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图 1为由N个阵元组成的1维光学相控阵。
所提出的设计方法是将第i个和第i+1个阵元之间的间隔Si(1≤i≤N-1)通过余弦函数得到:
$ {S_i} = A\left[{B-C\cos \left( {D \times i \times 2\pi /N} \right)} \right] $
(1) 式中,A为长度单位,用来确定间隔与波长的量级关系; B,C,D均为无量纲量,其中,A×B为间隔的中间值,A×C为变化范围,D用来改变空间频率,N为波导数。这种阵列可以看成间隔值为A×B的均匀阵列被施加余弦形式的微扰得到的,由于周期性被破坏,任意方向θ上的远场总振幅不再遵守简单的表达式[11],而应表示为[15]:
$ E\left( \theta \right) = \sum\limits_{N = 0}^{N- 1} {\exp \left[{{\rm{j}}\frac{{2\pi }}{\lambda }\sum\limits_{i = 0}^{N-1} {{S_i}\left( {\sin \theta-\sin {\theta _0}} \right)} } \right]} $
(2) 式中,λ和θ0分别表示工作波长和光束扫描角度。
如图 2所示,考虑N=16,图 2a中解释了所设计的1×16光学相控阵原理。主要关键元件有:由1×4多模干涉耦合器2阶级联组成的1×16分束器、16个独立控制的调制器、S形弯曲波导组成的过渡区和相位补偿区、间隔余弦分布的输出波导阵列。使用SOI平台设计的好处之一在于Si(折射率nSi=3.47)和SiO2(折射率nSiO2=1.45)有很高的折射率对比度,另外,考虑到结构紧凑性,所有的光学器件均为矩形波导。输入光选用1.55μm的TE偏振,因为它比TM偏振光具有更高的光束限制[10],此条件下,采用的矩形波导的单模横截面结构和对应的TE偏振基模如图 2b所示。
TE偏振光通过输入波导耦合到光路,被光束分束器均匀地分到16个通道中,之所以用多模干涉耦合器而不用星形耦合器,是因为多模干涉耦合器分束更加均匀[9]。以最小化多模干涉耦合器的相位误差[16]为目标,优化输入和输出波导为2.40μm。然后光束经过线性变化的锥形结构变为单模传输。接下来,采用的调制器为独立控制,这样,每一个通道所应施加的相位均可以通过对2π取余得到。
光路中的S形弯曲波导[17]有两个作用:一是作为过渡区改变传输方向,连接1阶和2阶多模干涉耦合器以及调制器和输出波导阵列; 另一个是当调制器没有施加任何操作时,补偿由1×4多模干涉耦合器因输出波导位置不同[16]和两个过渡区带来的各支路相位差,以标准化器件,使光束不发生偏转,指向0°方向。
当(1)式中的A=λ,B=3.5,C=2,D=1,N=16时,输出波导阵列位置分布即为图中所示,相邻间隔的最小值为2.56μm,足以避免波导之间的耦合现象,总的横向尺寸为84.48μm。
基于波导间隔余弦分布的光学相控阵研究
Study on optical phased arrays based on waveguide spaced cosine distribution
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摘要: 为了提高稀疏光学相控阵的精度和效率,采用输出波导间隔成余弦分布的结构,基于绝缘体上硅平台设计出1×16光学相控阵; 结合有效折射率法和2-D有限差分传播法进行了远场强度分布仿真模拟。结果表明,边瓣抑制比从89.72%减小到41.46%,主瓣半峰全宽从1.20°被压缩到0.81°; 这种设计方法能够显著抑制栅瓣,进一步压缩主瓣。该研究在机器人避障、无人驾驶、目标探测等光束偏转领域将有广泛的应用前景。Abstract: In order to improve the precision and efficiency of sparse optical phased array, 1×16 optical phased array was designed based on silicon-on-insulator(SOI) platform by using the structure of spaced cosine distribution of output waveguides. Combining the effective refractive index method and 2-D finite difference beam propagation method, the far-field intensity distribution was simulated. The results show that, the side lobe suppression ratio decreases to 41.46% from 89.72%, and the full width at half maximum of the main lobe is compressed to 0.81° from 1.20°. This design method can significantly suppress the grating lobes and further compress the main lobe, and has a promising future in the field of beam deflection, such as robot obstacle avoidance, pilotless, target detection and so on.
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