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近年来,光学滤波器被用于实现光信号的多维度(包括幅度、相位等)、高精细操控,例如:纳米颗粒检测[1]、片上光信号处理[2]、高灵敏度光学传感[3]、微波光子学[4]等,因此亟需能够对光学滤波器多维光谱响应特性进行精细表征的光学矢量分析技术。
光干涉法[5-6]和调制相移法[7-8]是两种最常用的光学矢量分析方法,均借助于激光器的波长扫描来实现光学滤波器频响的测量。然而,由于可调谐激光器的波长稳定性和可重复性较差,这两种方法的频率分辨率只能达到百兆赫兹量级,无法实现高Q值光学滤波器频响的精细测量[9]。
为了提高频率分辨率,文献[10-15]提出了基于微波光子技术的光学矢量分析方案。通过电光调制,将光域内的波长扫描转至电域内进行,借助于高精细的电谱扫描和分析技术,已实现频率分辨率334 Hz的幅频和相频响应测量[15]。然而,目前已见报道的基于微波光子技术的光学矢量分析在测量频响时采用逐个频率点扫描的方式,高的频率分辨率意味着要扫描更多的频率点,大大增加了测量所需的时间(一般所需时间为数秒以上)。
本文提出了一种基于微波光子扫频的超快、高精细光学矢量分析技术方案,并对其进行了实验。实验中,以一段非零色散位移光纤的布里渊增益谱作为测试对象,对其幅频和相频响应进行测量,频率分辨率达到20 kHz,测量时间仅需20 μs。
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图1为本文提出的基于微波光子扫频的超快、高精细光学矢量分析技术方案示意图。其工作原理简述如下:可调谐激光二极管(laser diode, LD)输出直流光,进入偏置于最小透射点的双臂驱动马赫-曾德尔电光调制器(dual-arm-driven Mach-Zehnder electro-optic intensity modulator, DD-MZM);DD-MZM的一个射频口输入高功率电学线性调频(electrical linear frequency modulated, ELFM)信号,产生各阶调制边带,利用光学带通滤波器(optical bandpass filter, OBPF)滤出高阶边带作为宽带光学线性扫频信号,用于实现待测器件(device under test, DUT)频响特性的快速扫描;DD-MZM的另一个射频口输入单音本振(local oscillator, LO)微波信号,用于在光电探测时实现光学线性扫频信号的下变频;ELFM信号和LO信号通过10 M的同步信号进行同步;下变频后的扫频信号映射了DUT的频响特性,由电子模数转换器(analog-to-digital converter, ADC)实现数字化,在数字域内经过系统频响校准后,恢复出DUT的幅频和相频响应。
可调谐LD输出窄线宽直流光,其光场为:
$${E_{\rm{1}}}\left( t \right) = {E_c}\exp \left( {{\rm{j}}{\omega _c}t} \right)$$ (1) 式中,
${E_c}$ 和${\omega _c}$ 分别为直流光的振幅与角频率。DD-MZM的两个射频口分别输入ELFM信号和单音LO信号,调制后的光场可表示为:$$\begin{split} & \quad {E_{\rm{2}}}\left( t \right) = \frac{{\sqrt {\rm{2}} }}{{\rm{2}}}{E_c}\exp \left( {{\rm{j}}{\omega _c}t} \right) \times \\ & \left\{ \begin{aligned} & \exp \left[ {{\rm{j}}{m_{\rm{1}}}\cos \left( {{\omega _{{\rm{LO}}}}t} \right) + {\rm{j}}\phi } \right] + \\ & \exp \left[ { - {\rm{j}}{m_{\rm{2}}}\cos \left( {{\omega _{\rm{0}}}t + {\text π} \gamma {t^2}} \right)} \right] \\ \end{aligned} \right\} \end{split} $$ (2) 式中,
${m_{\rm{1}}}$ 和${m_2}$ 分别为LO信号和ELFM信号的调制系数;${\omega _{\rm{LO}}}$ 为LO信号的角频率;${\omega _{\rm{0}}}$ 和$\gamma $ 分别为ELFM信号的初始角频率与啁啾率;$\phi $ 为直流偏置引入的相移。将DD-MZM的直流偏置设置在最小透射点,即$\phi {\rm{ = }}\pi $ ,实现光载波抑制。ELFM的调制系数${m_{\rm{2}}}$ 足够大,实现谐波扫描,扩展测量带宽。LO为小信号,可忽略高阶调制边带。与此同时,设置OBPF的中心波长与带宽,只保留光载波一侧的调制边带。因此,OBPF的输出光场为:$${E_{\rm{3}}}\left( t \right) = {E_{\rm{LO}}}\left( t \right) + {E_{{\rm{ELFM}}}}\left( t \right)$$ (3) $${E_{\rm{LO}}}\left( t \right){\rm{ = }}{A_{\rm{LO}}}\exp \left( {{\rm{j}}{\omega _c}t +{\rm{j}} {\omega _{\rm{LO}}}t} \right)$$ (4) $${E_{{\rm{ELFM}}}}\left( t \right){\rm{ = }}\sum\limits_{n = 1}^N {{A_{{\rm{ELFM}},n}}\exp \left[ {{\rm{j}}{\omega _c}t + {\rm{j}}n\left( {{\omega _{\rm{0}}}t + {\text π} \gamma {t^2}} \right)} \right]} $$ (5) 式中,
${E_{\rm{LO}}}\left( t \right)$ 和${E_{{\rm{ELFM}}}}\left( t \right)$ 分别为OBPF通带内的LO和ELFM调制信号;N为OBPF通带内ELFM调制信号的谐波数;${A_{\rm{LO}}}$ 和${A_{{\rm{ELFM}},n}}$ 分别为LO和ELFM调制信号的振幅。当
${E_{\rm{3}}}\left( t \right)$ 通过DUT时,其中的${E_{{\rm{ELFM}}}}\left( t \right)$ 快速扫描DUT的频响特性,DUT的输出光场可表示为:$$\begin{split} & \qquad {E_{\rm{4}}}\left( t \right) = A\left( {{\omega _c} + {\omega _{\rm{LO}}}} \right) {A_{\rm{LO}}}\times\\ & \;\;\exp \left[ {{\rm{j}}{\omega _c}t + {\rm{j}}{\omega _{\rm{LO}}}t + {\rm{j}}\theta \left( {{\omega _c} + {\omega _{\rm{LO}}}} \right)} \right] + \\ & \qquad\quad \sum\limits_{n = 1}^N {A\left[ {{\omega _n}\left( t \right)} \right]} {A_{{\rm{ELFM}},n}}\times\\ & \exp \left[ {{\rm{j}}{\omega _c}t + {\rm{j}}n\left( {{\omega _{\rm{0}}}t + {\text π} \gamma {t^2}} \right) + {\rm{j}}\theta \left( {{\omega _n}\left( t \right)} \right)} \right] \end{split} $$ (6) 式中,
$A\left( \omega \right)$ 和$\theta \left( \omega \right)$ 分别表示DUT的幅频与相频响应;${\omega _n}\left( t \right)$ 为第n阶ELFM调制谐波的瞬时频率。当DUT的频响由第p阶ELFM调制谐波扫描得到时,通过设置单音LO信号的频率,则第p阶ELFM调制谐波可与LO调制信号在光电探测器(photodetector, PD)内拍频产生相对低频的线性调频光电流信号为:$$\begin{split} & I\left( t \right) = A\left( {{\omega _c} + {\omega _{\rm{LO}}}} \right)A\left( {{\omega _p}\left( t \right)} \right){A_{\rm{LO}}}{A_{{\rm{ELFM}},p}} \times\\ & \cos \left[ {p\left( {{\omega _0}t + {\text π} \gamma {t^2}} \right) - {\omega _{\rm{LO}}}t + \theta \left( {{\omega _p}\left( t \right)} \right) - \theta \left( {{\omega _c} + {\omega _{\rm{LO}}}} \right)} \right] \end{split}$$ (7) 从式(7)可以看到,光电流
$I\left( t \right)$ 携带了DUT的频响信息,通过分析$I\left( t \right)$ 的幅度与相位,即可获得DUT的矢量频响特性。需要说明的是,上述分析获得的频响特性包含了测量系统其余组件的频响信息,需要对测试结果进行校准。在校准过程中,将OBPF的输出端直接与PD相连,可获得校准光电流信号为:
$${I_{{\rm{cal}}}}\left( t \right) = {A_{\rm{LO}}}{A_{{\rm{ELFM}},p}} \cos \left[ {p\left( {{\omega _0}t + {\text π} \gamma {t^2}} \right) - {\omega _{\rm{LO}}}t} \right]\;$$ (8) 根据式(7)和式(8),通过式(9)可获得DUT的频率响应:
$$H\left[ {{\omega _p}\left( t \right)} \right] = \frac{{I\left( t \right) + {\rm{j}} {\rm{Hilbert}}\left[ {I\left( t \right)} \right]}}{{{I_{{\rm{cal}}}}\left( t \right) + {\rm{j}} {\rm{Hilbert}}\left[ {{I_{{\rm{cal}}}}\left( t \right)} \right]}}$$ (9) 式中,
${\rm{Hilbert}}\left[ \cdot \right]$ 代表希尔伯特变换。对于线性扫频光,频率分辨率为扫频光信号的带宽除以总采样点,可计算为:$${f_{{\rm{resoulution}}}} = {{{f_{{\rm{bandwidth}}}}} / {\left( {{f_{{\rm{sample}}}} T} \right)}}$$ (10) 式中,
${f_{{\rm{bandwidth}}}}$ 为扫频光信号带宽;${f_{{\rm{sample}}}}$ 为电子ADC采样速率;T为ELFM信号周期。
Research on Ultra-Fast Optical Vector Analysis Based on Microwave Photonic Frequency Sweeping
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摘要: 该文提出并验证了一种基于微波光子扫频的超快、高精度光学矢量分析技术方案。使用双臂驱动马赫−曾德尔电光调制器的一个射频端口加载线性调频信号,产生宽带光学线性扫频信号,实现待测器件频响特性的快速扫描。调制器的另一个射频端口加载单音本振微波信号,实现扫频信号的下变频,进而通过模数转换器实现低频数字化探测。然后利用希尔伯特变换进行信号处理后,获得待测器件的幅频和相频响应。最后实验测试了一段长度3 km的非零色散位移光纤中的布里渊增益幅频和相频响应,测量时间仅需20 μs,频率分辨率可达20 kHz。Abstract: An ultra-fast and high-resolution optical vector analysis scheme has been proposed and experimentally demonstrated. In the scheme, a broadband optical frequency-sweeping signal is generated by injecting a linearly frequency-modulated signal into one radio-frequency (RF) port of a dual-drive Mach-Zehnder electro-optic modulator, which is used to achieve fast scanning of the frequency response characteristic of the device under test (DUT). A single-tone microwave signal is injected into the other RF port of the modulator to realize down-conversion of the frequency-sweeping signal. The down-converted signal is then digitized by an analog-to-digital converter, and is processed through Hilbert transform to extract the amplitude- and phase-frequency response of the DUT. In the proof-of-concept experiment, the amplitude- and phase-frequency response of the Brillouin gain in a section of non-zero dispersion shifted fiber with a length of 3 km is accurately measured, where the measurement time is only 20 μs, and the frequency resolution reaches 20 kHz.
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