简化模式方法在倾斜光栅中的应用
文献类型：学位论文
| 作者 | 李树斌 |
| 学位类别 | 博士 |
| 答辩日期 | 2016 |
| 授予单位 | 中国科学院上海光学精密机械研究所 |
| 导师 | 周常河 |
| 关键词 | 简化模式方法 斜光栅 全息光栅 泰伯效应 双层光栅 |
| 其他题名 | Simplified Modal Method for Slanted Gratings |
| 中文摘要 | 光栅作为现代光学系统中重要的光学器件，广泛应用于生物成像、光栅光谱仪、高功率激光系统等领域。对于高密度的光栅，比较成熟的计算方法有严格耦合波方法，有限时域差分算法等，这些方法的优点是计算准确，但计算时间较长，给优化设计带来了不便。近年来，由于简化模式理论不仅能以全新的物理视角来解释光栅内部的衍射过程，而且可以指导光栅的设计工作，因此，受到许多研究人员的关注。但目前简化模式理论主要应用于矩形光栅、三角光栅、正弦光栅等。对于其它槽型的光栅，简化模式理论需要进一步的扩展。 本博士论文主要是进一步扩展了简化模式理论，详细分析了其在斜光栅、体全息光栅、双层光栅以及高密度光栅泰伯效应中的应用，具体内容包括： 1、斜光栅的简化模式理论 斜光栅具有非对称结构，可以实现一些特殊的功能。应用简化模式理论分析斜光栅，在布拉格角入射下，根据电磁场的边界条件和周期性条件，得到斜光栅的本征方程。对于亚波长斜光栅，其内部激发的光栅模式通常只有两个。在此情况下，复杂的光栅衍射过程可以近似等效为一个双光束干涉的过程。基于双光束干涉模型，经过理论推导即可得到衍射效率的解析表达式，这是传统的数值计算方法无法实现的。 不同于矩形光栅，斜光栅属于非对称结构，其内部激发的光栅模式相互作用也不同。在垂直入射的情况下，由于奇对称分布光栅模式（简称奇模）被激发，导致入射光能量可以全部耦合到-1级当中。据此，我们设计了一种高效率的斜光栅器件，该元件可以实现垂直入射下的-1级宽光谱高效率衍射。 2、体全息光栅的简化模式理论 为了扩展简化模式理论在体全息光栅中的应用，我们将量子力学中的微扰论引入到体全息光栅的研究中，并在此基础上得到了基于微扰理论的体全息光栅的本征方程。通过对本征方程的研究发现，对于亚波长体全息光栅，在布拉格角入射下，其衍射过程同样可以近似等效为一个双光束干涉过程。 此外，我们还推导了布拉格角失配条件下的简化模式理论，解释了宽光谱体全息光栅衍射特性，为宽光谱体全息光栅的设计提供了一种新方法。 3、偏振无关高密度光栅泰伯效应 我们设计了一种高密度光栅的偏振无关泰伯效应，并首次应用简化模式理论对光栅的泰伯效应进行理论分析，通过一系列数学解析式来分析光栅的衍射效率以及相位，深刻地解释了泰伯效应的物理内在机制，可用于指导光栅泰伯效应的设计。 4、双层光栅 我们设计了一种高衍射效率的双层动态调控光栅器件。当TE偏振光垂直入射时，该光栅可以使入射光能量主要分布在-1级透射光上，其衍射效率最大值高于97%。基于简化模式理论的分析表明，该衍射特性的物理本质源于双层光栅结构的非对称分布。在双层光栅结构中，上层光栅的两个偶对称分布光栅模式（简称偶模）在界面处将能量传输到第二层光栅的偶模和奇模中，由于奇模增强了光栅的-1级衍射，抑制了+1级的衍射，从而实现了-1级高衍射效率的效果。 |
| 英文摘要 | Gratings as key components have been widely used in modern optical systems, such as bioimage, high power laser systems, and grating spectrometer. For a high-density grating, we usually used the rigorous couple wave analysis or FDTD to calculate its diffraction efficiencies. But, these methods cost too long time to obtain accurate results, which is inconvenient for designing a grating. Fortunately, the simplified modal method not only offers physical insight for the diffraction process, but also gives us a useful design tool. However, the simplified modal method is only applied to rectangular grating, triangular grating and sinusoidal grating before. As for other grating profiles, we need to extend the application range of the simplified modal method. In this doctoral dissertation, we will apply the simplified modal method for the slanted grating, volume grating and double layers grating. Also, the simplified modal method is firstly introduced to interpret the Talbot effect: 1. Simplified modal method for the slanted grating. Because of the asymmetric structure of the slanted grating, the slanted grating can realize some special functions, which cannot be realized by a rectangular grating. So we will extend the simplified modal method for the slanted grating, which can be used as a guideline to design a slanted grating. Under the Bragg incidence, there are only two grating modes can be excited in the grating region, so the complicated diffraction process is very similar to the two-mode interferometers. Based on the two-beam interferometer, we can easily obtain the diffraction efficiencies. When the slanted grating is under the normal incidence, we find that the odd grating mode is also excited in the grating region, which can be attributed to the asymmetric structure. Because of existing of the odd grating mode, the electric field distribution is also asymmetric in the grating region. So the mode conversion and coupling can happen in a slanted grating, which can lead the mode to couple the energy into the first order. This is the physical reason of why a slanted grating can couple the energy into the first order. 2. Volume grating The simplified modal method is applied to the weakly modulation grating (holographic grating), which can show us a vividly physical image for the diffraction process. The simplified modal method can be used as a powerful tool to illustrate the relations among the depth, period, slanted angle, or the ratios among them and can give us an insightful physical image which cannot be obtained by a pure numerical method RCWA and Kogelnik’s coupled wave theory. Based on the two-beam interference, we can also obtain the expression of diffraction efficiency for the mismatch of Bragg angle or central wavelength. In the multi-modes region, the simple expressions can also be applied to the weakly modulation grating which has a big difference from the strong modulation grating. The mode splitting can occur in the holographic grating due to the perturbation of the weakly modulation. 3. Talbot effect Talbot effect is firstly observed in 1836 by Talbot, is a classical phenomenon. For a larger grating period, the Talbot effect is usually polarization-independent. For a high density grating, since the period is close to the wavelength, the diffraction process is polarization-dependent. So we have given a try that the polarization-independent Talbot effect exists for the high-density grating. We have designed a high-density grating which meets the conditions of polarization-independence. The near field distributions are same for both TE polarization and TM polarization. The simplified modal method, which has a vividly physical insight, is applyied to interpret the Talbot effect. In the grating region, there are only two even grating modes can be excited, so the diffraction properties can be determined by the interaction between the two even grating modes. We hope that the work laid in this paper can open a new realm of application of Talbot effect. 4. Double layers grating We report a novel optical structure of composite gratings that enables us to dynamically control the diffraction field. By tuning the gap and horizontal shift between composite gratings, the energy distribution into different orders can be controlled. For a particular example, the incident light can couple the mainly energy into the -1st order by this asymmetric structure under normal incidence. Significantly, we introduce the simplified modal method, which is a physical insight method, to illustrate diffraction process for tunable composite gratings. The physical reason of highly efficient -1st order is that the odd grating modes can also be excited in the asymmetric composite gratings, which plays the positive pole of enhancement for diffraction efficiency of -1st order. The controllability of diffraction field by the composite gratings opens a way to develop various active optical devices. We have extent the simplified modal method to the slanted grating, volume grating and double-layers grating. It will help us understand the diffraction process deeply. It offers us a new physical view to illustrate the complicated diffraction process. We believe that simplified modal method will attract more and more scientists’ interests. |
| 语种 | 中文 |
| 源URL | [http://ir.siom.ac.cn/handle/181231/15997]  |
| 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 | 李树斌. 简化模式方法在倾斜光栅中的应用[D]. 中国科学院上海光学精密机械研究所. 2016. |
入库方式： OAI收割
来源：上海光学精密机械研究所
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