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相控阵天线系统中波束形成网络的核心技术之一是微波信号的移相，然而电子移相技术中孔径效应和渡越时间限制了系统工作带宽[1]。基于光真延时(optical true time delay，OTTD)的光波束形成网络(optical beamforming network，OBFN)克服了孔径效应和渡越时间的限制，具有工作带宽大、重量轻、损耗低和抗电磁干扰等优势，因而成为相控阵天线系统领域的研究热点[2-4]。
光真延时网络作为光波束形成网络的核心部件受到了广泛关注，研究人员提出了多种技术实现OTTD，包括空间光调制技术[5-6]、光程切换技术[7-9]和光学色散技术[10-15]等。空间调制技术有利于实现集成化和空间多波束，但工作带宽受调制方式限制。光程切换技术具有结构简单的优势，但存在使用器件多和性能受开关指标限制的问题。光学色散技术通过控制光载波实现波束扫描，降低了系统中器件的数量和结构的复杂度，成为了具有吸引力的技术方案。基于光学色散技术的OTTD可以基于光学微环[10-11]、高色散光纤[12-13]、线性啁啾光栅[14-15]等器件实现。然而，基于光学微环的OTTD存在工作带宽限制；基于高色散光纤的OTTD可以实现大范围等延时差切换，但难以实现小步进调谐；基于线性啁啾光纤光栅的OTTD可以实现小步进等延时差调谐，但难以实现大范围切换。同时，基于高色散光纤和线性啁啾光纤光栅等色散器件的OTTD通常采用激光器波长调谐实现波束扫描，受激光器扫描速度限制。
为解决上述技术难题，本文中采用固定波长间隔的多波长激光器和光学色散器件实现OBFN中的核心部件OTTD。通过光开关实现N路高色散光纤路径切换获得大步进等延时差，进而实现波束指向的大范围和大步进调节；通过调谐线性啁啾光纤光栅色散系数连续调谐获得小步进等延时差，进而实现波束指向的小范围和小步进调节，最终实现大波束指向范围和精细步进调节的光波束形成网络。
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图 1所示为基于色散光学技术的光波束形成网络原理图。一束具有等波长间隔的多波长光波由多波长激光源产生，波长分别为λ1, λ2, λ3, …, λM，波长间隔为Δλ。具有M个波长的光波输入电光调制器中被微波信号调制，被调制后的光信号通过环形器传输至色散系数可调的线性啁啾光纤布喇格光栅(linear chirped fiber Bragg grating，LCFBG)中，不同的波长在LCFBG中不同位置反射，并通过环形器输入高色散光纤阵列中。高色散光纤阵列由两个1×N光开关和N路具有不同长度的高色散光纤组成，通过1×N光开关切换使得光信号通过不同长度的高色散光纤。通过高色散光纤阵列的光信号输入波分复用器中解调为M路不同波长的光信号，M路光信号通过不同长度的单模光纤传输后至M个光电探测器，M路光信号分别在光电探测器中转换为微波信号，并通过等距离天线阵列发射到空间中，形成具有M路OTTD的光波束形成网络。
Figure 1. The schematic of the proposed OBFN based on optical dispersion
在如图 1所示的光波束形成网络中，色散系数可调的LCFBG的色散系数为D1，单位为ps/(km·nm)；高色散光纤的色散系数为D2，单位为ps/nm。LCFBG的色散系数可以通过温度调节和长度拉伸等方法进行微调。N路高色散光纤的长度分别为F1, F2, F3, …, FN。因此, LCFBG与高色散光纤在波束形成网络中引入的等延时差为:
$ {\rm{\Delta }}{\mathit{\tau }_{\rm{1}}}{\rm{ = }}{\mathit{D}_{\rm{1}}}{\mathit{F}_\mathit{N}}{\rm{\Delta }}\mathit{\lambda }{\rm{ + }}{\mathit{D}_{\rm{2}}}{\rm{\Delta }}\mathit{\lambda } $
(1) 式中，第1项为LCFBG引入的等延时差，第2项为高色散光纤引入的等延时差。
多波长光信号经波分复用器解复用后传输光纤长度分别为L1, L2, L3, …, LM，各个光纤长度等延时差为Δτ2，因此如图 1所示的光波束形成网络中，M路OTTD等延时差为:
$ {\rm{\Delta }}\mathit{\tau }{\rm{ = \Delta }}{\mathit{\tau }_{\rm{1}}}{\rm{ + \Delta }}{\mathit{\tau }_{\rm{2}}} $
(2) 取天线距离为d=c/(2ƒ)，其中, c为光在真空中的传播速度, ƒ为微波信号的频率。光波束形成网络的指向角为：
$ \mathit{\theta }{\rm{ = arcsin(2}}\mathit{f}{\rm{\Delta }}\mathit{\tau }{\rm{)}} $
(3) 根据(1)式~(3)式，可通过光开关实现N路高色散光纤路径切换获得大步进等延时差，进而实现波束指向的大范围和大步进调节；通过调谐线性啁啾光纤光栅色散系数连续调谐获得小步进等延时差，进而实现波束指向的小范围和小步进调节，最终实现大波束指向范围和精细步进调节的光波束形成网络。
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以ƒ=20GHz微波信号为例。设计天线距离为d=c/(2ƒ)，激光器波长间隔为国际电信联盟标准波长间隔0.4nm，激光器波长范围为3.2nm，高色散光纤色散系数D1=600ps/(km·nm)，LCFBG色散系数调谐范围和步进分别为5ps/nm~20ps/nm和0.5ps/nm，高色散光纤通道数量为N=9，长度分别为F1=0m, F2=25m, F3=50m, F4=75m, F5=100m, F6=125m, F7=150m, F8=175m, F9=200m，光纤长度分别为L1=1000mm, L2=994.8mm, L3=989.6mm, L4=984.4mm, L5=979.2mm, L6=974mm, L7=968.8mm, L8=963.6mm，则各个光纤长度等延时差Δτ2=-26ps。
根据(1)式，固定LCFBG的色散系数，通过光开关切换光信号在色散光纤阵列中的传输路径，图 1所示系统中OTTD可以实现等延时差切换范围为0ps~48ps，步进为6ps，如图 2a所示。其中参考值为传输路径F1=0m时OTTD的等延时差。
Figure 2. Equally delay difference caused by the path switching of N-way high dispersion fiber or tuning the dispersion coefficient of the LCFBG
固定光信号在色散光纤阵列中的传输路径，通过调节LCFBG的色散系数，图 1所示系统中OTTD可以实现等延时差切换范围为0ps~6ps，步进为0.2ps，如图 2b所示。其中参考值为LCFBG色散系数为5ps/nm时OTTD的等延时差。
当Δτ2=-26ps时，根据(2)式计算得图 1所示系统中OTTD的等延时差切换范围为-24ps~+24ps, 步进为0.2ps，如图 3a所示。根据(3)式，光波束形成网络的波束指向切换步进如图 3b所示。图 1所示的光波束形成网络可以实现的波束指向角范围为-73.74°~ +73.74°，在波束指向0°附近，波束指向角度切换步进约为0.458°，切换色散光纤路径时，波束指向角度切换步进约为13.89°。
Figure 3. Equally delay difference and the beam pointing of OBFN
图 4为八阵元光波束形成网络切换色散光纤路径时波束指向图。图 4a和图 4b分别为极坐标图与笛卡尔坐标图。当指向角度大于60°时，波束宽度急剧增大，光波束形成网络无法提供有效的波束指向。图 5为调节LCFBG色散系数时波束指向图。图 5a和图 5b分别为极坐标图与笛卡尔坐标图。当波束指向角度切换步进约为0.458°时，波束指向变化不明显，无法形成有效的波束切换。这是由于天线阵元数目较少，波束宽度较宽，因此在波束指向小步进切换不明显。
Figure 4. Beam pointing diagram of an 8-array-elements OBFN when switching the path of high dispersion fiber
Figure 5. Beam pointing diagram of an 8-array-elements OBFN when tuning the dispersion coefficient of the LCFBG
这一问题可以通过提高天线阵元数目解决。图 1所示系统在不增加色散光纤阵列通道及LCFBG色散系数调节范围的情况下，只增加激光器波长数目和天线数目即可实现更多阵元的波束形成网络。图 6是仿真了64天线阵元光波束形成网络的波束指向图。其中，实现64天线阵元光波束形成网络时，激光器波长范围为25.6nm。结果表明，选择64天线阵元后，当指向角度大于60°时，光波束形成网络仍然可以提供有效的波束指向，实现了-73.74°~+73.74°波束指向范围内有效的波束切换；当波束指向角度切换步进约为0.458°时，波束指向变化明显，可形成有效的波束切换获得了步进约为0.458°的小步进波束指向切换。因此，基于图 1所示的光波束形成网络可以实现波束指向角度范围为-73.74°~+73.74°和切换步进为0.458°的相控阵天线系统。
Figure 6. Beam pointing diagram of an 64-array-elements OBFN
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基于光学色散原理实现了光波束形成网络。通过光开关实现N路高色散光纤路径切换，获得大步进等延时差，进而实现波束指向的大范围和大步进调节；通过调谐线性啁啾光纤光栅色散系数连续调谐获得小步进等延时差，进而实现波束指向的小范围和小步进调节，最终实现大波束指向范围和精细步进调节的光波束形成网络。与传统基于色散原理的光波束形成网络相比，本方案中使用固定等波长间隔的多波长光源，降低了解复用的技术难度，具有实现难度小的优势, 为实现大波束指向范围和小步进切换的相控阵天线系统提供了技术依据。
基于色散光学的光波束形成网络
An optical beamforming network based on dispersing optics
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摘要: 为了实现大波束指向范围和精细步进调节的光波束形成网络, 采用了基于光学色散实现光真延时的方法。通过光开关实现N路高色散光纤路径切换获得大步进等延时差, 实现了波束指向的大范围和大步进调节; 通过调谐线性啁啾光纤光栅色散系数连续调谐获得小步进等延时差, 实现了波束指向的小范围和小步进调节。结果表明, 波束指向角度范围为-73.74°~+73.74°, 切换步进为0.458°, 基于光学色散原理可以实现光波束形成网络的大波束指向范围和精细步进调节。这一结果对优化相控阵天线系统设计是有帮助的。Abstract: In order to implement the large beam pointing range and the fine step adjustment of an optical beamforming network (OBFN), a method of optical dispersion-based optical true time delay (OTTD) was adopted. The path switching of N-way high dispersion fiber was realized by the optical switch, and thus the equally large-step delay difference was realized, then the beam pointing with a large range and a stride adjustment was realized. By tuning the dispersion coefficient of the linear chirped fiber Bragg grating (LCFBG), the equally small-step delay difference was realized, and then beam pointing with a small range and a small-step adjustment was realized. The theoretical analysis and simulation verification of the above method were carried out, and a beam pointing angle range of -73.74°~+73.74° and a switching step of 0.458° was obtained. The result shows that the large beam pointing range and the fine step adjustment of the OBFN were realized based on optical dispersion, which is helpful to improve the system designing of phased-array antenna.
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Figure 2. Equally delay difference caused by the path switching of N-way high dispersion fiber or tuning the dispersion coefficient of the LCFBG
a—switching dispersive fiber b—tuning LCFBG dispersion coefficient
Figure 3. Equally delay difference and the beam pointing of OBFN
a—switching delay difference b—switching beam pointing
Figure 4. Beam pointing diagram of an 8-array-elements OBFN when switching the path of high dispersion fiber
a—polar coordinate diagram b—cartesian coordinate diagram
Figure 5. Beam pointing diagram of an 8-array-elements OBFN when tuning the dispersion coefficient of the LCFBG
a—polar coordinate diagram b—cartesian coordinate diagram
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