光纤光栅功能型滤波特性及其在光脉冲生成中的应用研究
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摘要
作为一种典型的全光纤式无源器件,光纤光栅(FBG)具有体积小、易与光纤耦合、损耗小等特点,在光纤通信和传感器领域有着重要应用和广阔前景。因而FBG滤波性能与器件的持续深入研究、优化,对于提升其性能和应用领域、对于更好地服务于光通信与信号处理有着重要意义。目前,虽然FBG的研究已取得一系列的理论和实验成果,但是伴随着新型光信息技术的发展和用户需求的不断增加,其滤波性能和应用面临着许多新的挑战和机遇。本文在已有的研究成果基础上,围绕FBG的新颖滤波性能及特色应用开展工作,大致分为三部分：FBG多信道滤波特性研究、FBG的特殊反射谱的设计、基于FBG的脉冲压缩和脉冲序列生成。
在本文研究过程中,先后采用了相位等效、傅里叶变换、传输矩阵法、泰勒级数展开等理论方法和仿真手段。首先,以相位空间的等效性,结合线性啁啾与相移技术,建立频域Talbot效应的通用化相位条件,以混合技术达到多信道密集化的效果；运用傅里叶变换法建立光栅折射率调制与反射谱之间的关联,设计得到余弦、二次函数型、直角梯形特殊反射谱；在上述设计结果的基础上,采用传输矩阵法对方案和性能进行验证,并为FBG在信号生成领域的应用提供了理论指导。其次,利用泰勒级数展开法分析光相位调制的频率啁啾特性,而后提出以高阶色散补偿(比如二阶、四阶色散)方案来补偿频率啁啾,实现脉冲压缩和生成。本文的主要取得的成果如下：
新型FBG滤波特性研究,集中在多功能型多信道滤波器、具有特殊函数型响应的光滤波器两个方向。推导得到通用化相位条件作为混合技术的基础；由于在通用化相位条件中,啁啾系数和相移对相位条件的贡献是等效的,可以通过啁啾系数和相移的不同排列来设计多信道滤波器,实现不同的信道间隔、色散补偿值。并且,可通过动态调节插入的相移值来实现可调色散补偿器。此后,基于对折射率调制的傅里叶变换分析,设计了具有特殊幅频响应、时延响应的多种FBG。特殊幅频响应包括非对称斜率三角形,二次函数型和四次函数型,指数函数型,直角梯形；特殊时延响应包括：线性、二次函数型、三次函数型,甚至可以拓展到更为复杂的形状。而后,基于传输矩阵法对滤波性能进行仿真验证,所获得结果和理论预期基本一致,达到了预期的效果。此类光栅可应用于高阶色散补偿、微波信号光子学产生、光脉冲信号生成、以及光电传感与解调中。
结合相位调制及啁啾FBG,提出并设计了多倍频(二倍频、四倍频等)重复速率的光脉冲序列生成方案。即一束光经相位调制后被分解为具有正交偏振态的两路信号,分别从相反方向注入一个啁啾光纤光栅的两端,由于干涉效应,奇数阶边带被消除,产生了一个具有偶数阶边带的归零码脉冲序列,生成两倍频重复速率归零码脉冲序列,其脉冲占空比为33%。进一步地,利用正弦信号调制线性偏振光,其偏振角相对于偏振调制器的主轴成45。；该信号输入到啁啾FBG,反射光经过偏振分束器将产生四倍频重复速率的脉冲序列。
基于相位调制和高阶色散补偿的光脉冲压缩与生成。针对外光相位调制的频率啁啾特性进行解析分析,对被调制光同时进行二阶色散和四阶色散补偿,被调制光的频率啁啾在一个相对更大的带宽中被补偿,有效地实现了对光脉冲的压缩,且具有更小的时间-带宽积和更大的峰值功率。在此基础上,基于重构-等效啁啾理论,设计了一个包含二阶色散和四阶色散补偿能力的SFBG来实施脉冲压缩。仿真结果表明,使用所设计的SFBG能够实现高阶色散补偿,压缩光脉冲的时间-带宽积为0.79。
As one classic of passive optical devices, fiber Bragg gratings are widely used in many practical applications, especially in fiber communications and optical sensing domain for their characteristics of compact size, compatibility to fiber and low transmission loss, etc. Detailed analysis on FBGs is extraordinarily important for the design and performance promotion, which would make the FBGs more useful in the optical communication systems. So far, lots of theoretical and experimental results have been presented on this topic. However, more and more challenges and opportunities for the FBGs will arise with the technolgy development and commercial demands. Based on the existing research results, we are going to study the novel performances and the applications mechanism of the FBGs, including the filtering characteristics, the design of the reflection spectrum, and the pulse compression and pulse train generation.
The equivalent phase, the Fourier transform, the transfer matrix, and the Taylor series expansion have been employed to analyze and verify the proposed schemes. Firstly, according to the equivalence in the phase domain, a general phase condition for the Talbot effect is obtained to develop the dense multi-channel effect by combining the linear chirp and phase shift. On the basis of the Fourier transform relationship between the index modulation of the grating and the reflection spectrum, cosine-shape, quadratic-function shape and right-angle-trapezoid-shape reflection spectra have been achieved. These proposed schemes are numerical demonstrated by the transfer matrix method, which can provide certain theorical reference for the pratical applications in optical signal processing. Secondly, the frequency chirp of phase modulated ligtht is analyzed using the Taylor series expansion method. Furthermore, we propose a frequency chirp compensation scheme by using high order dispersion compensation (e.g. second order and fourth-order dispersions), resulting in a effective pulse compression and generation. The content and results of this thesis are listed as follows.
Firstly, the thesis focuses on the novel filtering characteristics of FBG, including multi-function optical comb filter and the special spectrum response. The general phase condition can be derived to be the foundation of the hybrid technique, in which the chirp and the phase shift are equivalent. Thus, a comb filter with different channel spacings and dispersions is available by adjusting the distribution of the chirp and the phase shift. Futhermore, by tuning the phase shift of FBG dynamically, a tunable dispersion compensator can be realized. After analysis on the index modulation based on the Fourier transform, five special reflection spectra, such as quadratic function, right angle trapezoid function, and so on, are achieved, respectively. Moreover, special group delay responses have also been investigated based on the same approach, including linear shape, quadratic-function shape and so on. Using transfer matrix method, the numerical results agree well with the theoretical analysis results. This kind of filter can easily find applications in the signal generation and sensor area.
Secondly, a novel generation scheme for rate-multiplication pulse train (i.e. rate-doubled and rate-quadrupled) is presented based on the phase modulation and chirped FBG. After passing through the phase modulator, a beam will be separated into two orthogonally polarized signals which are then injected into the same chirped FBG in opposite directions. The odd-order side-lobes will be eliminated due to the interference, from which a return zero pulse train with double rate is generated with a duty ratio of33%. Furthermore, by applying the sine signal to modulate a linear polarized light, the polarization angle relative to the axis of the polarization modulator is set as45°. When the signal is transmitted in the chirped FBG, the reflected light then results in rate-quadrupled pulse sequence after passing through the polarizer.
Finally, the pulse compression and generation based on the phase modulation and high order dispersion compensation is investigated. Through compensating the second order and the fourth order dispersions of an external modulated light, the pulse compression is realized with a larger peak power and a smaller time-bandwidth products. Based on the reconstruction-equivalence chirp theory, a pulse compression scheme is proposed by using an SFBG including the second order and the fourth order dispersions. Simulation results show that the scheme can offer a time-bandwidth product of only0.79for pulse compression.
在本文研究过程中,先后采用了相位等效、傅里叶变换、传输矩阵法、泰勒级数展开等理论方法和仿真手段。首先,以相位空间的等效性,结合线性啁啾与相移技术,建立频域Talbot效应的通用化相位条件,以混合技术达到多信道密集化的效果；运用傅里叶变换法建立光栅折射率调制与反射谱之间的关联,设计得到余弦、二次函数型、直角梯形特殊反射谱；在上述设计结果的基础上,采用传输矩阵法对方案和性能进行验证,并为FBG在信号生成领域的应用提供了理论指导。其次,利用泰勒级数展开法分析光相位调制的频率啁啾特性,而后提出以高阶色散补偿(比如二阶、四阶色散)方案来补偿频率啁啾,实现脉冲压缩和生成。本文的主要取得的成果如下：
新型FBG滤波特性研究,集中在多功能型多信道滤波器、具有特殊函数型响应的光滤波器两个方向。推导得到通用化相位条件作为混合技术的基础；由于在通用化相位条件中,啁啾系数和相移对相位条件的贡献是等效的,可以通过啁啾系数和相移的不同排列来设计多信道滤波器,实现不同的信道间隔、色散补偿值。并且,可通过动态调节插入的相移值来实现可调色散补偿器。此后,基于对折射率调制的傅里叶变换分析,设计了具有特殊幅频响应、时延响应的多种FBG。特殊幅频响应包括非对称斜率三角形,二次函数型和四次函数型,指数函数型,直角梯形；特殊时延响应包括：线性、二次函数型、三次函数型,甚至可以拓展到更为复杂的形状。而后,基于传输矩阵法对滤波性能进行仿真验证,所获得结果和理论预期基本一致,达到了预期的效果。此类光栅可应用于高阶色散补偿、微波信号光子学产生、光脉冲信号生成、以及光电传感与解调中。
结合相位调制及啁啾FBG,提出并设计了多倍频(二倍频、四倍频等)重复速率的光脉冲序列生成方案。即一束光经相位调制后被分解为具有正交偏振态的两路信号,分别从相反方向注入一个啁啾光纤光栅的两端,由于干涉效应,奇数阶边带被消除,产生了一个具有偶数阶边带的归零码脉冲序列,生成两倍频重复速率归零码脉冲序列,其脉冲占空比为33%。进一步地,利用正弦信号调制线性偏振光,其偏振角相对于偏振调制器的主轴成45。；该信号输入到啁啾FBG,反射光经过偏振分束器将产生四倍频重复速率的脉冲序列。
基于相位调制和高阶色散补偿的光脉冲压缩与生成。针对外光相位调制的频率啁啾特性进行解析分析,对被调制光同时进行二阶色散和四阶色散补偿,被调制光的频率啁啾在一个相对更大的带宽中被补偿,有效地实现了对光脉冲的压缩,且具有更小的时间-带宽积和更大的峰值功率。在此基础上,基于重构-等效啁啾理论,设计了一个包含二阶色散和四阶色散补偿能力的SFBG来实施脉冲压缩。仿真结果表明,使用所设计的SFBG能够实现高阶色散补偿,压缩光脉冲的时间-带宽积为0.79。
As one classic of passive optical devices, fiber Bragg gratings are widely used in many practical applications, especially in fiber communications and optical sensing domain for their characteristics of compact size, compatibility to fiber and low transmission loss, etc. Detailed analysis on FBGs is extraordinarily important for the design and performance promotion, which would make the FBGs more useful in the optical communication systems. So far, lots of theoretical and experimental results have been presented on this topic. However, more and more challenges and opportunities for the FBGs will arise with the technolgy development and commercial demands. Based on the existing research results, we are going to study the novel performances and the applications mechanism of the FBGs, including the filtering characteristics, the design of the reflection spectrum, and the pulse compression and pulse train generation.
The equivalent phase, the Fourier transform, the transfer matrix, and the Taylor series expansion have been employed to analyze and verify the proposed schemes. Firstly, according to the equivalence in the phase domain, a general phase condition for the Talbot effect is obtained to develop the dense multi-channel effect by combining the linear chirp and phase shift. On the basis of the Fourier transform relationship between the index modulation of the grating and the reflection spectrum, cosine-shape, quadratic-function shape and right-angle-trapezoid-shape reflection spectra have been achieved. These proposed schemes are numerical demonstrated by the transfer matrix method, which can provide certain theorical reference for the pratical applications in optical signal processing. Secondly, the frequency chirp of phase modulated ligtht is analyzed using the Taylor series expansion method. Furthermore, we propose a frequency chirp compensation scheme by using high order dispersion compensation (e.g. second order and fourth-order dispersions), resulting in a effective pulse compression and generation. The content and results of this thesis are listed as follows.
Firstly, the thesis focuses on the novel filtering characteristics of FBG, including multi-function optical comb filter and the special spectrum response. The general phase condition can be derived to be the foundation of the hybrid technique, in which the chirp and the phase shift are equivalent. Thus, a comb filter with different channel spacings and dispersions is available by adjusting the distribution of the chirp and the phase shift. Futhermore, by tuning the phase shift of FBG dynamically, a tunable dispersion compensator can be realized. After analysis on the index modulation based on the Fourier transform, five special reflection spectra, such as quadratic function, right angle trapezoid function, and so on, are achieved, respectively. Moreover, special group delay responses have also been investigated based on the same approach, including linear shape, quadratic-function shape and so on. Using transfer matrix method, the numerical results agree well with the theoretical analysis results. This kind of filter can easily find applications in the signal generation and sensor area.
Secondly, a novel generation scheme for rate-multiplication pulse train (i.e. rate-doubled and rate-quadrupled) is presented based on the phase modulation and chirped FBG. After passing through the phase modulator, a beam will be separated into two orthogonally polarized signals which are then injected into the same chirped FBG in opposite directions. The odd-order side-lobes will be eliminated due to the interference, from which a return zero pulse train with double rate is generated with a duty ratio of33%. Furthermore, by applying the sine signal to modulate a linear polarized light, the polarization angle relative to the axis of the polarization modulator is set as45°. When the signal is transmitted in the chirped FBG, the reflected light then results in rate-quadrupled pulse sequence after passing through the polarizer.
Finally, the pulse compression and generation based on the phase modulation and high order dispersion compensation is investigated. Through compensating the second order and the fourth order dispersions of an external modulated light, the pulse compression is realized with a larger peak power and a smaller time-bandwidth products. Based on the reconstruction-equivalence chirp theory, a pulse compression scheme is proposed by using an SFBG including the second order and the fourth order dispersions. Simulation results show that the scheme can offer a time-bandwidth product of only0.79for pulse compression.
引文
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