光梳状滤波器在光通信和微波信号处理中的研究及应用
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摘要
光梳状滤波器具有独特的周期性幅度滤波或相位滤波性能,因而在光通信和微波信号处理领域倍受关注。诸如,取样光纤光栅(SFBG)型、Mach-Zehnder干涉仪型、高双折射光纤型等梳状滤波器已广泛应用于波分复用/解复用器、多信道色散补偿器、高速光脉冲源、微波滤波器、以及实时微波频率测量技术等。与此同时,伴随着新技术和新需求的不断涌现,光梳状滤波器的研究和应用正面临着许多新的挑战和机遇。以此为选题背景,本文对SFBG型和高双折射光纤型梳状滤波器进行了研究:从理论上着手研究了SFBG型梳状滤波器的信道中心波长分布规律和滤波信道密集化技术;从新型应用的角度出发,设计了基于高双折射光纤型梳状滤波器的实时微波频率测量方案和基于等效梳状滤波效应的重复速率可调型光脉冲序列生成方案。
SFBG型梳状滤波器的理论研究和分析主要借助于Fourier级数法、Fourier变换法和传输矩阵法。运用Fourier级数法、Fourier变换法推导得到信道中心波长、滤波信道间隔的理论结论,再用传输矩阵法数值验证结论的正确性。对高双折射光纤型梳状滤波器和等效梳状滤波效应的应用研究侧重于新方案设计,然后搭建实验平台论证新方案的有效性和优势。基于以上分析方法和研究思路,本文的主要研究内容和成果如下:
深入研究了均匀、切趾型、大啁啾型SFBG信道中心波长的分布规律。在均匀和切趾型SFBG中,利用Fourier级数法将SFBG分解成一系列子光栅,单独求解每个子光栅的反射峰波长,即SFBG各阶信道的中心波长;其分布规律受占空比、取样周期和相位匹配条件的影响。针对大啁啾型SFBG,将啁啾效应等效成离散相移,以Fourier变换法获得Talbot效应下的波长偏移量;此偏移量与均匀SFBG信道中心波长之和为大啁啾效应下的信道中心波长。
首次提出在SFBG中应用周期性啁啾结构实现滤波信道密集化。周期性啁啾结构由多个结构一致的啁啾周期(或超结构)构成。啁啾效应导致的相位分布同时满足Talbot相位条件和相位空间2π的整数倍等效关系,从而以频域Talbot效应实现了信道密集化。并对周期性啁啾结构进行了扩展:将相位条件由二次扩展到高次,将结构设计的自由度从一维扩展到三维。
探讨了取样方案在设计超窄带平坦滤波器和一维光子晶体型滤波器中的推广应用。基于SFBG的等效相移技术和光栅的多相移技术在SFBG的-1阶反射带上形成一个窄带(约为数十皮米)、平坦的透射峰,即超窄带平坦滤波器。将一维光子晶体中高、低折射率层交替排列的反转等效定义为π相移跳变,借助优化算法获得相位跳变点,从而将二元相位取样方案巧妙地用于设计一维光子晶体型梳状滤波器。
应用色散光纤或偏振调制器(PolM),分别设计了具有可调谐测量频段或宽带测量频段的实时微波频率测量方案。利用色散光纤的色散斜率,构建两个不同的色散导致的微波功率衰减函数,并从两者的比值中反解得到微波频率;以调整波长间隔的方式改变功率衰减函数,实现了可调谐的测量范围。借助PolM和检偏器,同步得到两个调制深度一致的强度调制光和相位调制光。引入色散效应,由相位调制和强度调制光信号分别得到两互补型微波功率衰减函数;对比两互补型衰减函数计算出微波频率,扩大了频率测量范围。
应用高双折射光纤型梳状滤波器,设计了两种基于光功率检测的实时微波频率测量方案。载波抑制型小信号调制下,将经微波信号调制的两路光信号的载波波长分别置于Sagnac环梳状谱的波峰和波谷处进行滤波,然后对比两波长上的光功率得到待测微波频率。采用单个光波长和一对互补型梳状滤波器实现了更为稳定的频率测量方案。同样在载波抑制型小信号调制下,光信号的载波波长同时置于一对互补型梳状滤波器中一个滤波谱的波峰和另一个滤波谱的波谷:检测并对比两滤波器输出端的光功率从而获得微波频率。后一种方案不仅减少了光源的数目,而且完全消除了光源功率波动对频率测量的影响。
设计了重复速率简易可调的高速光脉冲序列生成方案。结合PolM和偏振分束器,奇次、偶次光边带在两个偏振态上得以分离,实现了等效梳状滤波效应:其频率选取间隔随驱动微波频率而自动调整,无需额外的物理调节机制。基于等效梳状滤波效应,生成了二倍频重复速率的归零码(RZ)和载波抑制归零码(CS-RZ)光脉冲序列,大为简化了重复速率的调节过程。
Due to their cyclical amplitude filtering or phase filtering characteristics, the comb filters have attracted great interest in optical communications and microwave signal processing. For instance, the sampled fiber Bragg grating- (SFBG), the Mach-Zehnder interferometer- and high birefringence fiber (HBF)-based comb filters can find applications in the wavelength division multiplexer/demultiplexer, the multi-channel dispersion compensator, the high-speed pulse generator, the microwave filter, the instantaneous microwave frequency measurement, and so on. At the same time, along with the emergence of novel technologies and requirements, the research and the application about the optical comb filters are facing new challenges and opportunities. Against such a profound background, in this dissertation the investigation on the SFBG- and the HBF-based comb filters has been performed. Firstly, the peak wavelengths of reflection channels and the channel density techniques are theoretically investigated for the SFBG-based comb filters. Secondly, instantaneous microwave frequency measurement approaches using HBF-based comb filters are proposed and demonstrated. Finally, based on the equivalent comb filtering effect, a simple approach is designed to generate pulse trains with a tunable repetition rate.
During the theoretical investigation and analysis on the filtering characteristics of SFBGs, three analysis tools have been used, i.e., the Fourier series method, the Fourier transform method, and the transfer matrix method. With the Fourier series method and the Fourier transform method, results and conclusions which describe the peak wavelengths or the channel spacing are derived. The transfer matrix method is then adopted to verify the derived results or conclusions. As for the HBF-based comb filter and the equivalent comb filtering effect, the application investigation focuses on the proposal of novel approaches or architectures. Related experiments have been performed to confirm the effectiveness and the advantages of proposed approaches. According to the analysis tools and the design ideas aforementioned, the main research work and results are listed in the following.
An in-depth analysis about the distribution of peak wavelengths of SFBGs has been conducted. The uniform or apodized SFBG is decomposed into a number of ghost gratings using Fourier series method. All peak wavelengths of SFBG are obtained as the peak wavelength of each ghost grating is calculated. The peak wavelengths of SFBG are associated with the duty cycle, the sampling period, and the phase-matching condition. While in the SFBG having large chirp effect, the chirp effect is transformed into discrete phase shifts to implement the Fourier transform, with the wavelength drift induced by Talbot effect being derived. The sums of this wavelength drift and the peak wavelengths of uniform SFBG are the peak wavelengths of SFBG having large chirp.
The periodic chirp structure is firstly proposed to get narrow channel spacing in the spectrum of SFBG. The periodic chirp structure consists of a number of identical chirp structures (or superstructures). The channel density can be realized by the spectral Talbot effect, as long as both the phase condition for Talbot effect and the equivalence of integer multiple of 2πin the phase plane are satisfied. Moreover, the periodic chirp structure can be further extended, with the phase condition being extended from parabolic to the high-order and the design degree being extended from one-dimensional to three-dimensional.
The sampling approaches can find applications in designing the ultra-narrow, flat-top filter and the one-dimension photonic crystal-based filter. The combination of the equivalent phase shift (EPS) technique in SFBG and the multiple phase shift technique in fiber grating is able to open an ultranarrow (several tens of pico-meter) and flat transmission peak in the -1~(st) reflection band of SFBG. Namely, ultra-narrow and flat-top filters have been achieved. In the one-dimension photonic crystal, the inversion in the alternate arrange of low- and high- refractive index layers is defined as the equivalentπphase shift. A number of phase transmit points are then obtained using optimal algorithms. Therefore, the binary sampling function can be used to implement comb filters based on one-dimension photonic crystal.
Instantaneous microwave frequency measurement approaches with a tunable measurement range or a wideband measurement range, are designed by the use of a length of dispersive fiber or a polarization modulator (PolM). Due to the dispersion slope of the dispersive fiber, two different microwave power fading functions caused by dispersion effect are detected, with the microwave frequency being calculated from the ratio of two functions. Since different fading functions can be achieved by adjusting the wavelength spacing, a tunable measurement range has been achieved. With the joint function of a PolM and a polarizer, a phase-modulated lightwave and an intensity-modulated lightwave, with an identical modulation index, are simultaneously generated. Two complementary microwave power fading functions resulted from dispersion effect are detected from the two modulated lightwaves. By estimating the microwave frequency from the ratio of the two complementary functions, a large measurement range is realized.
Two frequency measurement approaches in the way of optical power detection are proposed by using HBF-based comb filters. Under the condition of the carrier-suppressed, small-signal modulation, two lightwaves are modulated by an unknown microwave signal to generate±1~(st) optical sidebands. The two carriers of the two lightwaves are located at a peak and a valley of the Sagnac loop's comb response, to perform two complementary comb filtering functions. The frequency to be measured is estimated by detecting the optical powers at two lightwaves. Moreover, a more stable measurement approach is implemented by using a single lightwave and a complementary comb filter pair. In a similar way, the carrier-suppressed, small-signal modulation is employed. The carrier of the modulated lighwave is simultaneously set at the peak of one transmission comb and the valley of the other complementary transmission comb. The microwave frequency is then estimated by monitoring the optical powers from the two outputs of the filter pair. In the latter approach, the setup is greatly simplified and the influence of the optical power fluctuations on the frequency measurement is eliminated completely.
A simple approach is proposed and implemented to generate high-speed pulse trains having a tunable repetition rate. The odd- and the even-order sidebands are separated along the two polarization states by the use of a PolM and a polarization beam splitter, leading to an equivalent comb filtering effect. The comb spacing of the equivalent comb filtering effect varies automatically with the microwave frequency, without additional tuning mechanism. With the equivalent comb filtering effect, return-to-zero (RZ) and carrier-suppressed return-to-zero (CS-RZ) pulse trains having a repetition rate twice of the microwave frequency are generated, leading to the adjustment of the repetition rate greatly simplified.
SFBG型梳状滤波器的理论研究和分析主要借助于Fourier级数法、Fourier变换法和传输矩阵法。运用Fourier级数法、Fourier变换法推导得到信道中心波长、滤波信道间隔的理论结论,再用传输矩阵法数值验证结论的正确性。对高双折射光纤型梳状滤波器和等效梳状滤波效应的应用研究侧重于新方案设计,然后搭建实验平台论证新方案的有效性和优势。基于以上分析方法和研究思路,本文的主要研究内容和成果如下:
深入研究了均匀、切趾型、大啁啾型SFBG信道中心波长的分布规律。在均匀和切趾型SFBG中,利用Fourier级数法将SFBG分解成一系列子光栅,单独求解每个子光栅的反射峰波长,即SFBG各阶信道的中心波长;其分布规律受占空比、取样周期和相位匹配条件的影响。针对大啁啾型SFBG,将啁啾效应等效成离散相移,以Fourier变换法获得Talbot效应下的波长偏移量;此偏移量与均匀SFBG信道中心波长之和为大啁啾效应下的信道中心波长。
首次提出在SFBG中应用周期性啁啾结构实现滤波信道密集化。周期性啁啾结构由多个结构一致的啁啾周期(或超结构)构成。啁啾效应导致的相位分布同时满足Talbot相位条件和相位空间2π的整数倍等效关系,从而以频域Talbot效应实现了信道密集化。并对周期性啁啾结构进行了扩展:将相位条件由二次扩展到高次,将结构设计的自由度从一维扩展到三维。
探讨了取样方案在设计超窄带平坦滤波器和一维光子晶体型滤波器中的推广应用。基于SFBG的等效相移技术和光栅的多相移技术在SFBG的-1阶反射带上形成一个窄带(约为数十皮米)、平坦的透射峰,即超窄带平坦滤波器。将一维光子晶体中高、低折射率层交替排列的反转等效定义为π相移跳变,借助优化算法获得相位跳变点,从而将二元相位取样方案巧妙地用于设计一维光子晶体型梳状滤波器。
应用色散光纤或偏振调制器(PolM),分别设计了具有可调谐测量频段或宽带测量频段的实时微波频率测量方案。利用色散光纤的色散斜率,构建两个不同的色散导致的微波功率衰减函数,并从两者的比值中反解得到微波频率;以调整波长间隔的方式改变功率衰减函数,实现了可调谐的测量范围。借助PolM和检偏器,同步得到两个调制深度一致的强度调制光和相位调制光。引入色散效应,由相位调制和强度调制光信号分别得到两互补型微波功率衰减函数;对比两互补型衰减函数计算出微波频率,扩大了频率测量范围。
应用高双折射光纤型梳状滤波器,设计了两种基于光功率检测的实时微波频率测量方案。载波抑制型小信号调制下,将经微波信号调制的两路光信号的载波波长分别置于Sagnac环梳状谱的波峰和波谷处进行滤波,然后对比两波长上的光功率得到待测微波频率。采用单个光波长和一对互补型梳状滤波器实现了更为稳定的频率测量方案。同样在载波抑制型小信号调制下,光信号的载波波长同时置于一对互补型梳状滤波器中一个滤波谱的波峰和另一个滤波谱的波谷:检测并对比两滤波器输出端的光功率从而获得微波频率。后一种方案不仅减少了光源的数目,而且完全消除了光源功率波动对频率测量的影响。
设计了重复速率简易可调的高速光脉冲序列生成方案。结合PolM和偏振分束器,奇次、偶次光边带在两个偏振态上得以分离,实现了等效梳状滤波效应:其频率选取间隔随驱动微波频率而自动调整,无需额外的物理调节机制。基于等效梳状滤波效应,生成了二倍频重复速率的归零码(RZ)和载波抑制归零码(CS-RZ)光脉冲序列,大为简化了重复速率的调节过程。
Due to their cyclical amplitude filtering or phase filtering characteristics, the comb filters have attracted great interest in optical communications and microwave signal processing. For instance, the sampled fiber Bragg grating- (SFBG), the Mach-Zehnder interferometer- and high birefringence fiber (HBF)-based comb filters can find applications in the wavelength division multiplexer/demultiplexer, the multi-channel dispersion compensator, the high-speed pulse generator, the microwave filter, the instantaneous microwave frequency measurement, and so on. At the same time, along with the emergence of novel technologies and requirements, the research and the application about the optical comb filters are facing new challenges and opportunities. Against such a profound background, in this dissertation the investigation on the SFBG- and the HBF-based comb filters has been performed. Firstly, the peak wavelengths of reflection channels and the channel density techniques are theoretically investigated for the SFBG-based comb filters. Secondly, instantaneous microwave frequency measurement approaches using HBF-based comb filters are proposed and demonstrated. Finally, based on the equivalent comb filtering effect, a simple approach is designed to generate pulse trains with a tunable repetition rate.
During the theoretical investigation and analysis on the filtering characteristics of SFBGs, three analysis tools have been used, i.e., the Fourier series method, the Fourier transform method, and the transfer matrix method. With the Fourier series method and the Fourier transform method, results and conclusions which describe the peak wavelengths or the channel spacing are derived. The transfer matrix method is then adopted to verify the derived results or conclusions. As for the HBF-based comb filter and the equivalent comb filtering effect, the application investigation focuses on the proposal of novel approaches or architectures. Related experiments have been performed to confirm the effectiveness and the advantages of proposed approaches. According to the analysis tools and the design ideas aforementioned, the main research work and results are listed in the following.
An in-depth analysis about the distribution of peak wavelengths of SFBGs has been conducted. The uniform or apodized SFBG is decomposed into a number of ghost gratings using Fourier series method. All peak wavelengths of SFBG are obtained as the peak wavelength of each ghost grating is calculated. The peak wavelengths of SFBG are associated with the duty cycle, the sampling period, and the phase-matching condition. While in the SFBG having large chirp effect, the chirp effect is transformed into discrete phase shifts to implement the Fourier transform, with the wavelength drift induced by Talbot effect being derived. The sums of this wavelength drift and the peak wavelengths of uniform SFBG are the peak wavelengths of SFBG having large chirp.
The periodic chirp structure is firstly proposed to get narrow channel spacing in the spectrum of SFBG. The periodic chirp structure consists of a number of identical chirp structures (or superstructures). The channel density can be realized by the spectral Talbot effect, as long as both the phase condition for Talbot effect and the equivalence of integer multiple of 2πin the phase plane are satisfied. Moreover, the periodic chirp structure can be further extended, with the phase condition being extended from parabolic to the high-order and the design degree being extended from one-dimensional to three-dimensional.
The sampling approaches can find applications in designing the ultra-narrow, flat-top filter and the one-dimension photonic crystal-based filter. The combination of the equivalent phase shift (EPS) technique in SFBG and the multiple phase shift technique in fiber grating is able to open an ultranarrow (several tens of pico-meter) and flat transmission peak in the -1~(st) reflection band of SFBG. Namely, ultra-narrow and flat-top filters have been achieved. In the one-dimension photonic crystal, the inversion in the alternate arrange of low- and high- refractive index layers is defined as the equivalentπphase shift. A number of phase transmit points are then obtained using optimal algorithms. Therefore, the binary sampling function can be used to implement comb filters based on one-dimension photonic crystal.
Instantaneous microwave frequency measurement approaches with a tunable measurement range or a wideband measurement range, are designed by the use of a length of dispersive fiber or a polarization modulator (PolM). Due to the dispersion slope of the dispersive fiber, two different microwave power fading functions caused by dispersion effect are detected, with the microwave frequency being calculated from the ratio of two functions. Since different fading functions can be achieved by adjusting the wavelength spacing, a tunable measurement range has been achieved. With the joint function of a PolM and a polarizer, a phase-modulated lightwave and an intensity-modulated lightwave, with an identical modulation index, are simultaneously generated. Two complementary microwave power fading functions resulted from dispersion effect are detected from the two modulated lightwaves. By estimating the microwave frequency from the ratio of the two complementary functions, a large measurement range is realized.
Two frequency measurement approaches in the way of optical power detection are proposed by using HBF-based comb filters. Under the condition of the carrier-suppressed, small-signal modulation, two lightwaves are modulated by an unknown microwave signal to generate±1~(st) optical sidebands. The two carriers of the two lightwaves are located at a peak and a valley of the Sagnac loop's comb response, to perform two complementary comb filtering functions. The frequency to be measured is estimated by detecting the optical powers at two lightwaves. Moreover, a more stable measurement approach is implemented by using a single lightwave and a complementary comb filter pair. In a similar way, the carrier-suppressed, small-signal modulation is employed. The carrier of the modulated lighwave is simultaneously set at the peak of one transmission comb and the valley of the other complementary transmission comb. The microwave frequency is then estimated by monitoring the optical powers from the two outputs of the filter pair. In the latter approach, the setup is greatly simplified and the influence of the optical power fluctuations on the frequency measurement is eliminated completely.
A simple approach is proposed and implemented to generate high-speed pulse trains having a tunable repetition rate. The odd- and the even-order sidebands are separated along the two polarization states by the use of a PolM and a polarization beam splitter, leading to an equivalent comb filtering effect. The comb spacing of the equivalent comb filtering effect varies automatically with the microwave frequency, without additional tuning mechanism. With the equivalent comb filtering effect, return-to-zero (RZ) and carrier-suppressed return-to-zero (CS-RZ) pulse trains having a repetition rate twice of the microwave frequency are generated, leading to the adjustment of the repetition rate greatly simplified.
引文
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