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光栅耦合器天线是通过在波导中引入周期性刻槽结构,利用光栅布拉格衍射条件将波导中的光信号输出到自由空间中。
光学相控阵远场整体能量分布取决于每个天线阵元的向上衍射效率。当输入光进入光栅结构中时,如图1所示,将入射光波总能量记为Pin,由于光栅为周期性结构,使得折射率不连续,光波在传播方向上会有部分的反射和透射能量,分别记为Pback和Pt。其余能量由于结构对称性,会分别存在向自由空间中以及衬底的衍射分量,分别记为Pup和Pdown。
天线单元的向上衍射效率为天线向上衍射能量与总进入能量的比值:
$$\eta {\rm{ = }}\frac{{{P_{\rm up}}}}{{{P_{\rm in}}}}$$ (1) 向上衍射效率越高,天线输出能量越大,天线性能越好。对传统周期性刻蚀光栅结构,由于结构对称,根据布拉格衍射条件,光波向上衍射效率与向下衍射效率相同。因此,为了提高向上衍射效率,需要打破天线上下结构对称性,使得光波经天线单元后向上为相长干涉,向下为相消干涉。
又由衍射公式可知,单个天线的衍射因子为:
$${{D = }}\sin {c^2}\left( {\frac{{\pi a}}{\lambda }\sin \theta } \right)$$ (2) 式中:a为天线的尺寸。由上式可知天线尺寸越小,天线的远场衍射角就越大。同时考虑到阵元间隔需要尽可能小,因此对天线的设计要求之一便是尽可能减小其尺寸。为了保证光栅尺寸足够小,设计时需要尽量减少光栅的周期数,但是光栅周期数若过少则会降低其向上的辐射效率。因此需要兼顾较高的辐射效率与较小的尺寸,同时光栅的辐射场需要保证较为圆整。
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在MIT的方案中,采用五个光栅齿进行刻蚀,周期为0.72 μm,通过第一级浅刻蚀的方法增强向上衍射效率。参考文献[10]中提出,在直波导天线中,利用L型蚀刻加矩形支柱的周期性闪耀光栅结构,实现了极高的向上衍射效率。借鉴该研究思路,提出在扇形光栅结构中插入硅薄带,增加浅刻蚀区域,以期实现高天线发射效率。具体天线模型结构参数如图2 (a)所示,在原有设计理念的基础上,使用厚度为300 nm、折射率为3.48的硅芯层设计,增加了光栅散射强度,可以减少实现目标效率所需的周期数。中间层和上包层使用厚度均为2 μm、折射率为1.45的二氧化硅。硅衬底厚度对耦合性能影响极小,因此在仿真过程中使用2 μm的硅材料。硅芯层天线结构如图2 (b)所示,光栅周期选择为720 nm,其中光栅齿宽200 nm,齿间完全刻蚀区域宽度为370 nm。
图 2 天线模型。(a)波导结构; (b)波导芯层天线结构
Figure 2. Schematic diagram of waveguide structure. (a) Waveguide structure; (b) Waveguide core antenna structure
在确定基本结构的基础上,需要对缓冲区域半径R、光栅齿级数N1、浅刻蚀级数N2、浅刻蚀区域宽度W、浅刻蚀深度D、插入硅薄带位置P和硅薄带厚度T等七个变量进行优化。
对于光栅齿级数N1,浅刻蚀级数N2和硅薄带位置P,涉及到的数据点较少,因此采用列举法进行分析。
光栅齿级数N1受限于天线尺寸,级数过多会导致天线尺寸变大,天线远场衍射角减小,级数过少会导致光场能量逸散过多。因此分别考虑N1=3、N1=4和N1=5的光栅齿结构设计,分析其衍射效率变化,如表1所示。
表 1 光栅齿级数对衍射效率的影响
Table 1. Influence of number of grating teeth on diffraction efficiency
Number of grating teeth 3 4 5 Upward diffraction 57.2% 69.4% 71.6% Downward diffraction 9.6% 8.1% 8% Back reflection 6.2% 6.1% 5.8% Total incident energy 94% 93.7% 92.1% 根据表1可得,在其他参数固定的情况下,光栅齿数量越多,天线衍射效率越高。因此在对天线单元尺寸要求较高的情况下,可以考虑减少光栅齿数量,通过牺牲部分衍射效率来达到天线小型化的要求。
对于浅刻蚀级数N2
,在MIT的方案中,仅使用一级浅刻蚀结构实现了对向下衍射损失的有效抑制,增加了向上衍射效率。考虑利用多级浅刻蚀的方式来分析对天线衍射效率的影响,分别针对N2=1、N2=2、N2=3和N2=4的光栅结构进行了如图3所示的分析。 图 3 不同级数浅刻蚀对衍射效率的影响。(a)向上衍射;(b)向下衍射;(c)背反射;(d)总入射
Figure 3. Effect of different orders of shallow etching on diffraction efficiency. (a) Upward diffraction; (b) Downward diffraction; (c) Back reflection; (d) Total incidence
根据图3中数据分析得出,加入光栅浅刻蚀可以显著减少天线向下衍射损失,且浅刻蚀级数越多,天线向上衍射的效率就越高。
在此基础上,在其他参量固定的情况下考虑插入硅薄带,不同硅薄带位置对天线衍射效率的影响如表2所示。
表 2 硅薄带位置对天线衍射效率影响
Table 2. Influence of the position of the silicon ribbon on the diffraction efficiency of the antenna
Silicon ribbon position Don't insert Among 1, 2 teeth Among 1, 2, 3 teeth Among 1, 2, 3, 4 teeth Upward diffraction 68.2% 78.8% 77.8% 75.1% Downward diffraction 5.8% 4.1% 5.2% 4.6% Back reflection 6.2% 1.5% 1.23% 1% Total incident energy 91.3% 95.2% 95.7% 95.9% 从表2中的数据得出,插入硅薄带能够显著抑制天线背反射,增加向上衍射效率。然而插入多级硅薄带后,天线向上衍射效率相比于插入一级硅薄带出现了一定程度的下降,这里提取光信号传播过程进行分析。
如图4所示,光信号在传播过程中,能量主要集中在一、二级光栅齿,因此在其他齿间插入硅薄带会使得插入的其他能量损失大于增益,反而使得衍射效率降低,综合考虑仅在一、二级光栅齿间插入硅薄带。
对于缓冲区域半径R、浅刻蚀区域宽度W、浅刻蚀深度D和硅薄带厚度T,涉及到数据点较多,采用梯度下降算法原理进行优化分析。
定义天线向上衍射效率为函数
$\eta $ ,$\eta $ 为R、W、D、T的函数,首先确定基础值${\varTheta ^0}{\rm{ = }}\left( {{R_0},{W_0},{D_0},{T_0}} \right)$ ,初始学习率$\alpha $ ,梯度$\nabla {\rm{ = }}\left( {\dfrac{{\partial \eta }}{{\partial R}},\dfrac{{\partial \eta }}{{\partial W}},\dfrac{{\partial \eta }}{{\partial D}},\dfrac{{\partial \eta }}{{\partial T}}} \right)$ ,由此推出下一个数据点${\varTheta ^1} = {\varTheta ^0} + \alpha \nabla \eta \left( {{\varTheta ^0}} \right)$ ,依次迭代,结合仿真分析推导最大向上衍射效率对应的最优解。在优化过程中,发现在一定范围内,天线单元向上衍射效率与光栅齿长度成正比关系,但是增加光栅齿长度意味着要增大天线单元尺寸,因此在实际应用过程中可以根据对天线尺寸以及衍射效率的不同需求进行取舍。文中在保证相对优越天线性能的前提下,分别针对该天线单元减小设计尺寸和提高向上衍射效率的设计要求提出了两种设计方案。
第一种方案为天线小型化设计,如图5所示,该结构使用三级光栅结构,同时减小了光栅齿长度,以2.44 μm×2.72 μm的尺寸实现了在1550 nm波段67.2%的向上衍射效率,向下能量损失为5.6%,向后背反射损失为1.2%。
第二种方案为天线高衍射效率实现方案,结构如图6所示,该结构使用五级光栅,同时增加了光栅齿长度,以3.68 μm×4.17 μm的尺寸实现了在1550 nm波段81.6%的向上衍射效率,向下衍射损失为4%,背反射损失为1.1%。
影响天线输出耦合效率的一个关键因素是天线出射光场的聚焦度,在光学相控阵芯片与光纤进行耦合的过程中,光场能量越集中,与光纤耦合效率就越高,而弯曲波导光栅可以使光聚焦到光子线上,实现对光场的有效聚焦。将小型化天线结构与高衍射效率结构的远场光斑形态和能量分布进行了对比分析,如图7所示。
对比两种结构的远场分布图,得出扇形天线结构的远场分布均呈现规整的圆形或椭圆形分布,实现了对光波能量较好的汇聚作用。小型化方案中远场呈圆形分布,光场主要集中在20°远场范围内。而高衍射效率方案远场呈椭圆分布,长轴光场主要集中在远场15°范围内,短轴光场主要集中在10°远场范围内。高的能量集中度为天线与光纤的高耦合效率提供了可靠的保障。
Optimal design of silicon-based optical phased array sector antenna
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摘要: 在光学相控阵芯片中,天线单元的性能直接决定了波导中光波能量向外辐射的效率。在此基础上,主要针对扇形结构天线进行优化设计,通过对扇形天线增加浅刻蚀区域和硅薄带的设计,对天线向下衍射损失以及背反射损失进行了抑制,大幅提高了天线向上衍射效率。此外,分别对提高向上衍射效率和减小设计尺寸的设计要求制定了设计方案,对于高衍射效率方案,天线向上衍射效率达到81.6%,向下衍射减少到4%,背反射减少到1.4%;对于小型化方案,天线向上衍射效率达到67.2%,向下衍射减少到5.6%,背反射减少到1.2%,大幅提高了光学相控阵芯片集成度及发射效率。Abstract: In the optical phased array chip, the performance of the antenna unit directly determines the efficiency of the light wave energy in the waveguide to radiate outward. On this basis, the optimized design was mainly for the sector antenna. By adding a shallow etching area and a thin silicon strip to the sector antenna, the downward diffraction loss and back reflection loss of the antenna were suppressed, as well as the upward diffraction of the antenna was greatly improved. In addition, design schemes were formulated for the design requirements of improving the upward diffraction efficiency and reducing the design size. For the high diffraction efficiency scheme, the upward diffraction efficiency of the antenna reached 81.6%, the downward diffraction efficiency was reduced to 4%, and the back reflection was reduced to 1.4%. For the miniaturization scheme, the upward diffraction efficiency of the antenna was 67.2%, the downward diffraction was reduced to 5.6%, and the back reflection was reduced to 1.2%, which greatly improved the integration and emission efficiency of the optical phased array chip.
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表 1 光栅齿级数对衍射效率的影响
Table 1. Influence of number of grating teeth on diffraction efficiency
Number of grating teeth 3 4 5 Upward diffraction 57.2% 69.4% 71.6% Downward diffraction 9.6% 8.1% 8% Back reflection 6.2% 6.1% 5.8% Total incident energy 94% 93.7% 92.1% 表 2 硅薄带位置对天线衍射效率影响
Table 2. Influence of the position of the silicon ribbon on the diffraction efficiency of the antenna
Silicon ribbon position Don't insert Among 1, 2 teeth Among 1, 2, 3 teeth Among 1, 2, 3, 4 teeth Upward diffraction 68.2% 78.8% 77.8% 75.1% Downward diffraction 5.8% 4.1% 5.2% 4.6% Back reflection 6.2% 1.5% 1.23% 1% Total incident energy 91.3% 95.2% 95.7% 95.9% -
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