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近些年来，利用微波光子技术生成微波毫米波等高频信号的技术成为热点[1-5]，该技术已经成功应用到了诸如医学成像、雷达、无线通信等领域，相比于传统的电学方法生成高频信号的技术，光生微波毫米波信号具有频率高、带宽大、频谱纯度高且不易受电磁干扰等优势。
光生微波毫米波信号有很多技术，其中外调制技术系统简单、稳定性高且频率调谐性好，成为最具吸引力的方法。当前，针对四倍频[6-9]、六倍频[10-12]、八倍频[13-19]、十二倍频[20-22]微波毫米波信号生成的方案已经进行了广泛而深入的研究，更高倍频因子的方案也相继被提出。参考文献[23]中报道了采用级联双平行马赫-曾德尔调制器(dual-Mach-Zehnder modulator，DP-MZM)生成十六倍频光生毫米波的方案，系统复杂。参考文献[24]中报道了基于DP-MZM和光滤波器生成十六倍频的方案，相比于参考文献[23], 该方案更加复杂。参考文献[25]中报道了基于级联调制器的二十四倍频毫米波信号产生，该方案使用了一个DP-MZM、一个MZM，链路不止一个光电探测器(photodetector，PD)，系统也很复杂。
在参考文献[20]中，SHIH等人提出了基于DP-MZM与半导体光放大器(semiconductor optical amplifier，SOA)结合的十二倍频方案，生成了较高频率的信号。本文中将在SHIH等人所提方案的基础上，提出一种基于并联MZM和SOA结合生成二十四倍频毫米波信号的方案，鉴于光纤布喇格光栅(fiber Bragg grating，FBG)体积小、插入损耗低以及与普通通信光纤良好匹配的特点，本方案用FBG代替SHIH等人所用的梳状滤波器，可以实现二十四倍频本振信号的生成。将两个MZM都偏置在最小传输点(minimum transmission point, MATP)，通过设置其它参量以及调节调制指数生成±4阶边带，利用SOA的四波混频(four-wave mixing, FWM)效应生成±12阶边带，然后滤除±4阶边带后进行拍频，从而生成二十四倍频信号。
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所提出的二十四倍频方案如图 1所示。本方案中所用到的器件有连续激光器、射频(radio frequency, RF)信号源、直流源、马赫-曾德尔调制器、偏振控制器、半导体光纤放大器、相位移相器(phase shifter, PS)、布喇格光栅滤波器、光学衰减器(optical attenuator, OA)以及光电探测器。
Figure 1. Schematic diagram of microwave millimeter wave signal generation based on parallel MZM structure and SOA
设抽运激光器发出的光信号和微波源发出的电信号分别为：
$ {E_{{\rm{in}}}}\left( t \right) = {E_0}{\rm{exp}}(j{\omega _0}t){\rm{ }} $
(1) $ V\left( t \right) = {V_{{\rm{RF}}}}{\rm{sin}}({\omega _{{\rm{RF}}}}t) $
(2) 式中，E0是光场幅度，ω0是抽运光波频率，VRF是射频信号的幅度，ωRF是射频信号的角频率。
入射进两个子调制器的直流偏置电压用VDC, i(i=1, 2)表示，则由直流偏置所引入的相位差ϕi=πVDC, i/Vπ(i=1, 2)，其中Vπ是MZM的半波电压。
激光器发出的光波被一个马赫-曾德尔集成调制器所调制，该集成调制器由嵌入到MZM上下两臂的两个子调制器MZM-a和MZM-b构成。射入两个子调制器的射频信号相位相差π/2，每个子调制器的上下两臂的射频信号相位差为0。令MZM-a和MZM-b都偏置在MATP，即ϕ1=ϕ2=0，则经过并联MZM调制后的信号可以表示为：
$ \begin{array}{l} {E_{{\rm{out}}}}(t) = \frac{1}{4}{E_0}{\rm{exp}}\left( {{\rm{j}}{\omega _0}t} \right)\left\{ {{\rm{exp}}\left[ {{\rm{j}}m{\rm{sin}}\left( {{\omega _{{\rm{RF}}}}t} \right)} \right]} \right. + \\ {\rm{exp}}\left[ { - {\rm{j}}m{\rm{sin}}\left( {{\omega _{{\rm{RF}}}}t} \right)} \right]{\rm{exp}}\left( { - {\rm{j}}{\phi _1}} \right) + \exp \left[ {{\rm{j}}m{\rm{sin}}\left( {{\omega _{{\rm{RF}}}}t} \right. + } \right.\\ \left. {\left. {\left. {\Delta \phi } \right)} \right] + \exp \left[ { - {\rm{j}}m{\rm{cos}}\left( {{\omega _{{\rm{RF}}}}t + \Delta \phi } \right)} \right]\exp \left( { - {\rm{j}}{\phi _2}} \right)} \right\} = \\ \frac{1}{4}{E_0}{\rm{exp}}\left( {{\rm{j}}{\omega _0}t} \right)\sum\limits_{n = - \infty }^\infty {{{\rm{J}}_\mathit{n}}\left( m \right)\exp \left( {{\rm{j}}n{\omega _{{\rm{RF}}}}t} \right)} \left\{ {1 + {{\left( { - 1} \right)}^n} \cdot } \right.\\ \exp \left( { - {\rm{j}}{\phi _1}} \right) + \exp \left( {{\rm{j}}\mathit{n}\Delta \phi } \right) + {\left( { - 1} \right)^n}\exp \left( { - {\rm{j}}{\phi _2}} \right) \cdot \\ \left. {\exp \left( {{\rm{j}}\mathit{n}\Delta \phi } \right)} \right\} = \frac{1}{4}{E_0}{\rm{exp}}\left( {{\rm{j}}{\omega _0}t} \right)\sum\limits_{n = - \infty }^\infty {{{\rm{J}}_\mathit{n}}\left( m \right) \cdot } \\ \exp \left( {{\rm{j}}n{\omega _{{\rm{RF}}}}t} \right)\left\{ {1 + \exp \left( {{\rm{j}}\mathit{n}\Delta \phi } \right) + {{\left( { - 1} \right)}^n} \cdot } \right.\\ \left. {\left[ {\exp \left( { - {\rm{j}}{\phi _1}} \right) + \exp \left( { - {\rm{j}}{\phi _2}} \right)\exp \left( {{\rm{j}}\mathit{n}\Delta \phi } \right)} \right]} \right\}{\rm{ = }}\\ \frac{1}{4}{E_0}{\rm{exp}}\left( {{\rm{j}}{\omega _0}t} \right)\sum\limits_{n = - \infty }^\infty {{{\rm{J}}_\mathit{n}}\left( m \right)\exp \left( {{\rm{j}}n{\omega _{{\rm{RF}}}}t} \right) \cdot } \\ \left\{ {\left[ {1 + \exp \left( {{\rm{j}}\mathit{n}\Delta \phi } \right)} \right]\left[ {1 + {{\left( { - 1} \right)}^n}} \right]} \right\} \end{array} $
(3) 当$ \Delta \phi = \frac{{\rm{ \mathsf{ π} }}}{2}$时，(3)式可化为:
$ \begin{array}{l} {E_{{\rm{out}}}}(t) = \frac{1}{4}{E_0}{\rm{exp}}\left( {{\rm{j}}{\omega _0}t} \right)\sum\limits_{n = - \infty }^\infty {{{\rm{J}}_\mathit{n}}\left( m \right) \cdot } \\ \exp \left( {{\rm{j}}n{\omega _{{\rm{RF}}}}t} \right)\left\{ {\left( {{\rm{1 + }}{{\rm{j}}^n}} \right)\left[ {1 + {{\left( { - 1} \right)}^n}} \right]} \right\} \end{array} $
(4) 式中，Jn(m)为n阶贝塞尔函数。
由(1)式~(4)式可知：(1)当n=4k+1或n=4k+3(k为整数，下同)时，1+(-1)n=0，±1阶和3阶边带信号被抑制；(2)当n=4k+2时，1+jn=0，±2阶边带信号被抑制；(3)当n=4k时，Eout(t)≠0，载波和±4阶边带信号被保留，更高阶的信号由于功率过低，可以不用考虑。
令J0(m)=0，可抑制载波，如图 2所示。当m=2.405时，J0(m)=0。
Figure 2. Bessel function graph of the first kind of 0 order sideband and the 4th order siderband
当满足频率稳定、相位相关且偏振态相同的两个光波信号在非线性介质中传播时，会由于非线性极化作用发生混频效应，从而产生两个新的波长，这种现象被称为FWM。设抽运光频率为ω0，信号光频率为ω1，则经FWM效应后生成的两个谐波分量的频率分别为(2ω0－ω1)和(2ω1－ω0)，如图 3所示。
图 3 Schematic diagram of FWM
诸如高非线性光纤(high nonlinear optical fiber, HNLF)和SOA等非线性器件都可以发生FWM、交叉增益调制(cross gain modulation, XGM)、交叉相位调制(cross phase modulation, XPM)等非线性效应。FWM的产生要求各信号光的相位匹配，当各信号光在光纤的零色散附近传输时，材料色散对相位失配的影响很小，因而较容易满足相位匹配条件，容易产生四波混频效应。本方案中，从DP-MZM中产生的光信号满足频率稳定、相位相关等条件，此时，其它的非线性效应的影响很小，可以忽略不计。因此，将采用SOA进行FWM。
如前面所述，生成的±4阶边带信号在经过FWM后将产生±12阶边带信号，分别为ωidler, 1=2ω0－ω1=-12和ωidler, 2=2ω1－ω0=+12。经两级FBG滤除±4阶边带信号后，只剩下±12阶边带信号，最后经PD拍频便可生成纯净的二十四倍频信号。
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针对提出的二十四倍频信号生成方案，作者利用OptiSystem软件进行了仿真实验。
如图 1所示，连续激光器发出的光信号中心频率为193.1THz，功率为0dBm，线宽为10MHz；射频源信号频率为5GHz，初始相位为0；MZM-a和MZM-b参量设置一样，消光比为50dB，半波电压为4V，插入损耗为5dB，设置射频调制电压为6.127V，直流偏置电压为4V和0V；SOA注入电流为0.08A；FBG 1中心频率为193.12THz，带宽为35GHz，FBG 2中心频率为193.08THz，带宽同样为35GHz; 光学衰减器衰减量为5dB, 光电探测器增益为20；响应度为5A/W。
如图 4a所示，在设置消光比为50dB的情况下，并联MZM输出的频谱图中±4阶边带信号占据主导，而其它谐波则被极大的抑制，虽然仍有±1阶边带信号，但光学边带抑制比(optical sideband suppression ratio，OSSR)仍然达到了35dB。图 4b显示了经SOA混频后的频谱图。可以看到, 由于FWM效应生成了±12阶边带信号。图 4c显示了经两级FBG滤除±4阶边带后的频谱图，OSSR为29dB。图 4d为PD输出的二十四倍频信号电谱图。由图可知，在输入射频信号5GHz时，生成了120GHz的微波信号，且射频杂散抑制比(radio frequency spurious suppression ratio，RFFSR)为22dB，具有很高的纯度。
Figure 4. a—output spectrum of parallel MZM b—output spectrum of SOAc—output spectrum of FBG 2 d—output electricity spectrum of PD
为了验证二十四倍频方案的频率可调谐性，调整射频信号的频率，观察PD输出的电谱图如图 5所示。由图 5可知，当射频信号在4GHz~7GHz之间调谐时，所生成的二十四倍频信号仍然具有很高的RFFSR，说明该二十四倍频结构可以实现获得96GHz~168GHz的高频微波信号。
Figure 5. a—output electricity spectrum of PD when RF is 4GHz b—output electricity spectrum of PD when RF is 7GHz
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本文中介绍了一种基于并联MZM和SOA结合实现输入信号二十四倍频的方案，在输入信号为5GHz时，生成了120GHz的高频微波信号，RFFSR为22dB，当输入信号频率在4GHz~7GHz范围内调节时，可以获得96GHz~168GHz的高频微波信号，频谱纯度也很高。从理论上分析验证了该方案实现二十四倍频的可行性，为高频微波毫米波信号的生成提供了更高的倍频方法。本方案虽然可以生成较高倍频数的信号，但是信号的RFSSR也只维持在22dBm的水平，相较于已有的四倍频、八倍频信号的RFSSR可以达到30dBm以上、甚至40dBm以上的水平，本方案还有所差距。所以，既要考虑高倍频因子，也要考虑信号的高性能，这是以后努力的方向。
基于并联调制器的高倍频毫米波信号生成
Generation of high frequency millimeter wave signal based on parallel modulators
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摘要: 为了获得更高频率的信号，采用了一种基于并联马赫-曾德尔调制器（MZM）和半导体光纤四波混频效应的二十四倍频光生毫米波方案。本振信号被并联MZM调制后可以获得高纯度的±4阶边带，在四波混频效应下，又可以生成±12阶边带，用级联的布喇格光栅滤波器滤除±4阶边带，经光电探测器拍频便可生成二十四倍频信号。结果表明，当输入本振信号为5GHz时，生成的120GHz高频微波毫米波信号射频杂散抑制比为22dB，频谱纯度很高，且具有很好的可调谐性。该研究为高频微波毫米波信号的生成提供了更高的倍频方法。Abstract: In order to get higher frequency signal, a 24-tupling frequency microwave millimeter-wave signal generation scheme based on parallel Mach-Zehnder modulators (MZM) and semiconductor optical amplifier (SOA) four-wave mixing effect was presented and simulated.The local oscillator signal was modulated by parallel MZM to obtain high-purity ±4 sidebands.Under the four-wave mixing effect, the ±12 sidebands were generated.The ±4 sideband was filtered by cascaded Bragg grating filters.After the beat frequency of photoelectric detector, 24-tupling frequency signal was generated.The results show that, when input local oscillator signal is 5GHz, radio frequency spurious rejection ratio of the generated 120GHz high frequency microwave millimeter wave signal is 22dB.The spectrum purity is high, and the tunability is good.This study provides a high frequency doubling method for the generation of high frequency microwave and millimeter wave signal.
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Figure 1. Schematic diagram of microwave millimeter wave signal generation based on parallel MZM structure and SOA
Figure 2. Bessel function graph of the first kind of 0 order sideband and the 4th order siderband
Figure 4. a—output spectrum of parallel MZM b—output spectrum of SOAc—output spectrum of FBG 2 d—output electricity spectrum of PD
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