栅对与光栅干涉仪和激光干涉仪相比，由于不涉及光的干涉过程，可以极大地减少环境气流扰动对测量的影响，可以预期将会逐渐受到关注，在精密位移测量领域得到应用。 运用简化模式方法分析了该光栅对的衍射过程，模拟结果与严格耦合波方法非常接近，证实了简化模式方法分析动态调控光栅对的有效性，为动态调控光栅对的衍射过程给出了清晰的物理图像，可以为设计动态调控光栅对提供指导。; Grating is well known as the most common artifact with a periodic structure. The developing of fabrication technology improves the precision and density of grating fabrication. Because of this, the utilities of grating has been much extended, and the theory of grating diffraction is drawing attentions from more researchers. Simplified model method describe the diffraction inside gratings with simple and clear physics view, and is a powerful tool for designing rectangular, triangular, sinuous groove gratings. Further understanding and extending simplified modal method are of important help to grating designing. This thesis is mainly about further researching and extending the simplified modal method: we analyzed the symmetries of grating modes, proposed a multi-reflection mode based on simplified modal method, and designed a new optical component based on dynamic grating pair. The thesis contains: 1. Dispersion equation and symmetries of grating modes Symmetries of grating modes play import roles in grating diffraction. In this thesis, we first demonstrate the equivalence of symmetries of grating modes and the symmetric mode equation, then proposed that symmetries only exist when grating is under normal incidence or a incidence of Bragg angle. A new method for solving effective indices based on symmetric mode method is proposed and it is more efficient than the traditional method. As incidence of Bragg angle is quite common for grating design, this method is a greating improvement for designing gratings with simplified modal method. With the help of symmetries of modes and the symmetric modal equation, we designed a novel five port beam splitter based on a single groove grating. Since single groove grating is easy to fabricate, this beam splitter grating may draw some attention and a promised practical outlook. 2. A multi-reflection model based on simplified modal method and application We proposed a multi-reflection model based on simplified modal method for analyzing diffraction of high-contrast grating under incidence of an arbitrary angle. In this model, mode coupling is considered and the multi-reflection of grating modes is completely described by a matrix form. This model is used to analyzing a guided mode brewster grating filter. In this case, the simulation result of our model is with good agreement with rigorous coupling wave analysis, even when only two modes are taken into consideration. A Fabry-Perot condition for evaluating the wavelength of resonance is also introduced. Comparing to traditional method, this condition can predict wavelength of resonance more precisely. 3. Design of dynamic grating pair A dynamic grating pair for displacement measurement is designed, exploiting the property of grating pair that diffraction efficiency will change periodically when the the two gratings are moving relatively. The periodic signal of this grating pair has a good contrast and has only one extreme point in one period, which is good for electronic division of the signal. Comparing to laser interferometers and grating interferometers, this grating pair is less sensitive to disturbance of air flow, and may have practical use in the high precision displacement measurement. Simplified modal method is used to analyze the diffraction process of the grating pair, the simulation result is in a good agreement with rigorous coupling wave analysis, indicating the effectivity of simplified modal method on this grating pair. Simplified modal method provide a clear physic view for diffraction of dynamic grating pair and can guide the design of dynamic grating pair. |
| 学科主题 | 光学工程 |
| 源URL | [http://ir.siom.ac.cn/handle/181231/31058]  |
| 专题 | 中国科学院上海光学精密机械研究所 |
| 作者单位 | 中国科学院上海光学精密机械研究所 |
| 推荐引用方式 GB/T 7714 | 项长铖. 高密度光栅中的简化模式方法[D]. |
入库方式： OAI收割
来源：上海光学精密机械研究所
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