二次布拉格角入射下深刻蚀亚波长光栅的简化模式分析
文献类型：学位论文
| 作者 | 孙竹梅 |
| 学位类别 | 硕士 |
| 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 | 严格耦合波方法 简化模式方法 光栅分束器的归一化设计 二次布拉格角入射 深刻蚀亚波长光栅 |
| 其他题名 | Simplified modal analysis of deep-etched subwavelength gratings under second Bragg incidence |
| 中文摘要 | 本论文主要以亚波长光栅为研究对象，分析了二阶布拉格角入射下光栅的衍射特性及其应用。二阶布拉格角入射下，当光栅周期是入射光波长的1-2 倍时，只存在三个透射衍射级，并且光栅区域中只有限个数的传播模式（通常为三个，本文也涉及了四个光栅模式的情况）被激发，传播模式的有效折射率差和光栅深度决定了光栅各个衍射级的衍射效率。亚波长光栅的这种独特的衍射特性可以大大简化其理论分析，为新型光学器件的设计奠定了理论基础。本硕士论文主要包含以下几个方面的工作： a) 基于亚波长深刻蚀石英光栅衍射的物理机制，提出了二次布拉格角入射下矩形光栅的归一化设计方法。根据简化模式理论，二次布拉格角入射下，矩形光栅的衍射通常可通过三个传播的光栅模式的干涉来分析。对于低对比度光栅（光栅脊与沟槽的有效折射率之比小于2），光栅模式在不同介质的界面处的反射可以忽略，只需要分析前向传播的光栅模式。由于倏逝波模式与入射光的耦合效率低，并且在传播方向上呈指数衰减，在深刻蚀光栅中，可以忽略倏逝波模式对衍射过程的影响，只需通过分析被入射光激发的传播模式之间的能量耦合过程，即可揭示光栅衍射的物理过程。通过分析入射光，传播模式和衍射级次的顺序耦合，可以获得光栅各级次衍射效率的解析表达式，从而指导深刻蚀光栅的设计，简化了光栅的设计过程。我们基于简化模式方法，分析了不同工作波长下，光栅参数和入射光的偏振方向对光栅衍射效率和分束比的影响，得出光栅的衍射效率取决于光栅的相对参数，即光栅的实际长度参数与工作波长的比值，而非绝对光栅参数。据此，如果针对光栅的某一功能设计一组相对光栅参数，根据光栅的实际工作波长对这些参数进行缩放，即可将同一光栅参数设计值应用于不同的工作波长的光栅设计中，有效的避免了重复性计算，对工程技术人员具有重要的指导意义。此外，该方法也为光栅带宽特性的分析提供了便捷方法。 b) 在归一化方法的指导下，我们设计了二阶布拉格角入射下的 1×2 分束器，并且研究了该分束器的偏振特性。通过分析光栅参数和入射光的偏振方向对光栅衍射效率的影响，给出了二次布拉格角入射下，1×2分束光栅设计的经验公式。该工作发表在 [JOSA A, Vol. 32, 1952-1957 (2015)] 上。此外，归一化的简化模式理论也可以指导双功能偏振选择分束光栅的设计，据此设计了二次布拉格角入射下，对 TM 偏振光能实现 1×2 分束、对 TE 偏振光能实现 -2 级高效率衍射的偏振选择光栅分束器，并分析了光栅参数的制造容差。此外，研究了光栅模式有效折射率分布的特点，并发现：在 TM 偏振光入射下，存在使得光栅模式1和光栅模式2的有效折射率相等的光栅参数（光栅相对周期和占空比）；在另一些特定的光栅参数下，TE 和 TM 偏振光激发的光栅模式1和光栅模式2的有效折射率均相等。据此，设计了对 TE 偏振光实现 1×2 分束、对 TM 偏振光实现 0 级高透过率的偏振选择光栅分束器，并给出了其他形式的高效率双功能光栅的设计法则。 c) 分析了二次布拉格角入射下双层光栅的衍射特性。光栅的衍射过程在本结构中可以描述如下：入射光场与第一层光栅模式在入射界面的发生耦合，随后第一层光栅中的模式传播到两层光栅的界面，将能量耦合到第二层光栅模式中，第二层光栅模式传播到出射界面与透射衍射级耦合，根据此过程可以求得光栅的衍射效率。通过分析光栅模式的奇偶对称性，可以进一步简化该方法的求解过程。在该方法的基础上，我们设计了 TM 偏振光入射下 -2级高衍射效率宽带双层光栅分束器，分析了通过简化模式方法和严格耦合波方法求得的光栅衍射效率的差异的产生原因，指出了倏逝波在光栅相对深度小于倏逝深度时对光栅衍射效率的影响。由于光栅模式的奇偶对称性对该方法的分析过程中具有重大影响，因此我们分析了不同光栅相对周期和占空比下，TE 偏振光和TM 偏振光入射时光栅模式的奇偶对称性分布，并得到如下结论：对任意偏振光入射时，若光栅参数在使得光栅模式有效折射率相等的光栅参数对的两侧，相应的光栅模式的奇偶性发生改变。由于光栅模式的耦合仅存在于奇偶对称性相同的光栅模式中，因此，通过分析上下两层光栅中被激发的光栅模式的奇偶性，不仅可以对光栅内部能量的传播及分布有进一步的认识，还可以简化光栅衍射效率的计算。 本硕士论文，包括了深刻蚀石英光栅的归一化简化模式分析、单层及双层光栅分束器设计和光栅模式特性分析等方面的主要研究结果。这些工作将进一步加深科研工作者对亚波长光栅衍射过程的理解，大大简化了光栅的设计过程，有利于新型光栅在实际生产中的推广。 |
| 英文摘要 | For high-density fused silica gratings under second Bragg incidence, only several (usually three) propagating grating modes are excited. When the period of the grating is in the range of one to two times of the wavelength, only three transmitted diffraction orders are supported by the structure. These unique properties of subwavelength grating ultimately simplify the analysis process, paving a solid way for the theoretical design of novel polarization-related beam splitters using high-density fused silica gratings. Several research aspects on this topic are included in this master dissertation: a) Based on the physical process of the diffraction induced by deep-etched subwavelength gratings, we proposed the unified design method for the analysis of dielectric rectangular gratings under second Bragg incidence. For a low-contrast grating (typically, index ratio of the ridge and the groove is smaller than 2), the backward propagating modes and the consequent multiple reflection effect can be reasonably neglected. For gratings whose depth is larger than the incident wavelength, the diffraction could be described by the coupling of the propagating grating modes, as the evanescent modes are weakly excited and their energies decay exponentially along the propagation to the exit surface. As mentioned above, only three modes are excited, therefore, the diffraction process could be reasonably described by the interference of these forward propagating modes. Based on simplified modal method, we thoroughly analyzed the dependence of the diffraction efficiency and splitting property on grating parameters under different incident wavelength, yielding that the diffraction efficiency of different diffracted orders essentially depends on the relative grating parameters instead of the absolute ones. The relative grating parameters are defined as the ratio of the absolute grating parameters to the incident wavelength. Based on the above modal description, the value of the effective index is determined by the relative period and duty cycle. Combined with optimized relative depth, various diffraction patterns could be obtained. The benefits of this method are studied in detail in this paper. When applied to different wavelengths, a definite diffraction pattern could be achieved by simply scaling the grating parameters while keeping the set of the optimized relative grating parameters steady, which would definitely reduce the computational expense during optimization process. Besides, this method provides a concise way to obtain the bandwidth for a grating working under any specified wavelengths. b) On the basis of the unified modal method, gratings with even splitting pattern under second Bragg incidence are explicitly presented, and the relative grating parameters are then optimized according to RCWA method. The dependence of splitting properties on the polarization of incident light and relative grating parameters is minutely studied. Further, the quantitative relationships among grating parameters are revealed in two empirical equations, thus making the realization of the desired function suitable for various circumstances without complicated and repetitive calculation. Besides, the distinctions of the performance between TE and TM polarized light are intensively studied using SMM and RCWA, and the results from these two methods are unanimous. Two gratings with specific duty cycles are optimized for TE and TM polarization respectively to achieve even split and high diffraction efficiency, and the fabrication tolerance of duty cycle and relative depth are discussed for gratings with the optimized parameters. This work is published on [JOSA A, Vol. 32, 1952-1957 (2015)]. Besides, based on the unified modal method, we design a dual-function polarization-selected beam splitter under second Bragg incidence, functioning as a two-port beam splitter for TM polarization and as a grating with highly efficient -2nd diffraction order for TE polarization. Then we focus on the study of the properties of the modes excited in the grating region by TE and TM polarized light. For gratings with specific relative grating period and duty cycle, the second and third grating modes excited by TM polarized light share equal effective indices, while for some other parameter pairs, the effective indices of the second and third modes excited by TE and TM polarized incident light are all the same. We elaborate these gating parameters and the effective indices of the excited grating modes. With these data in hand, we design another dual function beam splitter under second Bragg incidence, which works as a two-port beam splitter for TE polarization and a highly efficient transmission grating for TM polarization. Grounded on the grating parameters for the special effective mode indices and that for the two port beam splitters described above, we could basically design various dual function grating splitters, and the general rules are specified in this paper. c) To better the diffraction properties and enrich the grating design, we study the diffraction of the two-layer grating under second Bragg incidence. The diffraction process is described by the energy flow in the grating region as follows: the energy of the incident light is coupled to the grating modes in the first layer at the incident plane, then modes in the first layer propagate to the interface between the first and second grating layers, coupling to the modes in the second layer, finally the energy carried by the modes in the second layer reach the exit surface and coupled to the diffraction orders. By calculating the coupling coefficients and the effective index of the grating modes, we could easily obtain the efficiency of the diffraction orders. In this method, the reflection of the grating modes at the interface of the grating layers is neglected. The difference between the calculated efficiencies obtained from this method and that from rigorous coupled wave analysis is ascribed to the evanescent modes excited in the second grating layer as the relative depth of this layer is smaller than 0.5 in our design. Specifically, the coupling of the field only happens between modes, incident or transmitted fields with same odd-even symmetrical distribution. By further studying the symmetry of the grating modes, we could make the proposed method even simpler. The reverse of the symmetry of the grating modes happens at the points of the grating parameter pairs (relative period and duty cycle) where the effective indices of the corresponding grating modes are equal. This dissertation includes my main research on unified simplified modal method, single-layer and dual-layer grating beam splitters, and the analysis of the excited grating modes. This work will enrich our understanding of the diffraction process for gratings under second Bragg incidence, and simplify the design process, which would finally benefit the practical applications of novel high-performance grating beam splitters. |
| 语种 | 中文 |
| 源URL | [http://ir.siom.ac.cn/handle/181231/17020]  |
| 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 | 孙竹梅. 二次布拉格角入射下深刻蚀亚波长光栅的简化模式分析[D]. 中国科学院上海光学精密机械研究所. 2016. |
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来源：上海光学精密机械研究所
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