Modal analysis of deep-etched low-contrast two-port beam splitter grating

Modal analysis of a deep-etched low-contrast two-port beam splitter grating under Littrow mounting is presented. The guideline for the design of a subwavelength transmission fused-silica phase grating as high-efficiency grating, polarizing beam splitter (PBS), and two-port beam splitter, is summarized. As an example, a polarization-independent two-port beam splitter grating is designed at wavelength of 1064 nm. We firstly analyzed the physical essence of the grating by the simplified modal method. The guideline for the grating design and the approximate grating parameters are obtained. Then using the rigorous coupled-wave analysis (RCWA) with parameters varying around the approximate ones, optimum grating parameters can be determined. With the design guideline, the time for the rigorous calculation of the grating profile parameters can be reduced significantly.     

共振域矩形介质光栅的逆向设计

采用模态法研究了共振域光栅分束器及闪耀光栅等光学器件的设计原理及逆向设计方法,给出了-1级非偏振闪耀光栅的典型设计示例。研究表明,自准直角入射时,光束在光栅内传输将激发产生离散模,通过调节离散模透过光栅传输时的累积相位差,可对衍射光进行调控,实现偏振(非偏振)分束、偏振(非偏振)闪耀等功能。采用严格耦合波法对基于模态法逆向设计的-1级非偏振石英闪耀光栅的几何参数进行验证,计算结果显示两者非常吻合,证明了该方法的正确性。     

Polarizing beam splitter of a deep-etched fused-silica grating

We described a highly efficient polarizing beam splitter (PBS) of a deep-etched binary-phase fused-silica grating, where TE- and TM-polarized waves are mainly diffracted in the -1st and 0th orders, respectively. To achieve a high extinction ratio and diffraction efficiency, the grating depth and period are optimized by using rigorous coupled-wave analysis, which can be well explained based on the modal method with effective indices of the modes for TE/TM polarization. Holographic recording technology and inductively coupled plasma etching are employed to fabricate the fused-silica PBS grating. Experimental results of diffraction efficiencies approaching 80% for a TE-polarized wave in the -1st order and more than 85% for a TM-polarized wave in the 0th order were obtained at a wavelength of 1550 nm. Because of its compact structure and simple fabrication process, which is suitable for mass reproduction, a deep-etched fused-silica grating as a PBS should be a useful device for practical applications.     

亚波长金属偏振分束光栅设计分析

结合有效介质理论和薄膜光学的抗反射设计方法,设计了基于0.65μm工作波长的亚波长金属偏振分束光栅,给出了光栅的优化设计参数,采用严格耦合波理论分析了光栅的偏振分束特性.结果表明,亚波长金属光栅对TE偏振表现为金属膜特性,具有高反射,对TM偏振表现为介质膜特性,具有高透射,在-30°<θ<30°的大入射角范围和0.47μm<λ<0.80μm的宽入射波谱内,该光栅的透射光和反射光均具有高偏振消光比和低插入损耗的特点. 关键词： 亚波长金属偏振分束光栅 有效介质理论 薄膜光学 严格耦合波理论     

Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm

We describe polarization-independent triangular-groove fused-silica gratings illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. The physical mechanisms of the grating can be shown clearly by using the simplified modal method with consideration of the corresponding accumulated average phase difference of two excited propagating grating modes, which illustrates that the grating structure depends mainly on the ratio of the average effective indices difference to the incident wavelength. Exact grating profile is optimized by using the rigorous coupled-wave analysis (RCWA). With the optimized grating parameters, the grating exhibits diffraction efficiencies of greater than 90% under TE- and TM-polarized incident lights for 101 nm spectral bandwidths (1500-1601 nm) and it can reach an efficiency of more than 99% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, coating of dielectric film layers, the designed triangular-groove fused-silica grating should be of great interest for DWDM application.     

The design of a polarizing beam splitter made from a dielectric rectangular-groove grating

It has been reported that a polarizing beam splitter based on a rectangular-groove grating (a grating polarizing beam splitter) can be easily designed for specific applications using the modal method. In this paper, the eigenvalue equation of the modal method is transformed to a new form. Using this new form of the eigenvalue equation, it is shown that the design of a grating polarizing beam splitter can be independent of the incident wavelength. The period and the groove depth can be designed using values normalized to the incident wavelength, which apply to a range of wavelengths as long as the effects of dispersion can be neglected. Numerical simulations of fused silica gratings are presented and analyzed. It is concluded that the preferable choice for the grating period is 0.8–0.9 times the incident wavelength.     

Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings

We investigated the use of a deep-etched fused-silica grating with triangular-shaped grooves as a highly efficient polarizing beam splitter (PBS). A triangular-groove PBS grating is designed at a wavelength of 1550 nm to be used in optical communication. When it is illuminated in Littrow mounting, the transmitted TE- and TM-polarized waves are mainly diffracted in the minus-first and zeroth orders, respectively. The design condition is based on the average differences of the grating mode indices, which is verified by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient over the C+L band range for both TE and TM polarizations (>97.68%). It is shown that such a triangular-groove PBS grating can exhibit a higher diffraction efficiency, a larger extinction ratio, and less reflection loss than the binary-phase fused-silica PBS grating.     

高密度相位光栅的偏振选择性

高密度光栅具有与传统光栅不同的性质,其衍射特性往往是偏振相关的。本文针对1550nm波长TE/TM偏振入射光和0.5的光栅占空比,利用严格耦合波分析数值计算了不同光栅周期下0级及-1级的衍射效率。研究表明,相比周期为1550nm的光栅,当周期为1200nm时,偏振相关衍射效应明显增强,当光栅周期为890nm时,TE偏振光的衍射效率随着光栅深度呈正余弦变化,而TM偏振光的衍射效率始终集中在0级,具有偏振选择性。通过模式方法,利用模式中的有效折射率概念,研究了不同周期下被入射光所激发的两种光波模式通过光栅区域传播所累积的相位差;基于双光束干涉,模拟了0级和-1级的衍射效率。结果表明,利用严格耦合波分析的数值计算结果符合模式方法的理论预期,对于高密度相位光栅的偏振选择性给予了合理的物理机制解释。     

Optimal design of sub-wavelength metal rectangular gratings for polarizing beam splitter based on effective medium theory

A novel optimal design of sub-wavelength metal rectangular gratings for the polarizing beam splitter (PBS) is proposed. The method is based on effective medium theory and the method of designing single layer antireflection coating. The polarization performance of PBS is discussed by rigorous couple-wave analysis (RCWA) method at a wavelength of 1550~nm. The result shows that sub-wavelength metal rectangular grating is characterized by a high reflectivity, like metal films for TE polarization, and high transmissivity, like dielectric films for TM polarization. The optimal design accords well with the results simulated by RCWA method.     

Metal-mirror-based grating for high-efficiency element in dense wavelength division multiplexing

It is desirable to obtain high efficiency with polarization-independence and wideband properties for incident wavelength. A metal-mirror-based grating is presented to diffract the incident wave into reflection orders with high efficiency for TE and TM polarization. The modal method and rigorous coupled-wave analysis (RCWA) are used together to optimize a metal-mirror-based grating effectively. From the analysis of the modal method, it is feasible to realize such a grating with the prescribed grating duty cycle and period. Accurate parameters of the grating depth and thickness of the connecting layer are optimized using RCWA. Compared with the reported binary simple grating, high efficiency can be improved greatly for the incident wavelength of 1550 nm in dense wavelength division multiplexing. The diffraction investigation indicates that a wideband property for incident wavelength can be obtained for such a novel metal-mirror-based grating.     

Polarization properties of subwavelength metallic gratings in visible light band

Optical polarization properties of aluminum, gold and aluminum/gold subwavelength metallic gratings (SWMGs) are investigated numerically in the visible light band. Their performance as polarizing beam splitters are simulated with RCWA for varied metallic materials, grating depth and incident angle. Metallic waveguide theory is applied to explain the performance difference between Au and Al grating. A new type of Al/Au bimetallic is also investigated numerically for potential applications. PACS 42.79.Dj; 42.81.Gs; 73.20.Mf     

Polarizing beam splitter of two-layer dielectric rectangular transmission gratings in Littrow mounting

We theoretically investigated the design of polarizing beam splitters (PBS) of two-layer dielectric rectangular transmission gratings in Littrow mounting. The PBS grating is aimed to separate TE and TM polarized waves into two different transmitted orders, i.e. the 0th and −1st orders. The polarization-dependent diffraction process is analyzed by using a simplified modal method. The mode reflection and transmission at the interface of the two layers are illustrated. Design equations are given based on the average mode indices of the even and odd modes inside the grating region, which are verified by using rigorous coupled wave analysis. Moreover, with simulated annealing algorithm, two kinds of two-layer PBS gratings are optimized for operation over the C-band (1520-1570 nm). Compared with the single-layer transmission PBS gratings, such two-layer scheme exhibits a great flexibility of design. The PBSs of two-layer dielectric transmission gratings should be useful for practical applications.     

Design of a 50/50 splitting ratio non-polarizing beam splitter based on the modal method with fused-silica transmission gratings

The optical design of a beam splitter that has a 50/50 splitting ratio regardless of the polarization is presented. The non-polarizing beam splitter (NPBS) is based on the fused-silica rectangular transmission gratings with high intensity tolerance. The modal method has been used to estimate the effective index of the modes excited in the grating region for TE and TM polarizations. If a phase difference equals an odd multiples of π/2 for the first two modes (i.e. modes 0 and 1), the incident light will be diffracted into the 0 and ?1 orders with about 50% and 50% diffraction efficiency for TM and TE polarizations, respectively.     

可见光波段双层浮雕型导模共振滤波器设计与分析

基于傅里叶模式理论分析了双层浮雕型导模共振光栅的共振效应,分别讨论了光栅的槽深、剩余厚度、周期以及填充系数对峰值反射率、带宽、旁带反射率的影响. 数据计算表明,欠刻蚀情形的误差宽容度远远优于过刻蚀情形,两者在光栅槽深相对误差小于15％的范围内,都能保证共振峰的衍射效率高于99.5%,在相同的误差范围内,共振峰线宽的相对误差将分别达到7％和60％,因此厚度误差集中反映在对共振线宽的改变上. 另外,光栅周期和填充系数的变化将明显改变共振峰中心波长和线宽. 关键词： 导模共振 平面波导 窄带滤波     

Deep silicon grating as high-extinction-ratio polarizing beam splitter

A deep binary silicon grating as high-extinction-ratio reflective polarizing beam splitter （PBS） at the wavelength of 1550 nm is presented. The design is based on the phenomenon of total internal reflection （TIR） by using the rigorous coupled wave analysis （RCWA）. The extinction ratio of the rectangular PBS grating can reach 2.5~105 with the optimum grating period of 397 nm and groove depth of 1.092 μm. The efficiencies of TM-polarized wave in the 0th order and TE-polarized wave in the -1st order can both reach unity at the Littrow angle. Holographic recording technology and inductively coupled plasma （ICP） etching could be used to fabricate the silicon PBS grating.     

Connecting-layer-based polarizing beam splitter grating with high efficiency for both TE and TM polarizations

We describe a novel polarizing beam splitter (PBS) of transmission connecting-layer-based grating, which can show high efficiency for TE polarization in the ?1st order and TM polarization in the 0th order. According to the modal method, grating duty cycle and period are prescribed to obtain high efficiency for TM polarization. Using the rigorous coupled-wave analysis, grating depth and thickness of the connecting layer are optimized to achieve high efficiency for TE polarization. The presented PBS has advantages of wideband properties for incident wavelength and angle. Most importantly, the efficiency is improved greatly for TE polarization compared with the reported PBS based on fused-silica grating.     

基于亚波长偏振光栅的偏振光分束器设计

利用琼斯矩阵和矢量傅里叶系数方法分析了二元亚波长偏振光栅的偏振特性和衍射效率,并给出了相应的数学解析式.研究发现,通过入射光的偏振可以控制不同衍射输出级的偏振态,且0级输入偏振态与输出偏振态始终相同,而其它级次除线偏光外都与入射偏振态相反.当二元亚波长偏振光栅的位相延迟分别设置为0.62π和π时,可以将二元亚波长偏振光栅设计为1→3或1→2的偏振光分束器,且分束器具有衍射效率高、宽带宽、对入射角的变化不甚敏感的特点.     

非对称偏振分束光栅的矢量衍射优化设计

基于严格耦合波理论分析了一种非对称偏振分束光栅的设计。这种偏振分束光栅分别在1级和0级衍射级次上衍射TE和TM偏振波。介绍了利用遗传算法设计偏振分束光栅的方法,并给出了优化实例。仿真结果表明:在设计波长为1.55时,TE偏振波在1级的衍射效率大于93%,TM偏振波在0级的衍射效率大于99%,此时1级和0级的透射消光比分别达到了9914.1和46841.5。通过对设计结果的分析发现,该偏振分束光栅在设计波长附近100nm的波长范围内都具有较高的消光比(大于100),达到了较好的偏振分束效果。     

滑动盖板对一维微尺度光栅红外辐射特性影响

电磁波入射到微尺度周期性结构表面时,一定条件下将在某一波段产生异常光吸收现象。基于该特性,本文提出了单边移动盖板光栅和双边移动盖板光栅两种光栅结构,并使用严格耦合波分析(RCWA)方法对TM波垂直入射的一维微尺度光栅表面辐射特性进行了分析,研究了滑动盖板的厚度和位置对光栅表面结构辐射特性的影响。结果表明,相同盖板厚度,双边移动盖板光栅形成的发射率峰较单边移动盖板光栅形成的发射率峰具有较宽的半高全宽(FWHM),但峰值较低;随盖板向关闭侧移动,高发射率峰对应波长向长波方向移动;随盖板厚度增加,发射率峰向长波方向移动,其中双边移动盖板光栅结构形成的发射率峰变宽,峰值变小。     

厄米-高斯光束通过正弦和矩形浮雕光栅传输特性的比较研究

使用严格的傅里叶模式理论和反射-透射系数矩阵递推算法(RTCM)，对不同阶数的厄米-高斯光束通过特征尺寸与波长可比拟的正弦和矩形浮雕光栅中的传输特性做了详细的研究和比较.结果表明，入射光束的初始场分布和浮雕光栅的结构影响浮雕光栅内的光强分布.矩形浮雕光栅对光束匀滑效果优于正弦形浮雕光栅.