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超长分布式2阶喇曼放大器是通过使信号光在光纤传输系统中均匀传输来抑制放大自发辐射噪声的。它的系统结构如图 1所示。
抽运光经过一个功率均分的光耦合器(optical coupler, OC)分为两路光分别通过两个波分复用器(wavelength division multiplexing, WDM)进入光纤。而进入光纤的抽运光在传输的过程中发生了受激喇曼散射效应,产生了1阶斯托克斯光。产生的1阶斯托克斯光的波长恰好等于所用光纤光栅的中心波长,这样在整个传输光纤上便可以产生大量该波长的激光。接着,光信号再经过隔离器之后通过波分复用器进入光纤。随着信号光在光纤上进行传输,产生的波长等于1阶斯托克斯光的大量激光通过受激喇曼散射效应对信号光进行放大。最后,在光纤的另一端,信号光经过一个中心波长等于信号光波长的光滤波器进行滤波。
在传输的过程中,除了信号光与抽运光本身功率的衰减之外,放大自发辐射以及双瑞利散射也是需要考虑的会对功率产生影响的因素。对于以上提到的这些因素,各信号光、抽运光以及噪声的之间的关系可以见下式[12]:
$ \begin{array}{l} \pm \frac{{{\rm{d}}{P_{ \pm 1}}}}{{{\rm{d}}z}} = - {\alpha _1}{P_{ \pm 1}} - {g_1}\frac{{{v_1}}}{{{v_2}}}{P_{ \pm 1}}\left\{ {{P_{ + 2}} + {P_{ - 2}} + 4h{v_2}\Delta {v_2} \times } \right.\\ \;\;\;\;\;\;\;\left. {\left[ {1 + \frac{1}{{\exp \left[ {h\left( {{v_1} - {v_2}} \right)/\left( {{K_{\rm{B}}}T} \right)} \right] - 1}}} \right]} \right\} + {\varepsilon _1}{P_{ \mp 1}} \end{array} $
(1) $ \begin{array}{l} \pm \frac{{{\rm{d}}{P_{ \pm 2}}}}{{{\rm{d}}z}} = - {\alpha _2}{P_{ \pm 2}} + {g_1}\left\{ {{P_{ \pm 2}} + 2h{v_2}\Delta {v_2} \times } \right.\\ \left. {\left[ {1 + \frac{1}{{\exp \left[ {h\left( {{v_1} - {v_2}} \right)/\left( {{K_{\rm{B}}}\rm{T}} \right)} \right] - 1}}} \right]} \right\}\left( {{P_{ + 1}} + {P_{ - 1}}} \right) - \\ {g_2}\frac{{{v_2}}}{{{v_{\rm{s}}}}}{P_{ \pm 2}}\left\{ {{P_{\rm{s}}} + {N_{ + {\rm{s}}}} + {N_{ - {\rm{s}}}} + 4h{v_{\rm{s}}}\Delta {v_{\rm{s}}} \times } \right.\\ \left. {\left[ {1 + \frac{1}{{\exp \left[ {h\left( {{v_2} - {v_{\rm{s}}}} \right)/\left( {{K_{\rm{B}}}T} \right)} \right] - 1}}} \right]} \right\} + {\varepsilon _2}{P_{ \mp 2}} \end{array} $
(2) $ \frac{{{\rm{d}}{P_{\rm{s}}}}}{{{\rm{d}}z}} - {\alpha _{\rm{s}}}{P_{\rm{s}}} + {g_2}{P_{\rm{s}}}\left( {{P_{ + 2}} + {P_{ - 2}}} \right) $
(3) $ \begin{array}{*{20}{c}} {\frac{{{\rm{d}}{N_{ + {\rm{s}}}}}}{{{\rm{d}}z}} = - {\alpha _{\rm{s}}}{N_{ + {\rm{s}}}} + {g_2}\left\{ {{N_{ + {\rm{s}}}} + 2h{v_{\rm{s}}}\Delta {v_{\rm{s}}} \times } \right.}\\ {\left. {\left[ {1 + \frac{1}{{\exp \left[ {h\left( {{v_2} - {v_{\rm{s}}}} \right)/\left( {{K_{\rm{B}}}T} \right)} \right] - 1}}} \right]} \right\} \times }\\ {\left( {{P_{ + 2}} + {P_{ - 2}}} \right) + {\varepsilon _{\rm{s}}}{N_{ - {\rm{s}}}}} \end{array} $
(4) $ \begin{array}{*{20}{c}} { - \frac{{{\rm{d}}{N_{ - {\rm{s}}}}}}{{{\rm{d}}z}} = - {\alpha _{\rm{s}}}{N_{ - {\rm{s}}}} + {g_2}\left\{ {{N_{ - {\rm{s}}}} + 2h{v_{\rm{s}}}\Delta {v_{\rm{s}}} \times } \right.}\\ {\left. {\left[ {1 + \frac{1}{{\exp \left[ {h\left( {{v_2} - {v_{\rm{s}}}} \right)/\left( {{K_{\rm{B}}}T} \right)} \right] - 1}}} \right]} \right\} \times }\\ {\left( {{P_{ + 2}} + {P_{ - 2}}} \right) + {\varepsilon _{\rm{s}}}\left( {{P_{\rm{s}}} + {N_{ + {\rm{s}}}}} \right)} \end{array} $
(5) 式中,下标+和-分别代表前向和背向传输方向,下标1, 2, s分别代表1阶抽运、2阶抽运和信号光,Pi(i=1, 2), Ps, Ns分别代表抽运功率、信号功率以及噪声功率,νi(i=1, 2, s)表示抽运光与信号光的频率值,Δνi(i=2, s)代表了信号与2阶抽运的有效带宽,gi(i=1, 2)是每一个喇曼转换的喇曼增益系数,αi(i=1, 2, s)是各频率的衰减系数,h是普朗克常数,KB是玻尔兹曼常数,T是绝对温度,εi(i=1, 2, s)是各频率的双瑞利散射系数。
上述耦合方程组的边界条件如下:
$ \left\{ \begin{array}{l} {P_{ + 1}}\left( 0 \right) = {P_{ - 1}}\left( L \right) = {P_0}\\ {P_{ + 2}}\left( 0 \right) = {R_1}{P_{ - 2}}\left( 0 \right)\\ {P_{ - 2}}\left( L \right) = {R_2}{P_{ + 2}}\left( L \right)\\ {N_{ + {\rm{s}}}}\left( 0 \right) = {N_0}\\ {N_{ - {\rm{s}}}}\left( L \right) = 0\\ {P_{\rm{s}}}\left( 0 \right) = {P_{{\rm{in}}}} \end{array} \right. $
(6) 式中,P0表示前向以及背向抽运功率大小,一般情况下如(6)式所示两者相等,Pin表示信号光的初始功率、N0表示信号光的初始噪声功率,R1和R2分别代表光纤两端的光纤光栅的有效反射率,L是传输光纤的长度。
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将上述分布式2阶喇曼放大器用于光载射频传输,其结构如图 2所示。
Figure 2. Radio-over-fiber transmission link model based on ultra-long distributed second-order Raman amplifier
对该系统采用的调制方式为一臂强度调制,另一臂光信号直接通过,则光信号和射频信号经过调制器,可以得到:
$ {y_{{\rm{in}}}}\left( t \right) = \frac{{{E_0}\sqrt {{\alpha _{{\rm{MZM}}}}} }}{2}\left[ {1 + {{\rm{e}}^{{\rm{j}}\mathit{\Phi }\left( t \right)}}} \right]{{\rm{e}}^{{\rm{j}}{\omega _0}t}} $
(7) 式中,αMZM是调制器的插入损耗因子; E0为光源输出场强的最大值; ω0为光信号频率; $ \mathit{\Phi} \left( t \right) = \frac{{{\rm{ \mathsf{ π} }}{V_{{\rm{DC}}}}}}{{{V_{\rm{ \mathsf{ π} }}}}} + \frac{{{\rm{ \mathsf{ π} }}{V_{{\rm{RF}}}}(t)}}{{{V_{\rm{ \mathsf{ π} }}}}} $为调整后光信号的相位变化,其中,Vπ为调制器的半波电压,VDC是加在调制器上直流偏置电压,本文中取$ {V_{{\rm{DC}}}} = \frac{1}{2}{V_{\rm{ \mathsf{ π} }}} $,VRF(t)=VRFcos(ωRFt)为所调射频信号,ωRF是射频信号频率。
在RoF链路中,信号光在光纤中的色散会对RoF系统造成影响[16-20]。链路中,射频信号调制到光信号的上下边带上,这两个边带之间有一定的频率,那么由于色散的影响将会产生相应的相位差。结合光纤损耗,并考虑光纤色散的影响,那么系统的传输函数可以写成[19]:
$ H\left( \omega \right) = \sqrt {{\alpha _{{\rm{loss}}}}} \exp \left[ {\frac{{\rm{j}}}{2}{\beta _2}L{{\left( {\omega - {\omega _0}} \right)}^2}} \right] $
(8) 式中,αloss=αlinkαMZM,整个RoF链路的总损耗,包括调制器的影响和光链路及其连接处引入的损耗; β2为光纤的2阶色散参量。
对(7)式做贝塞尔展开,仅保留直流信号与1阶信号,做傅里叶变换,与(8)式的系统传输函数作用,将结果进行傅里叶逆变换,再考虑链路损耗以及超长分布式2阶喇曼放大器的增益,根据光电探测器的原理,可以得到光电探测器上产生1阶信号输出电流为:
$ \begin{array}{*{20}{c}} {{I_{\rm{f}}} = - \eta {P_0}{\alpha _{{\rm{loss}}}}{G_{\rm{R}}}{{\rm{J}}_1}\left( m \right)\cos \left( {{\omega _{{\rm{RF}}}}t} \right) \times }\\ {\left[ {\cos \left( {\frac{{{\beta _2}}}{2}L{\omega _{{\rm{RF}}}}^2} \right) + \sin \left( {\frac{{{\beta _2}}}{2}L{\omega _{{\rm{RF}}}}^2} \right)} \right]} \end{array} $
(9) 式中,η为光电探测器的响应度,P0=E02为光信号的光强,GR为喇曼放大器引入的增益,J1(m)为1阶贝塞尔函数,其中$ m = \frac{{{\rm{ \mathsf{ π} }}{V_{{\rm{RF}}}}(t)}}{{{V_{\rm{ \mathsf{ π} }}}}} $为调制度。
1阶射频信号增益为[20]:
$ \begin{array}{*{20}{c}} {G = \left\{ {\frac{{{\rm{ \mathsf{ π} }}\eta {\alpha _{{\rm{loss}}}}{G_{\rm{R}}}{P_0}R}}{{2{V_{\rm{ \mathsf{ π} }}}}}\left[ {\cos \left( {\frac{{{\beta _2}}}{2}L{\omega _{{\rm{RF}}}}^2} \right) + } \right.} \right.}\\ {{{\left. {\left. {\sin \left( {\frac{{{\beta _2}}}{2}L{\omega _{{\rm{RF}}}}^2} \right)} \right]} \right\}}^2}} \end{array} $
(10) 式中,R为阻抗匹配时的电阻值。
基于超长分布式2阶喇曼放大器的光载射频传输
Radio-over-fiber transmission based on ultra-long distributed 2-order Raman amplifier
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摘要: 为了提升光载射频传输链路的链路增益以及传输距离,采用了L波段的超长分布式2阶喇曼放大器结构对光信号进行放大。从理论上对分布式2阶喇曼放大器以及光载射频传输链路的原理进行了解释,利用信号光、1阶抽运光、2阶抽运光以及噪声之间的耦合方程组分析了它们之间的关系,并且得到了基于超长分布式2阶喇曼放大器的光载射频传输系统的1阶射频信号增益。通过数值仿真以及系统实验得到了抽运功率大小对超长分布式2阶喇曼放大器的开关增益的影响、光载射频传输系统在0GHz~7GHz范围内的频率响应及其射频增益以及该光载射频传输链路在应用超长分布式2阶喇曼放大器后的相位噪声情况。结果表明,光载射频传输在超长分布式2阶喇曼放大器的作用下获得了28.1dB的链路增益,在距离为80.94km的光链路上实现了近似无损传输,射频信号开关增益与射频信号频率无关。该研究在光载射频链路的长距离传输中有重要的应用价值。
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关键词:
- 光纤放大器 /
- 光载射频传输 /
- 超长分布式2阶喇曼放大器 /
- 光纤色散 /
- 相位噪声
Abstract: In order to improve the link gain and transmission distance of radio-over-fiber (RoF) frequency transmission link, ultra-long distributed second-order Raman amplifier structure in L band was used to amplify the light signal. The principle of the distributed 2-order Raman amplifier and the RoF transmission link were explained theoretically. The relationships among them were analyzed by using the coupling equations between signal light, 1-order pumping light, 2-order pumping light and noise. The 1-order radio frequency (RF) signal gain of a RoF transmission system based on ultra-long distributed 2-order Raman amplifier was also obtained. Through numerical simulation and system experiment, the effect of pumping power on on-off gain of ultra-long distributed 2-order Raman amplifier, frequency response and RF gain of RoF transmission system in the range of 0GHz~7GHz, and phase noise of RoF transmission link after the application of ultra-long distributed 2-order Raman amplifier were obtained. The results show that the link gain of 28.1dB is obtained by RoF transmission after the application of an ultra-long distributed 2-order Raman amplifier. Approximate lossless transmission is achieved in optical link with a distance of 80.94km. The on-off gain of RF signal is independent of the frequency of RF signal. The study has important application value in long distance transmission of optical radio frequency links. -
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