【作者】 王斌；

【导师】 吴一辉；

【作者基本信息】 中国科学院研究生院(长春光学精密机械与物理研究所) ， 机械制造及其自动化， 2014， 博士

【摘要】 亚波长介质光栅是伴随纳米制造技术发展起来的一种新型光栅。它具有高衍射效率的特点，因此在光通讯、光计算、全息摄影、光学度量、激光脉冲压缩等光学元器件中有重要应用,相关研究受到广泛关注。为提高亚波长介质光栅设计的计算效率，提高其结构性能的可预见性，本文重点开展了其简化算法的研究。在对影响严格耦合波法（RCWA）计算精度的因素进行分析的基础上，提出采用该方法所获光栅衍射效率作为光栅设计理论值的条件及误差参考。对已有简化模式法（SMM）进行了深入分析并与RCWA计算结果进行了对比研究，找到了已有的SMM算法计算误差较大的原因；以三角形介质光栅为例，提出了一种从多层膜反射和薄膜导纳刻画各个模式反射率的修正算法（MSMM），利用该新型物理模型修正后的计算结果与RCWA的计算结果对比分析表明，修正后的MSMM方法与RCWA的计算偏差大大缩小。利用该方法，通过计算光栅导纳随光栅周期的变化规律，分别对矩形和三角形光栅的衍射效率进行了研究。矩形光栅导纳随着占宽比变化仅在空气导纳附近较小范围内，说明亚波长矩形介质光栅的反射率和光栅的占宽比相关性较小；通过分析得出矩形介质光栅无法得到接近100%的透射效率。给出了入射角一定的情况下，不同周期的三角形光栅反射率的变化规律。以此为基础设计出TE偏振和TM偏振同时能达到衍射效率超过99.9%的三角形介质光栅。应用MSMM分析了光栅衍射效率和光栅结构参数之间的关系，并优化设计出双端口光栅分束器。研究了光栅的矩形结构、三角形结构在偏振无关、偏振相关情形下的分束性能。设计得到的偏振无关光栅分束器在1020nm-1100nm波段，TE波和TM波的0级和-１级衍射效率都在50%左右；偏振相关分束器在该波段的消光比也都在10以上。对于亚波长三角形、正弦形和矩形介质光栅，该方法将衍射效率表达成相位差偏移和光栅与空气导纳之差引起的反射，比RCWA更直观的展示了光栅衍射的物理过程。相比只提供初值的SMM，MSMM可以直接用来进行优化计算。因此该算法对于加深对该类介质光栅的认识以及设计优化具有积极作用。更多还原

【Abstract】 Dielectric subwavelength grating is a new type grating developing with evolutionof nano technology. Because of high efficiency, it is used frequently in opticalcommunication, computation, metrology, holography, laser pulse compression andso on. Many researchers focused on this issue. For the purpose of increasing thespeed of calculation in designing dielectric subwavelength gratings and giving agood prediction of grating structure, the simplified method will be researched in thispaper.In this paper, the factors of computational accuracy are analyzed when therigorous coupled wave analysis (RCWA) method is used to design a grating. Thisanalysis shows the result that RCWA could be used to be a reference as a theoreticalvalue for other algorithm in grating design.The simplified modal method (SMM) is analyzed and the deviation betweenSMM and RCWA is calculated to find the reason of its big error. Take a triangulargrating as an example, which is seen as multilayer films and the each layer owns anew effective index. The reflection and transmission of grating could becharacterized by optical admittance of the films. Then formulas of gratingtransmission in SMM are modified by reflection. The calculation by this modifiedsimplified modal method (MSMM) is a better approximation to RCWA than othermethods. Based on MSMM, for a rectangular grating, although the admittance changeswith duty cycle, its variation range is very near the admittance of air. This means thereflection of rectangular grating will not change a lot when duty cycle is changed.And a rectangular grating cann’t get transmission efficiency near100%. Then themode indices and admittance versus the period of triangular gratings and the dutycycle of rectangular grating are analyzed. A grating with transmission efficiencymore than99.9%for both TE and TM-polarized light is designed.The relations between grating structure and transmission efficiency areanalyzed by MSMM. The splitting result of rectangular and triangular grating areanalyzed for both TE and TM polarization.Based on these calculations,1×2beamsplitters are designed and optimized by MSMM. A polarization-independent splittergrating will get a good splitting result at the band1020nm-1100nm. Thetransmission efficiency of0th and-1st order for both TE and TM polarization is nearto50%at this band. The extinction ratio of a polarization-dependent splitter is biggerthan10at this band.Contrast to RCWA, MSMM gives a clear physical explanation of gratingdiffraction by considering the transmission efficiency as the result of phase shift ofmodes and difference of grating admittance and aerial admittance. This method canbe applicable to triangular, sinusoidal and rectangular gratings. Because it can beused to optimize the grating parameters directly, MSMM is better than SMM whichonly gives starting value of grating parameters. Thus MSMM gives a goodunderstanding on dielectric subwavelength gratings and is useful in designing andoptimizing them.更多还原