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如图1(a)所示,光子储备池整体结构由输入层、储层和读出层(全光训练读出)三部分组成。输入层结构如图1(b)所示,由耦合比为0.5的3个2×1多模干涉仪(Multi-mode Interference, MMI)组成,光信号经输入层均分4路进入储层;储层由12个定向耦合器(Directional Coupler, DC)作为节点,两节点间由波导(Waveguide, WG)相连,采用螺旋拓扑规律组成梅花型网格结构,具有波长敏感特性,可提高滤波器的调谐灵敏度。输入层输出的4路光信号由储层中心4个节点进入,由于中心节点的4个端口均与波导相连,需在中心节点处额外引入4个DC作为输入节点,输入节点的4个端口分别与输入信号、终端、中心节点端口以及波导相连,其中输入节点分光比设置为0.9,偶数路输出节点分光比设置为0.45,其余节点分光比设置为0.5,储层中波导长度均设置为500 μm,光信号经输入节点进入储层,按拓扑规律沿不同路径传输,并在节点处发生干涉并重新组合,重组后的光信号由储层外围的8个节点输出进入读出层;读出层由8个光调制器(Optical Modulator , OM)以及7个2×1 MMI组成,信号进入读出层的OM后,经过对每路光信号的幅度以及相位进行加权调节,调节后的光信号由2×1 MMI拟合成一路光信号,经光放大器进行功率放大后输出。其中在储层波导上添加微型加热电极,如图1(a)中红色部分,基于硅材料的热光效应,改变波导的相对折射率引起信号的相位变化;在读出层光调制器上下臂上同样添加微型加热电极改变其相位值,实现读出权重的赋值。
图 1 光子储备池结构。(a)整体结构;(b)输入层结构
Figure 1. Structure of photonic reservoir computing. (a) Overall structure; (b) Input layer
基于集成光子储备池的光子滤波器系统实验装置如图2所示,激光器输出功率为1 mW、中心波长为1550 nm的光信号,经单模光纤(Single Mode Fiber, SMF)和偏振控制器(Polarization Controller, PC)对光信号的偏振态进行控制,采用垂直耦合方式,将输入光通过如图1(b)中输出层的TE光栅耦合器进入光子储备池芯片中,经过光子储备池对信号处理后,通过光栅耦合到输出光纤,最后由光谱分析仪(Optical Spectrum Analyzer, OSA)对光滤波器的FSR、中心波长以及滤波波形进一步分析,芯片中的相移器均由电压源阵列(Voltage Source Array, VSA)进行驱动。
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引入散射矩阵,对光子储备池各个端口之间的映射关系进行描述[1,17]。如图1所示,该结构分为输入层、储层、读出层三部分,不考虑端口处的反射现象,每一部分均可用唯一对应的散射矩阵描述。
1)输入层:输入层由2×1 MMI器件连接而成,MMI是一种无源器件,主要起到功率分配作用,即可作为合束器又可作为分束器,其输入输出端口均为单模波导,具有结构紧凑、易于制作、损耗小、制作容差性好、偏振相关性小等优点。同时可以通过级联多个MMI实现光功率的按比例分配。在输入层中通过级联3个1×2 MMI将一路光信号的功率均分四路进入储层。
采用的2×1 MMI的耦合比为0.5,1个2×1 MMI具有3个端口,其端口间的映射关系表示为:
$$ \left( {\begin{array}{*{20}{c}} {{E_{M,t1}}} \\ {{E_{M,t2}}} \\ {{E_{M,t3}}} \end{array}} \right) = \sqrt {{{10}^{0.1{L_M}}}} \left( {\begin{array}{*{20}{c}} 0&{\dfrac{1}{2}}&{\dfrac{1}{2}} \\ {\dfrac{1}{2}}&0&0 \\ {\dfrac{1}{2}}&0&0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} {{E_{M,i1}}} \\ {{E_{M,i2}}} \\ {{E_{M,i3}}} \end{array}} \right) $$ (1) 式中:${E_{M,t1}}$、${E_{M,t2}}$、${E_{M,t3}}$为2×1 MMI端口处的透射光场;${E_{M,i1}}$、${E_{M,i2}}$、${E_{M,i3}}$为2×1 MMI端口处的输入光场;${L_M}$为2×1 MMI器件的损耗,单位为dB。
根据公式(1)可得到2×1 MMI作为分束器时,其两个输出端口与输入端口的映射关系为:${E_{{\text{out}}1}} = {E_{{\rm{out}}2}} = \dfrac{1}{2}\sqrt {{{10}^{0.1{L_M}}}} {E_{{\rm{in}}}}$,作为分束器时,其输入输出端口的映射关系为:${E_{{\rm{out}}}} = \dfrac{1}{2}\sqrt {{{10}^{0.1{L_M}}}} ({E_{{\rm{in}}1}} + {E_{{\rm{in}}2}})$。
信号经输入层一分四路,对输入层的1个输入端口、4个输出端口之间的映射关系描述为:
$$ \left( {\begin{array}{*{20}{c}} {{E_{t1}}} \\ \vdots \\ {{E_{t4}}} \end{array}} \right) = {W_{{\rm{in}}}}{E_{{\rm{in}}}} $$ (2) 式中:${E_{t1}}$、${E_{t2}}$、${E_{t3}}$、${E_{t4}}$为输入层输出端口处的透射光场;${E_{{\rm{in}}}}$为光子储备池输入端口处的输入光场;${W_{{\rm{in}}}}$为光子储备池输入权重,其值随机产生并固定不变,无需进行训练。根据公式(1),结合输入层中2×1 MMI的连接方式,由传递矩阵法计算${W_{{\rm{in}}}}$得:
$$ {W_{{\rm{in}}}} = {10^{0.1{L_M}}}\left( {\begin{array}{*{20}{c}} {{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{4}}}} \right. } {\text{4}}}} \\ {{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{4}}}} \right. } {\text{4}}}} \\ {{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{4}}}} \right. } {\text{4}}}} \\ {{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} {\text{4}}}} \right. } {\text{4}}}} \end{array}} \right) $$ (3) 2)储层:输入层输出的四路信号进入储层,储层由WG、DC器件连接而成,如图3(a)所示,WG器件具有2个端口,端口间的映射关系表示为:
图 3 光子储备池中器件模型示意图。(a)波导; (b)定向耦合器;(c)光调制器
Figure 3. Schematic diagram of device model in photonic reservoir computing. (a) Waveguide; (b) Directional coupler; (c) Optical modulation
$$ \left( {\begin{array}{*{20}{c}} {{E_{W,t1}}} \\ {{E_{W,t2}}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&{t\exp (j\phi )} \\ {t\exp (j\phi )}&0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} {{E_{W,i1}}} \\ {{E_{W,i2}}} \end{array}} \right) $$ (4) $$ t = 1{0^{\tfrac{{ - {L_W} * L * 1{0^{ - 4}}}}{{20}}}} $$ (5) $$ \phi = {\phi _2}{{ - }}{\phi _1} = 2\pi L{n_{{\rm{eff}}}}/\lambda $$ (6) 式中:${E_{W,t1}}$、${E_{W,t2}}$为波导端口处的透射光场;${E_{W,i1}}$、${E_{W,i2}}$为波导端口处输入光场;$t$为波导的透射率;${L_W}$为波导的损耗;$L$为波导长度;$\phi $为波导的相位变化;${\phi _1}$和${\phi _2}$分别为波导两端的相位值;$\lambda $为信号的中心波长;${n_{{\rm{eff}}}}$为波导在$\lambda $处的有效折射率。
根据公式(4)可以看出信号经过波导后,信号的幅度变化与透射率t有关,而t的值由波导的损耗以及波导长度决定;信号的相位变化与传输信号的中心波长、波导长度以及波导的有效折射率有关,因而通过热调改变硅波导的折射率可对光信号的相位进行调制。
如图3(b)所示,DC器件具有4个端口,各个端口间的映射关系表示为:
$$ \left( {\begin{array}{*{20}{c}} {{E_{D,t1}}} \\ {{E_{D,t2}}} \\ {{E_{D,t3}}} \\ {{E_{D,t4}}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&{\sqrt {1 - \kappa } }&{\sqrt \kappa \exp \left( {j\dfrac{\pi }{2}} \right)}&0 \\ {\sqrt {1 - \kappa } }&0&0&{\sqrt \kappa \exp \left( {j\dfrac{\pi }{2}} \right)} \\ {\sqrt \kappa \exp\left( {j\dfrac{\pi }{2}} \right)}&0&0&{\sqrt {1 - \kappa } } \\ 0&{\sqrt \kappa \exp \left( {j\dfrac{\pi }{2}} \right)}&{\sqrt {1 - \kappa } }&0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} {{E_{D,i1}}} \\ {{E_{D,i2}}} \\ {{E_{D,i3}}} \\ {{E_{D,i4}}} \end{array}} \right) $$ (7) 式中:${E_{D,t1}}$、${E_{D,t2}}$、${E_{D,t3}}$、${E_{D,t4}}$为DC端口处的透射光场;${E_{D,i1}}$、${E_{D,i2}}$、${E_{D,i3}}$、${E_{D,i4}}$为DC端口处输入光场;$\kappa $为DC耦合系数。
光信号经储层中心4节点进入储层,按螺旋拓扑路径传输后,经外围的8节点输出。利用散射矩阵,对储层4个输入端口、8个输出端口间的频域关系描述为:
$$ \left( {\begin{array}{*{20}{c}} {{E_{t5}}} \\ \vdots \\ {{E_{t12}}} \end{array}} \right) = {W_{{\rm{res}}}}\left( {\begin{array}{*{20}{c}} {{E_{i1}}} \\ \vdots \\ {{E_{i4}}} \end{array}} \right) $$ (8) 式中:${E_{t5}} \cdots {E_{t12}}$为储层输出端口处的透射光场;${E_{i1}} \cdots {E_{i4}}$为储层输入端口处的输入光场;即输入层输出端口处的透射光场;${W_{{\rm{res}}}}$矩阵为光子储备池连接权重,其矩阵大小为(8×4),一经产生就固定不变,同样不需要进行训练。根据信号在储层的传输路径以及公式(4)、(7),由传递矩阵法进行计算,由于计算量非常庞大,${W_{{\rm{res}}}}$具体数值计算需由计算机辅助完成。
3)读出层:读出层由OM及2×1 MMI组成,其中2×1 MMI作为合束器使用,将7个2×1 MMI进行连接,将输出的8路信号拟合成一路。如图3(c)所示,OM器件具有2个端口,端口间的映射关系表示为:
$$ \left( {\begin{array}{*{20}{c}} {{E_{O,t1}}} \\ {{E_{O,t2}}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&{\cos\dfrac{{({\varphi _a} - {\varphi _b})}}{2}\exp \left(j\dfrac{{({\varphi _a} + {\varphi _b})}}{2}\right)} \\ {\cos\dfrac{{({\varphi _a} - {\varphi _b})}}{2}\exp \left(j\dfrac{{({\varphi _a} + {\varphi _b})}}{2}\right)}&0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} {{E_{O,i1}}} \\ {{E_{O,i2}}} \end{array}} \right) $$ (9) 式中:${E_{O,t1}}$、${E_{O,t2}}$为OM端口处的透射光场;${E_{O,i1}}$、${E_{O,i2}}$为OM端口处输入光场;${\varphi _a}$、${\varphi _b}$分别为OM上、下干涉臂的相位值。
根据公式(9)可以看出信号经过光调制器后,信号的幅度变化与调制器上下臂相位差值有关,信号的相位变化与调制器上下臂相位和有关,因而通过热调改变调制器上下臂中硅波导的折射率可实现光信号的相位和幅度的调整,从而将训练权重赋值到储层输出的各路光信号。
由储层输出的8路信号进入读出层后,通过OM对每路信号分别赋予合适的权重,经2×1 MMI拟合成1路输出,对读出层输入输出端口间的映射关系描述为:
$$ {E_{{\rm{out}}}} = {W_{{\rm{out}}}}\left( {\begin{array}{*{20}{c}} {{E_{i5}}} \\ \vdots \\ {{E_{i12}}} \end{array}} \right) $$ (10) 式中:${E_{{\rm{out}}}}$为光子储备池输出端口处的光场;${E_{i5}} \cdots {E_{i12}}$为读出层输入端口的光场,即储层输出端口的透射光场;${W_{{\rm{out}}}}$为光子储备池的读出权重,其值需要对储层输出信号进行训练得到。根据公式(1)、(9)以及器件在读出层的连接方式,计算${W_{{\rm{out}}}}$得:
$$ {W_{{\rm{out}}}} = \frac{1}{8}{\left( {{{10}^{0.1{L_M}}}} \right)^{\tfrac{3}{2}}}{\left( {\begin{array}{*{20}{c}} {{W_{{\rm{Amp1}}}}\exp \left( {j{\varphi _{w1}}} \right)} \\ \vdots \\ {{W_{{\rm{Amp8}}}}\exp \left( {j{\varphi _{w8}}} \right)} \end{array}} \right)^{\rm{T}}} $$ (11) $$ {W_{{\rm{Amp}}i}} = \cos \frac{{({\varphi _{{\rm{a}}i}} - {\varphi _{{\rm{b}}i}})}}{2} $$ (12) $$ {\varphi _{{\rm{w}}i}} = \frac{{({\varphi _{{\rm{a}}i}} + {\varphi _{{\rm{b}}i}})}}{2} $$ (13) 式中:${W_{{\rm{Amp}}i}}$、${\varphi _{{\rm{w}}i}}$分别为读出层中第$i$路光信号赋值的幅度权重及相位权重;${\varphi _{{\rm{a}}i}}$、${\varphi _{{\rm{b}}i}}$分别为第$i$路OM上、下干涉臂的相位值。利用训练得到${W_{{\rm{Amp}}i}}$及${\varphi _{{\rm{w}}i}}$值,通过热调对OM器件上、下臂的${\varphi _{{\rm{a}}i}}$、${\varphi _{{\rm{b}}i}}$参数进行调整。
结合公式(2)、(8)、(10),整个光子储备池输入端口与输出端口之间传输响应关系表示为:
$$ {E_{{\rm{out}}}} = {W_{{\rm{out}}}}{W_{{\rm{res}}}}{W_{{\rm{in}}}}{E_{{\rm{in}}}} $$ (14) 由上式可知,通过对光子储备池内读出权重、连接权重、输入权重的确定,得到整个结构输入端与输出端的频域响应。
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利用PSO优化算法对读出权重的幅度${W_{{\rm{Amp}}i}}$、相位${\varphi _{{\rm{w}}i}}$共16个参数进行寻优,其中${W_{{\rm{Amp}}i}}$的参数寻优范围为(0~1),${\varphi _{{\rm{w}}i}}$参数寻优范围为(0~2π),设置初始种群数为50,惯性权重为0.8,加速常数均为2,空间维数为16,通过不断更新粒子速度和位置寻找损失函数的最小值,得到最优的权重参数值。利用损失函数定量判断训练效果的优劣,当损失函数值越小,训练得到的权重值越接近理想值,将损失函数定义为:
$$ Fitness = \frac{1}{n}\min \sum {{{\left[ {\alpha (\left| {{y_{{\rm{pred}}}}} \right| - \left| {{y_{{\rm{label}}}}} \right|)} \right]}^2}} $$ (15) 式中:$n$为总的采样点数目;$\left| {{y_{{\rm{pred}}}}} \right|$为训练波形幅值;$\left| {{y_{{\rm{label}}}}} \right|$为理想波形幅值;$\alpha $为调节系数,将理想波形幅度值与训练波形幅度值之间的误差进行放大或缩小,最终拟合出理想波形效果。其$\alpha $值描述为:
$$ \alpha = \left\{ \begin{gathered} a,{\left| {{y_{{\rm{label}}}}} \right|_{\max }} \geqslant \left| {{y_{{\rm{label}}}}} \right| \geqslant x \\ b,x > \left| {{y_{{\rm{label}}}}} \right| \geqslant {\left| {{y_{{\rm{label}}}}} \right|_{\min }} \\ \end{gathered} \right. $$ (16) 式中:${\left| {{y_{{\rm{label}}}}} \right|_{\max }}$为理想幅值的最大值;${\left| {{y_{{\rm{label}}}}} \right|_{\min }}$为理想幅值的最小值;$a$与$b$为$\alpha $参数在$\left| {{y_{{\rm{label}}}}} \right|$不同范围内的设定值;$x$为设定在${\left| {{y_{{\rm{label}}}}} \right|_{\max }}$与${\left| {{y_{{\rm{label}}}}} \right|_{\min }}$之间的任意实数值。在拟合不同的波形时,无需改变光子储备池的结构以及器件参数值,只需调整$a$、$b$、$x$的取值,通过对权重进行训练优化,得到所需要的滤波效果,从而实现基于光子储备池的光滤波器可重构特性。
与其他光波导网络的算法训练过程相比,仅对光子储备池的读出权重${W_{{\rm{out}}}}$进行训练,无需训练其输入权重及储层连接权重,大大减少了训练过程中训练负担。其次,采用粒子群算法训练时,可通过当前搜索的最优值寻找全局最优,这种算法具有训练规则简单、易实现、精度高、收敛快的优势。
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根据图1搭建仿真模型,考虑储层中波导的实验制造误差,在波导上添加−π~π范围内的随机相位,对储层输出的8路信号进行仿真。
如图4所示,每路信号光谱的FSR相同,均为1.18 nm,其中第1路信号与第2路信号光谱形状相同,但第2路信号光功率高于第1路信号。由图1可知,信号在储层传输过程中,第1路输出信号的传输路径与第2路输出信号路径相似,差别在于两路输出节点处连接的波导路径,由于波导固有损耗,使得两路光谱所对应的光功率不同,但光谱形状不变。由图4(c)~(h)可知,第3、4路、第5、6路、第7、8路均有相同的规律。
图 4 储层输出的8路信号光谱图。(a)第1路;(b)第2路;(c)第3路;(d)第4路;(e)第5路;(f)第6路;(g)第7路;(h)第8路
Figure 4. 8 channel signal spectra of reservoir output. (a) Rout 1; (b) Rout 2; (c) Rout 3; (d) Rout 4; (e) Rout 5; (f) Rout 6; (g) Rout 7; (h) Rout 8
为解决目前滤波器所实现的滤波波形单一问题,文中提出的基于光子储备池的光滤波器利用粒子群算法对读出层训练,寻找多组读出权重参数,实现两种滤波波形,此节以经典的IIR型及FIR型两种不同的滤波功能实现为例进行说明。对图4中的8路信号进行线性拟合,通过对读出层权重训练以及$\alpha $值的相关参数调整,实现IIR型和FIR型光滤波器。如图5、图6所示,分别为IIR型光滤波器与FIR型光滤波器的仿真结果。
图 5 IIR型光滤波器仿真训练效果。(a) IIR滤波谱拟合效果图;(b)Fitness曲线
Figure 5. Simulation training effect of IIR optical filter. (a) IIR filter spectrum fitting rendering; (b) Fitness curve
图 6 FIR型光滤波器仿真训练效果。(a) FIR滤波谱拟合效果图;(b) Fitness曲线
Figure 6. Simulation training effect of FIR optical filter. (a) FIR filter spectrum fitting rendering; (b) Fitness curve
对IIR型光滤波器进行分析,由公式(16)知,$\alpha $值由$a$、$b$、$x$ 3个参数确定,通过多次调整$a$、$b$、$x$的值并进行仿真,找到最小Fitness值所对应的$\alpha $值以及权重值,如表1、表2所示。
表 1 IIR型光滤波器对应α值的设定参数
Table 1. Setting parameters of the corresponding α of IIR optical filter
|ylabel|max |ylabel|min a b x 1 0.05 4.5 1 0.95 如图5(a)所示,理想波形与训练波形基本完全贴合,在波谷处有少许波动,但仍能实现IIR型滤波器的滤波功能,实现的IIR光滤波器的FSR为1.18 nm,3 dB带宽为0.18 nm,消光比为30 dB左右。图5(b)为误差值随迭代次数的变化,随着迭代次数的增加,误差值呈阶梯状下降趋势。在训练初始阶段,由于粒子本身具有较强的扩展搜索空间能力,其寻找最优解的速度比较快,随着迭代次数增加,误差值快速下降;在迭代过程中,粒子群算法容易陷入局部最优空间,随着迭代次数增加,Fitness值下降缓慢,甚至保持不变,当粒子跳出局部最优时,Fitness值进一步下降;在迭代结束阶段,Fitness值在0.022附近基本保持平稳。由此可以看出,PSO算法的参数搜索速度快,但容易陷入局部最优,需要对加速常数值以及惯性权重进行合理配置,平衡粒子的全局和局部搜索能力。
对FIR型光滤波器进行权重拟合,理想波形的幅度范围在(0~0.81)之间,通过多次仿真对比,找到最小Fitness值所对应的$\alpha $相关参数以及权重值,如表3、表4所示。
表 2 IIR型光滤波器8路信号权重训练值
Table 2. IIR optical filter 8 channel signal weight training value
IIR 1st 2nd 3rd 4th 5th 6th 7th 8th WAmp 0.496 0.015 0.847 0.358 0.240 0.649 0.865 0.641 φw 4.717 0.593 5.01 1.176 4.072 0.173 2.180 1.935 表 3 FIR型光滤波器对应α值的设定参数
Table 3. Setting parameters of the corresponding α of FIR optical filter
|y’label|max |y’label|min a’ b’ x’ 0.81 0 2 4 0.4 表 4 FIR型光滤波器8路信号权重训练值
Table 4. FIR optical filter 8 channel signal weight training value
FIR 1st 2nd 3rd 4th 5th 6th 7th 8th WAmp 0.966 0.452 0.998 0.928 0.685 0.991 0.997 0.766 φw 3.258 2.861 3.097 5.189 3.080 0.259 6.282 5.246 如图6所示,为训练得到的FIR型滤波谱以及Fitness曲线。由FIR光谱图看出,训练得到的光谱波形与理想波形相比,在波形顶部两者相差较大,其余部分贴合较好。实现的FIR光滤波器的FSR为1.18 nm,3 dB带宽为0.77 nm,消光比为50 dB左右。顶部毛刺较多的原因在于光信号在储层中既有前向传输又有反馈配置,不同路径的信号在DC节点处发生多次干涉并重组。
如图4所示,由储层输出的每路光信号均具有不同程度的毛刺,仅通过读出层的光调制器对8路信号进行权重赋值并线性拟合,其训练波形的波动很难消除。由Fitness曲线图看出,其下降趋势与IIR型滤波器的Fitness曲线相近,误差值随迭代次数的增加呈阶梯状趋势下降,Fitness值在0.11附近基本保持平稳。对比图5(a)与图6(a),可以看出,FIR型训练波形顶部波动比IIR型训练波形底部波动大,原因在于波形顶部相较于底部所对应的光功率较大,权重值对于波形顶部影响较大。
通过对IIR型及FIR型光滤波器仿真结果分析可知,在给定理想目标波形情况下,利用粒子群算法对储层的输出信号进行权重训练,使训练得到的滤波波形不断逼近理想波形,进而获得最优权重系数,当滤波波形无限接近时,所实现的光滤波器相关滤波参数便与期望实现的滤波器参数基本一致,从而所设计的该光滤波器的相关滤波参数精确度较高。
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以IIR型的训练波形为例,通过对储层中WG、DC器件参数调整,分析WG长度、DC分光比对滤波谱参数的影响。
如图7所示,给出在不同波导长度下IIR型光滤波谱的变化情况,从光谱图看出,随着波导长度的变化,滤波谱形状保持不变,滤波谱的FSR随着波导长度的增加而减小。对图7的仿真数据进一步分析,得到IIR型光滤波谱FSR随波导长度的变化。如图8所示,波导长度与FSR成负相关,随着波导长度的增加,相应的FSR变小。对数据点进行多项式拟合,得到FSR随波导长度变化曲线,可以看出,FSR与波导长度并不符合严格的线性关系。由此可见,波导长度是影响FSR的主要因素,根据实际应用要求,通过对储层中波导长度的调整实现对FSR的灵活控制。
图 7 储层中波导在不同长度下的IIR滤波谱。(a)波导长度为400 μm ;(b)波导长度为500 μm ;(c)波导长度为600 μm
Figure 7. IIR filter spectrum of waveguide at different lengths in reservoir. (a) Waveguide length of 400 μm; (b) The waveguide length of 500 μm; (c) The waveguide length of 600 μm
保持输入节点DC分光比与储层奇数路输出节点DC分光比不变,对储层偶数路输出节点DC的分光比进行调整。由图9可以看出,DC分光比由0.45变化至0.75过程中,光谱形状保持不变,但对于波形峰值功率影响较大,光功率由1 mW降低至0.67 mW。由此可见,根据实际需要,通过对储层偶数路输出节点分光比进行设置,实现不同滤波强度的调节。
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在光滤波器滤波波长可调谐仿真中,通过对光滤波器的透射谱分析,得到波导上的相位对滤波波长偏移的影响。
图10给出在不同相移量下光滤波器透射端光功率随波长的变化。从光谱图中显示,添加在波导上相位变化(0~3π/2)时,波形形状保持不变、自由光谱范围保持为1.18 nm,但滤波中心波长实现了在一个自由光谱范围内连续可调谐。与目前基于Sagnac环结构实现的光滤波器中心波长调谐范围在0.5 nm内相比,该滤波器的中心波长的调谐范围提高两倍。因此,利用热调方法对储层波导上的相位进行控制,可以实现光滤波器中心滤波波长的可调谐。
Tunable optical filter with integrated photonic reservoir computing
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摘要: 为了适应滤波、波分复用等不同的应用场景,光子滤波器需要具备可调谐以及滤波形状可变的功能。提出一种集成光子储备池结构的新型可调谐光滤波器。该结构由输入层、储层、读出层三部分组成,输入层由2×1多模干涉仪组成,储层由定向耦合器以及波导组成,按螺旋拓扑规律相互连接组成梅花型网格,匹配粒子群寻优算法进行全光域训练,利用读出层的热光调制器和相移器对光信号的幅度和相位进行调整,实现无限冲激响应型与有限冲激响应型可调谐光滤波器。以无限冲激响应型光滤波器仿真结果为例,分析其自由光谱范围与储层中波导长度的关系,以及定向耦合器分光比对透射端透过率的影响。通过设置储层中波导的相位在0~3/2π范围内变化,实现了光滤波器中心波长在一个自由光谱范围(1.18 nm)内的连续可调。该滤波器采用集成光子储备池与粒子群算法结合方案设计,无需考虑储层光网络传输路径的权重配置,仅对读出层权重进行训练,大大简化了网络训练过程。同时,该滤波器具有尺寸小、功耗低、灵活性高、算法可控滤波参数的优势,广泛应用于集成微波光子学和光通信领域中。Abstract:
Objective A tunable optical filter is the key component in the optical communication systems and optical processing systems. By tuning the central wavelength, it can be used to choose a signal with arbitrary wavelength according to the practical requirement. However, due to the high loss and large size, optical filter based on discrete devices cannot meet the requirements of some photonic signal processor. Recently, based on Mach-Zehnder interferometers network and ring-assisted Mach-Zehnder interferometer, some research groups have proposed integrated optical filter. However, this type of optical filter has the disadvantages of being difficult to train and having a single waveform, which restricts its application in the fields of multi-purpose adaptive signal processing. For improving the flexibility of optical filter, a novel tunable optical filter with an integrated photonic reservoir computing (RC) is proposed. Since the filtering properties can be controlled by intelligence algorithm, this optical filter, which improves the flexibility in applications, can be widely applied in optical cross interconnection system and microwave photon signal shaping. Methods Firstly, the structure of integrated photonic RC is constructed in detail, and scattering matrix theory is used to analyze the transmission function of integrated photonic RC. Then, the simulated transmission spectra of the reservoir are carried out by simulation software. Particle swarm optimization (PSO) algorithm is matched for training reservoir transmission spectra in optical domain to find optimal weights. Based on thermo-optical effects, optical weights are implemented by optical modulators (OMs). During training the weights in readout layer, OMs are used to adjust the amplitudes and phases of the optical signal. Using this integrated photonic RC chip, the infinite (IIR) and finite (FIR) impulse response optical filters are realized. Finally, by adjusting the parameters of waveguide (WG) and directional coupler (DC) in the reservoir, the filtering properties is studied. Results and Discussions The achieved IIR and FIR optical filter waveform are almost exactly matched to the ideal waveform (Fig.5(a), Fig.6(a)). The error value of the training results decreases in a step-like trend with the increase of the number of iterations, and eventually tends to be stable (Fig.5(b), Fig.6(b)). Based on the IIR optical filter simulation results, the effect of the free spectral range (FSR) on the WG length is analyzed (Fig.8). The WG length is negatively correlated with the FSR. As the WG length increases, the corresponding FSR becomes smaller. In addition, the influence of the DC splitting ratio on the transmission power is analyzed (Fig.9). According to the actual needs, the adjustment of different filtering intensities is achieved by setting the splitting ratio of the even number of output nodes of the reservoir. Moreover, the filtering wavelength, which is influenced by the phase of the WG in the reservoir from 0 to 3/2π, is continuously adjustable in the FSR of 1.18 nm (Fig.10). Conclusions In this study, a novel tunable optical filter basd on 12-node plum shaped integrated photonic RC chip is constructed. The PSO algorithm is used for training photonic RC weights to realize the IIR and FIR optical filters. The control of FSR is achieved by adjusting the length of the waveguide in the reservoir. Under the constant filter waveform, the filtering wavelength can be continuously tuned in the FSR by adjusting the phase of the WG in the reservoir (0-3π/2). The feasibility of this optical filter is verified by theory and simulation, and its tailorable performance can be used in multi-purpose adaptive signal processing application. -
表 1 IIR型光滤波器对应α值的设定参数
Table 1. Setting parameters of the corresponding α of IIR optical filter
|ylabel|max |ylabel|min a b x 1 0.05 4.5 1 0.95 表 2 IIR型光滤波器8路信号权重训练值
Table 2. IIR optical filter 8 channel signal weight training value
IIR 1st 2nd 3rd 4th 5th 6th 7th 8th WAmp 0.496 0.015 0.847 0.358 0.240 0.649 0.865 0.641 φw 4.717 0.593 5.01 1.176 4.072 0.173 2.180 1.935 表 3 FIR型光滤波器对应α值的设定参数
Table 3. Setting parameters of the corresponding α of FIR optical filter
|y’label|max |y’label|min a’ b’ x’ 0.81 0 2 4 0.4 表 4 FIR型光滤波器8路信号权重训练值
Table 4. FIR optical filter 8 channel signal weight training value
FIR 1st 2nd 3rd 4th 5th 6th 7th 8th WAmp 0.966 0.452 0.998 0.928 0.685 0.991 0.997 0.766 φw 3.258 2.861 3.097 5.189 3.080 0.259 6.282 5.246 -
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