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光波束形成包括接收波束和发射波束,通常在收发链路通过环形器互联可以共用一套延时网络。文中不失一般性,通过分析接收方向的波束形成来阐述色散延时的光波束形成方案。
图1为基于色散延时的光波束形成方案框图。天线接收微波信号,并经过低噪声放大器(LNA)进行前级放大,随后通过电光变换,将微波信号加载到光信号上。其中,每个电光变换通道对应的光波长不同,且随着天线通道依次变化。值得注意的是,图1中每个电光变换通道不仅可以对应一个单独的天线单元,也可以对应多个天线单元组合构成的集合。不同波长的光信号通过WDM合成一路光信号,进入光开关阵列。由于不同波长的光信号在色散介质中的延时量不同,各个天线通道间可以形成渐变的相位关系,并通过光电探测器(PD)进行波束合成。因此,通过改变阵列光开关的状态,可以对链路中色散延时总量进行切换,以实现波束的扫描。
常用的色散介质包括光纤、光栅或其他色散介质,其色散延时原理一致,非线性的修正方法类似。文中以现阶段工程化成熟度更高的光纤色散为例进行分析。
波长间隔为
Δλ的两个光波长,在长度为L、色散系数为D(λ)的介质中产生的相对延时差为: $$\Delta \tau {{ = D}}\left( \lambda \right) \times L \times \Delta \lambda $$ (1) 值得注意的是,色散系数D(λ)除包含线性项外,还包含了非线性项,会对相对延时量产生影响,并在多通道波束合成时改变波束合成质量。设定光纤在波长λ处的色散斜率为S,则色散斜率与该波长的色散系数D之比为相对色散斜率RDS,即RDS=S/D。则
$$D(\lambda ) = S(\lambda - {\lambda _0}) + {D_0} = {D_0}(1 + RDS×\Delta \lambda )$$ (2) 式中:D0为波长为λ0时的色散系数;Δλ为波长λ与基准波长λ0之差。而公式(2)中的第二项即为色散系数的非线性变化。通常而言,尽管色散系数会随着波长有微小变化,但在一定波段范围内,RDS基本保持不变。因此,更高阶的非线性色散量可以忽略。
另一方面,波束指向θ与各通道间延时差可以表述为:
$$\theta = \arcsin \left( {{{\Delta \tau \times c}/ d}} \right)$$ (3) 式中:c为光速;d为通道间隔。将公式(1)~(2)代入公式(3)中,即可得到波束指向与色散系数的关系为:
$$\theta = \arcsin \left( {{{{{{D}}_0}\left( {1 + {{RDS}} \times \Delta \lambda } \right) \times L \times \Delta \lambda \times c} / d}} \right)$$ (4) 值得注意的是,可以根据通道间距进行波长间隔的设计,因此,色散延时方案不仅适用于均匀分布的天线阵列,还可应用于稀疏阵等分布不均匀的天线阵列。
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之前的波束形成设计仅考虑了波束指向与色散系数的线性关系,即忽略公式(4)中的非线性项RDS×Δλ。在通道数较少或总延时量较小时,带来的非线性误差较小,波束方向图不会有明显的改变[15]。而随着通道数的增加,通道间的波长间隔增大,非线性项的误差不断累积,会改变雷达的波束方向图,因此需要对其中的非线性因子进行修正。
设定雷达第M个通道对应的光波长为λM,则第M个通道与第1个通道的对应的色散延时差为
${{{D}}_0} \left( {1 + {{RDS}} \times \Delta {\lambda _{{{M - }}1}}} \right) \times L \times \Delta {\lambda _{{{M - }}1}}$ ,其中已经将λM−λ1简记为ΔλM−1,D0为基准波长λ1时的色散系数。对于等间距的天线阵面而言,各通道的延时差应为线性关系,即第M个通道与第1个通道的延时差应为第2个通道与第1个通道延时差的(M−1)倍,因此有:$$\frac{{{{{D}}_0}\left( {1 + {{RDS}} \times \Delta {\lambda _{{{M - }}1}}} \right) \times L \times \Delta {\lambda _{{{M - }}1}}}}{{{{{D}}_0}\left( {1 + {{RDS}} \times \Delta {\lambda _{{\rm{2 - }}1}}} \right) \times L \times \Delta {\lambda _{{\rm{2 - }}1}}}}{{ = M - 1}}$$ (5) 可以看出,色散的非线性可以通过改变激光器波长的间隔Δλ进行修正,从而对色散介质的非线性效应进行补偿。将Δλ2−1作为各通道间波长间隔的基准量,通过公式(5)可以计算出第M个通道与第1个通道的激光器波长差为:
$$\Delta {\lambda _{{{M - }}1}}{\rm{ = }}\frac{{ - 1 + \sqrt {1 + 4{{RDS}}\left( {{{M - 1}}} \right)\Delta {\lambda _{{\rm{2 - }}1}}\left( {1 + RDS\Delta {\lambda _{{\rm{2 - }}1}}} \right)} }}{{2 \times {{RDS}}}}$$ (6) 选用商用G652光纤作为色散介质,其色散系数约为16 ps/nm·km,RDS约为0.003 nm−1,截取约5 km的光纤进行试验分析。根据1550 nm波段密集波分复用设定的激光器阵列波长,选取1532.681~1557.363 nm中连续32个波长,每个波长间隔100 GHz(约0.796 nm),按照顺序依次对应天线的每个通道,其中波长与天线通道的对应关系如图2(a)中蓝色线所示。测试每个通道与第32个通道(波长1532.681 nm)之间的色散延时差,结果如图2(b)中蓝色线所示,各通道间的延时差呈现一定的非线性弯曲,会导致光波束的散焦和畸变。
图 2 (a)各通道非线性修正前后对应的波长;(b)各通道非线性修正前后与第32通道的色散延时差
Figure 2. (a) Wavelengths versus channels without modification and with modification; (b) Relative dispersion delays of different channels to the 32nd channel without modification and with modification
在波长修正时,首先根据公式(6)确定各通道波长间隔比例,由于RDS>0,相邻通道间的波长间隔逐渐减小。若Δλ2−1仍为0.796 nm,则激光器波长与1550 nm波段标准通信波长的偏差值将逐渐增加。为沿用商用化波分复用器,降低光波束形成系统的成本,对Δλ2−1进行“拉伸”。与此同时,还需降低修正后各通道波长与标准通信波长差值的平均值,对所有激光器波长进行“平移”操作,以整体提升各通道的光合成性能。将Δλ2−1“拉伸”为0.862 nm且激光器波长整体“平移”−0.31 nm,此时,修正后各通道与标准通信波长差值的平均值仅为0.09 nm,能够在修正非线性色散的同时,兼顾使用低成本商用化器件。修正后的32通道波长如图2(a)中红色线所示,其与未调整时的波长差最大值约为0.2 nm,出现在第1、17和32通道。测试修正后的每个通道与第32个通道之间的色散延时差,从图2(b)中红色线可以看出,修正前后的最大延时差约为32 ps,出现在第17个通道。经过非线性修正,各通道间色散延时差的线性度提升,拟合系数R2=0.99998,有利于波束方向图质量的提升。
在波束指向计算中,选用单元间隔为15 mm的32单元天线阵列,共5级色散光纤,长度分别为170、340、680、1360、2720 m,分别级联在如图1所示的阵列光开关中。通过调整光开关“直通”和“交叉”态,可改变光合成时色散光纤的长度。因此,共有32种不同的开关状态组合,对应32种不同的色散光纤长度。基于5 km光纤时各通道色散延时差的测试结果,分析出不同光开关状态组合,波长修正前和修正后各通道间的延时差,并结合微波频率和天线单元间距仿真出该开关状态下的波束指向。而在所有光开关为直通状态(对应色散光纤长度为0)时,调整各通道初始延时差,使波束指向为−45°。仿真使用10 GHz作为特征频率,避免出现栅瓣。
图3(a)为激光器波长按照等间隔选择时所有开关状态下的波束指向。可以看出,在扫描角与初始角度(−45°)相差不大,即光纤长度短时色散的非线性累积效应不明显,波束方向图仍保持较好。但随着扫描角度的增加,未修正激光器波长的波束指向逐渐发生畸变,主瓣逐渐展宽且副瓣逐渐抬升,在波束指向42°时,波束合成效果差,出现了严重的散焦和畸变。这是由于在色散延时量增加后,相邻通道间延时差的非线性度增加,导致相邻通道间对应的波束指向偏离变大,波束没有形成聚焦。图3(b)为激光器波长通过非线性修正后波束指向的结果。可以看出,通过激光器波长对色散的非线性进行修正,波束形状畸变消失,在波束指向42°时,主副比仍保持在12.9 dB,印证了通过激光器波长对色散介质进行非线性修正后能够明显提升波束形成质量。
Nonlinear modification of dispersion delay for optical beam forming
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摘要:
光波束形成网络是光控相控阵雷达中的重要组成部分,有助于提升系统的宽带宽角扫描能力。利用光开关的切换,改变各收发通道间的相对延时量,从而实现波束指向的变化。在常用的技术中,色散延时是一种简洁的光波束形成实现方法,而色散线性项仅适用于色散量小且通道数少的情况。随着延时量的增加,非线性色散延时积累,会引起波束畸变。因此引入相对色散斜率(RDS)作为其非线性因子,并通过调整商用激光器波长来抵消色散介质的非线性效应。当RDS为0.003 nm−1时,激光器阵列的最大波长间隔从0.796 nm “拉伸”到0.862 nm,波长也整体“平移”−0.31 nm,修正波长与商用激光器波长的最大调整量为0.2 nm,可满足商用波分复用器的通带带宽,大扫描角时主瓣与副瓣之比从5 dB提升至12.9 dB。通过分析,RDS数值越小,激光器波长的修正量越小。因此,RDS是选择色散介质和调整激光器波长的重要参数,从而能够恢复波束畸变,以提升相控阵系统的成像、识别能力。
Abstract:Optical beam forming network is an important part in optically controlled phased array radar, which could improve the beam scanning ability with large bandwidth and direction angle. The direction of beam is usually controlled by optical switches to change relative delay of transmitting and receiving channels. Among commonly-used techniques, dispersion delay is a concision way to realize optical beam forming network. Linear dispersion is only applicable to beam forming with limited dispersion delay and channels. With the increase of delay, nonlinear dispersion delay accumulates, which distorts the beamform. Therefore, relative dispersion slope (RDS) was used as a nonlinear factor. Moreover, adjusting wavelengths of commercial lasers was raised to compensate the nonlinearity. If RDS was 0.003 nm−1, the maximum wavelength interval stretched from 0.796 nm to 0.862 nm and wavelengths shifted −0.31 nm. In this case, maximum difference between modified and commercial laser wavelengths was 0.2 nm, which was suitable for the passband of commercial wavelength division multiplexing devices. In the meantime, ratio of main to side lobe improved from 5 dB to 12.9 dB with large scanning direction. Based on the analysis, the smaller RDS value was, the less wavelengths modifications of lasers were. Therefore, RDS is a key parameter in choosing dispersion material and adjusting wavelengths of lasers. In this way, distorted beamform could be recovered. The abilities of imaging and identifying thus could be improved in phase arrayed systems.
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