基于光纤中受激布里渊散射效应的慢光特性研究
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摘要
控制光在光纤中的传播速度,尤其是减慢光速(即慢光),在全光信息处理、光纤传感和微波光子学等领域具有广阔的应用前景,对其进行研究具有重要的理论意义和应用价值。与其他慢光技术相比,基于光纤中受激布里渊散射效应(SBS)的慢光技术具有与光纤通信系统兼容、工作波长任意可调、延迟时间灵活可控和室温下工作等优点,近年来已成为慢光领域的研究热点。
由于本征布里渊增益谱的窄带宽、以及存在高阶色散和增益饱和的影响,通常情况下基于SBS的慢光难以获得大延迟量,且延迟信号存在较大失真,因而限制了其走向实际应用。针对存在的问题,本论文围绕抑制延迟信号失真和增大延迟量两个方面进行了深入研究。在抑制延迟信号失真方面,利用小信号分析方法和有限差分法求解SBS慢光耦合波方程,详细探讨了单脉冲、不同调制码型数据流和周期信号在本征洛伦兹型布里渊增益谱形状下的失真机理,并提出了相应的抑制方案；在增大延迟量方面,分别利用布里渊梳状谱和包含非线性光纤环镜(NOLM)的级联系统有效增强了SBS慢光的延迟性能。主要研究内容和成果如下：
(1)以均方根脉宽为衡量标准,研究单脉冲在SBS慢光中的展宽特性。利用均方根脉宽的频域表达式,首先计算了当脉冲载波位于布里渊增益谱中心时,由脉冲频谱的幅值改变和相位改变所引起的脉宽展宽量,明确了在不同参数下两种展宽因素对脉冲展宽量的贡献大小；然后针对脉冲载波偏离增益谱中心和优化布里渊增益谱形状两种脉冲展宽抑制方案,研究两种脉冲展宽抑制方案对两种展宽因素的影响。结果表明：当脉冲载波位于布里渊增益谱中心时,绝大多数情况下,脉冲频谱幅值的改变对延迟脉冲的展宽起主导作用,仅在脉冲频谱宽度远大于布里渊增益谱带宽且布里渊增益较小时,延迟脉冲的展宽主要由其频谱相位的改变引起；在小信号区域,通过脉冲载波偏离增益谱中心可以有效抑制延迟脉冲的展宽量,这得益于脉冲频谱幅值改变量的减小；对于洛伦兹型、高斯型和超高斯型布里渊增益谱,在相同增益谱带宽下,2阶超高斯型布里渊增益谱对脉冲的频谱幅值和频谱相位改变量同时最小,因而延迟脉冲的展宽量最小。
(2)以数据流为研究对象,首先研究占空比为50%的强度调制归零码(RZ-OOK)数据流在单色抽运光下的失真机理,进而针对不同扰动因素提出相应的优化方案,并从眼图张开度代价(EOP)、“1”码峰值延迟差异和延迟量三个方面对优化方案的性能进行了量化分析。结果表明：脉冲展宽引起的码间干扰和抽运光损耗引起的增益波动是导致数据流失真的两个主要因素；在相同码率下,选取具有更窄频谱宽度的调制码型可以有效抑制码问干扰,这有利于减小“1”码峰值延迟差异并增大数据流延迟量；在相同误码率下,具有更小脉冲峰值功率的调制码型有利于抑制抽运光损耗的产生,使其在大抽运光功率下具有更小的EOP；在相同抽运光功率下,利用多谱线抽运光增大布里渊增益谱宽度可改善数据流的EOP和“1”码峰值延迟差异,但是以牺牲延迟量为代价。
(3)针对周期信号的频谱特点,构造了一种可实现周期信号无失真延迟或超前的布里渊梳状谱,并推导出相应的数学表达式。在给定延迟量下,对于任意周期信号,利用该布里渊梳状谱表达式可以方便地得到所对应梳状谱抽运光的频谱分布及各谱线强度。在相同谱线数目下,与等间隔布里渊梳状谱相比,优化的布里渊梳状谱能有效抑制周期信号被延迟时的消光比波动。
(4)设计了一种宽带可调谐梳状谱信号产生方案并进行了实验验证,得到了谱线间隔为布里渊频移量、谱宽为-50GHz的梳状谱信号。该梳状谱信号产生方案具有实验装置简单、波长范围灵活可调的特点,进一步对多个光波长的梳状谱信号进行叠加,可获得频谱更宽且谱线间隔可调的梳状谱信号。在此基础上,数值分析了将实验所得梳状谱信号应用于准光存储技术时的信号延迟性能,结果表明：该梳状谱信号可以对高码率数据流进行有效延迟,其延迟带宽积远大于1,减小谱线间的峰值强度差异是改善延迟信号质量的关键。
(5)提出将NOLM应用于SBS慢光级联系统中以获得大延迟量的方案,并分别对单脉冲与数据流的延迟及展宽特性进行了分析。对于单脉冲：NOLM能有效抑制多级级联下延迟脉冲的展宽,因而可增大级联级数以获得更大的延迟量；在相同相对延迟量下,输出脉冲的展宽量可通过调节各级抽运光功率进行改变,在特定参数下可实现脉冲FWHM处的零展宽延迟；NOLM在压缩脉冲的同时将引入啁啾,且延迟脉冲前沿所对应的啁啾绝对值要略大于脉冲后沿,增大抽运光功率有利于减小多级级联所引入的啁啾量；优化布里渊增益谱的形状不但可以提高在级联系统中脉冲的相对延迟量,而且可以改善经NOLM压缩后的脉冲波形。对于数据流：当数据流的载波位于布里渊增益谱中心时,虽然NOLM同样能有效抑制数据流中脉冲的展宽,但增大了不同“1”码的幅值差异,限制了级联级数；采用信号载波偏离增益谱中心的方法,可以有效改善数据流中的“1”码幅值差异,有利于多级级联以增大延迟量。
The control of the speed of a light signal in an optical fiber, especially the reduction of light group velocity (namely slow light) is extremely useful due to its broad applications in all-optical information processing, optic sensor, microwave photonics and so on. Thus an extensive investigation on slow light in an optical fiber has important theoretical significance and application value. Recently, slow light based on stimulated Brillouin scattering (SBS) in an optical fiber has become a hot topic, which has many prominent advantages over other slow-light technologies, such as seamless integration with fiber-optic systems, flexibility of wavelength, controllable delay time and room-temperature operation.
However, due to the narrow Brillouin gain bandwidth, the influence of high-order dispersion and gain saturation, it is difficult to obtain large time delay, and the delayed signals suffer large distortion, which are regarded obstacles to its practical applications. To solve these problems, this dissertation addresses these issues by concentrating on two aspects, i.e. the suppression of distortion and the enhancement of time delay. On one hand, the distortion mechanisms of a single pulse, the data stream with different modulation format, as well as periodic signals in the intrinsic Brillouin gain spectrum with Lorentzian profile are thoroughly investigated by employing the small-signal analysis method and the finite difference method to solve the SBS slow light coupled wave equations, and several methods for reducing distortions in SBS based slow light systems are proposed. On the other hand, the Brillouin comb spectrum and a cascaded Brillouin slow light system with the nonlinear optical loop mirror (NOLM) have been applied to improve the delay performance. The main contributions of this dissertation are listed as follows:
(1) In SBS-based slow light, the pulse broadening characteristics of a single pulse were studied, while the amount of pulse broadening was measured by the root-mean-square (RMS) width of the pulse. With the help of the frequency domain expression of RMS, the pulse broadening associated with the variations in spectral amplitude and spectral phase of the pulse was calculated firstly when the signal carrier is aligned with the gain peak; the contribution of the two broadening factors to pulse broadening was clarified under various conditions. Then, the effects of the signal carrier deviates from the center of the gain peak and the optimized Brillouin gain spectrum on two broadening factors were further analyzed. In the case of a monochromatic pump field, the spectral-amplitude-distortion-induced pulse broadening plays a dominant role in most cases when the signal was located in the center of the Brillouin gain spectrum. When the spectrum width of a pulse is much larger than that of the Brillouin gain spectrum and the Brillouin gain is in small-signal regime, the spectral-phase-variation induced pulse broadening becomes the dominant one. In the small-signal regime, the pulse broadening can be suppressed effectively by detuning the Brillouin gain spectrum away from the signal carrier, which results from minor variations in spectral amplitude of the signal. Taking Lorentzian, Gaussian and super-Gaussian profiles of the Brillouin gain spectrum as example, the amount of distortions on the spectral amplitude and the spectral phase of the signal is the least simultaneously using the second-order super-Gaussian-shaped Brillouin gain spectrum for the same spectrum bandwidth, leading to the smallest pulse broadening is achieved.
(2) The distortion mechanisms of the RZ-OOK with a50%duty cycle in SBS-based slow light system were studied when a monochromatic pump field is used. To reduce the related distortions, then different distortion-suppression methods were proposed and numerically studied in terms of the eye-opening penalty (EOP), the peak-delay variances of different "1" bits and time delay. The results show that the distortion of data stream mainly attributes to two aspects, the pulse-broadening-induced intersymbol interference and the gain fluctuation caused by pump depletion. An advanced modulation format with a narrower spectral width can effectively suppress the intersymbol interference for a given bit rate, which is beneficial to reduce the peak-delay variances of different "1" pulses and to increase time delay. At the same bit error rate, the modulation formats with lower peak power are suggested to mitigate the EOP at higher pump level due to the gain saturation is effectively suppressed; while for a given pump power, a pump field with multi-line spectrum can improve the EOP and the peak-delay variances of different "1" bits at the cost of certain time delay.
(3) In accordance with the spectrum characteristics of the periodic signal, an optimized Brillouin comb spectrum with the ability to delay or advance periodic signal without distortion was designed, and the corresponding mathematical expressions were derived. For any periodic signals, the intensity and the position of each frequency component in a comb pump can be obtained conveniently by following the derived equations when the time delay is specified. Compared to the equally-spaced Brillouin comb spectrum with the same number of spectral lines, the optimized Brillouin comb spectrum removes the fluctuation of the extinction ratio during the delay process.
(4) A novel scheme to generate wideband-tunable comb spectrum signal was presented and experimentally demonstrated, where a comb spectrum signal with-50GHz bandwidth and a constant line spacing as large as the Brillouin frequency shift was obtained. The experimental setup of the comb spectrum signal generator is characterized by simple configuration and flexible wavelength. By combining multiple comb spectrum signals, the spectrum width and line spacing of the synthesized signal can be flexibly adjusted. The delay performance of the quasi-optical storage technology with the experimental obtained comb spectrum signal was numerically studied. The results indicate that data stream with high bite rate can be effectively delayed by employing the obtained comb spectrum signal, that the obtained delay-bandwidth product is much larger than1, and the quality of the delayed signal can be effectively improved by reducing the intensity differences among the comb lines.
(5) Aiming at enhancing time delay, the application of a nonlinear optical loop mirror (NOLM) in the SBS-based slow light cascaded system was proposed, and the delay and distortion characteristics of both a single pulse and data stream were investigated. For the single pulse, the NOLM can inhibit pulse broadening effectively in cascaded SBS-based slow light system, such that the number of stage is increased and a larger time delay is obtained. As a fixed relative delay is specified, the amount of pulse broadening of the output pulse can be modified by adjusting the pump power of each stage, and zero-broadening delay according to FWHM width can be realized at some specified parameters. Chirps induced by NOLM are imposed to a compressed pulse, and the chirp in the leading edge of the pulse is a larger than that in the trailing edge, which could be declined by adopting high power pump field. The optimization of the profile of the Brillouin gain spectrum in the cascaded Brillouin slow light system can not only increase time delay, but also improve the output profile of the compressed pulse via the NOLM. For the data stream, although the NOLM can effectively compensate pulse broadening, it increases "1"-level splitting, so the number of stage is limited."1"-level splitting can be greatly reduced by detuning Brillouin gain spectrum away from the signal carrier frequency, which is conducive to the multi-stage cascade to increase time delay.
由于本征布里渊增益谱的窄带宽、以及存在高阶色散和增益饱和的影响,通常情况下基于SBS的慢光难以获得大延迟量,且延迟信号存在较大失真,因而限制了其走向实际应用。针对存在的问题,本论文围绕抑制延迟信号失真和增大延迟量两个方面进行了深入研究。在抑制延迟信号失真方面,利用小信号分析方法和有限差分法求解SBS慢光耦合波方程,详细探讨了单脉冲、不同调制码型数据流和周期信号在本征洛伦兹型布里渊增益谱形状下的失真机理,并提出了相应的抑制方案；在增大延迟量方面,分别利用布里渊梳状谱和包含非线性光纤环镜(NOLM)的级联系统有效增强了SBS慢光的延迟性能。主要研究内容和成果如下：
(1)以均方根脉宽为衡量标准,研究单脉冲在SBS慢光中的展宽特性。利用均方根脉宽的频域表达式,首先计算了当脉冲载波位于布里渊增益谱中心时,由脉冲频谱的幅值改变和相位改变所引起的脉宽展宽量,明确了在不同参数下两种展宽因素对脉冲展宽量的贡献大小；然后针对脉冲载波偏离增益谱中心和优化布里渊增益谱形状两种脉冲展宽抑制方案,研究两种脉冲展宽抑制方案对两种展宽因素的影响。结果表明：当脉冲载波位于布里渊增益谱中心时,绝大多数情况下,脉冲频谱幅值的改变对延迟脉冲的展宽起主导作用,仅在脉冲频谱宽度远大于布里渊增益谱带宽且布里渊增益较小时,延迟脉冲的展宽主要由其频谱相位的改变引起；在小信号区域,通过脉冲载波偏离增益谱中心可以有效抑制延迟脉冲的展宽量,这得益于脉冲频谱幅值改变量的减小；对于洛伦兹型、高斯型和超高斯型布里渊增益谱,在相同增益谱带宽下,2阶超高斯型布里渊增益谱对脉冲的频谱幅值和频谱相位改变量同时最小,因而延迟脉冲的展宽量最小。
(2)以数据流为研究对象,首先研究占空比为50%的强度调制归零码(RZ-OOK)数据流在单色抽运光下的失真机理,进而针对不同扰动因素提出相应的优化方案,并从眼图张开度代价(EOP)、“1”码峰值延迟差异和延迟量三个方面对优化方案的性能进行了量化分析。结果表明：脉冲展宽引起的码间干扰和抽运光损耗引起的增益波动是导致数据流失真的两个主要因素；在相同码率下,选取具有更窄频谱宽度的调制码型可以有效抑制码问干扰,这有利于减小“1”码峰值延迟差异并增大数据流延迟量；在相同误码率下,具有更小脉冲峰值功率的调制码型有利于抑制抽运光损耗的产生,使其在大抽运光功率下具有更小的EOP；在相同抽运光功率下,利用多谱线抽运光增大布里渊增益谱宽度可改善数据流的EOP和“1”码峰值延迟差异,但是以牺牲延迟量为代价。
(3)针对周期信号的频谱特点,构造了一种可实现周期信号无失真延迟或超前的布里渊梳状谱,并推导出相应的数学表达式。在给定延迟量下,对于任意周期信号,利用该布里渊梳状谱表达式可以方便地得到所对应梳状谱抽运光的频谱分布及各谱线强度。在相同谱线数目下,与等间隔布里渊梳状谱相比,优化的布里渊梳状谱能有效抑制周期信号被延迟时的消光比波动。
(4)设计了一种宽带可调谐梳状谱信号产生方案并进行了实验验证,得到了谱线间隔为布里渊频移量、谱宽为-50GHz的梳状谱信号。该梳状谱信号产生方案具有实验装置简单、波长范围灵活可调的特点,进一步对多个光波长的梳状谱信号进行叠加,可获得频谱更宽且谱线间隔可调的梳状谱信号。在此基础上,数值分析了将实验所得梳状谱信号应用于准光存储技术时的信号延迟性能,结果表明：该梳状谱信号可以对高码率数据流进行有效延迟,其延迟带宽积远大于1,减小谱线间的峰值强度差异是改善延迟信号质量的关键。
(5)提出将NOLM应用于SBS慢光级联系统中以获得大延迟量的方案,并分别对单脉冲与数据流的延迟及展宽特性进行了分析。对于单脉冲：NOLM能有效抑制多级级联下延迟脉冲的展宽,因而可增大级联级数以获得更大的延迟量；在相同相对延迟量下,输出脉冲的展宽量可通过调节各级抽运光功率进行改变,在特定参数下可实现脉冲FWHM处的零展宽延迟；NOLM在压缩脉冲的同时将引入啁啾,且延迟脉冲前沿所对应的啁啾绝对值要略大于脉冲后沿,增大抽运光功率有利于减小多级级联所引入的啁啾量；优化布里渊增益谱的形状不但可以提高在级联系统中脉冲的相对延迟量,而且可以改善经NOLM压缩后的脉冲波形。对于数据流：当数据流的载波位于布里渊增益谱中心时,虽然NOLM同样能有效抑制数据流中脉冲的展宽,但增大了不同“1”码的幅值差异,限制了级联级数；采用信号载波偏离增益谱中心的方法,可以有效改善数据流中的“1”码幅值差异,有利于多级级联以增大延迟量。
The control of the speed of a light signal in an optical fiber, especially the reduction of light group velocity (namely slow light) is extremely useful due to its broad applications in all-optical information processing, optic sensor, microwave photonics and so on. Thus an extensive investigation on slow light in an optical fiber has important theoretical significance and application value. Recently, slow light based on stimulated Brillouin scattering (SBS) in an optical fiber has become a hot topic, which has many prominent advantages over other slow-light technologies, such as seamless integration with fiber-optic systems, flexibility of wavelength, controllable delay time and room-temperature operation.
However, due to the narrow Brillouin gain bandwidth, the influence of high-order dispersion and gain saturation, it is difficult to obtain large time delay, and the delayed signals suffer large distortion, which are regarded obstacles to its practical applications. To solve these problems, this dissertation addresses these issues by concentrating on two aspects, i.e. the suppression of distortion and the enhancement of time delay. On one hand, the distortion mechanisms of a single pulse, the data stream with different modulation format, as well as periodic signals in the intrinsic Brillouin gain spectrum with Lorentzian profile are thoroughly investigated by employing the small-signal analysis method and the finite difference method to solve the SBS slow light coupled wave equations, and several methods for reducing distortions in SBS based slow light systems are proposed. On the other hand, the Brillouin comb spectrum and a cascaded Brillouin slow light system with the nonlinear optical loop mirror (NOLM) have been applied to improve the delay performance. The main contributions of this dissertation are listed as follows:
(1) In SBS-based slow light, the pulse broadening characteristics of a single pulse were studied, while the amount of pulse broadening was measured by the root-mean-square (RMS) width of the pulse. With the help of the frequency domain expression of RMS, the pulse broadening associated with the variations in spectral amplitude and spectral phase of the pulse was calculated firstly when the signal carrier is aligned with the gain peak; the contribution of the two broadening factors to pulse broadening was clarified under various conditions. Then, the effects of the signal carrier deviates from the center of the gain peak and the optimized Brillouin gain spectrum on two broadening factors were further analyzed. In the case of a monochromatic pump field, the spectral-amplitude-distortion-induced pulse broadening plays a dominant role in most cases when the signal was located in the center of the Brillouin gain spectrum. When the spectrum width of a pulse is much larger than that of the Brillouin gain spectrum and the Brillouin gain is in small-signal regime, the spectral-phase-variation induced pulse broadening becomes the dominant one. In the small-signal regime, the pulse broadening can be suppressed effectively by detuning the Brillouin gain spectrum away from the signal carrier, which results from minor variations in spectral amplitude of the signal. Taking Lorentzian, Gaussian and super-Gaussian profiles of the Brillouin gain spectrum as example, the amount of distortions on the spectral amplitude and the spectral phase of the signal is the least simultaneously using the second-order super-Gaussian-shaped Brillouin gain spectrum for the same spectrum bandwidth, leading to the smallest pulse broadening is achieved.
(2) The distortion mechanisms of the RZ-OOK with a50%duty cycle in SBS-based slow light system were studied when a monochromatic pump field is used. To reduce the related distortions, then different distortion-suppression methods were proposed and numerically studied in terms of the eye-opening penalty (EOP), the peak-delay variances of different "1" bits and time delay. The results show that the distortion of data stream mainly attributes to two aspects, the pulse-broadening-induced intersymbol interference and the gain fluctuation caused by pump depletion. An advanced modulation format with a narrower spectral width can effectively suppress the intersymbol interference for a given bit rate, which is beneficial to reduce the peak-delay variances of different "1" pulses and to increase time delay. At the same bit error rate, the modulation formats with lower peak power are suggested to mitigate the EOP at higher pump level due to the gain saturation is effectively suppressed; while for a given pump power, a pump field with multi-line spectrum can improve the EOP and the peak-delay variances of different "1" bits at the cost of certain time delay.
(3) In accordance with the spectrum characteristics of the periodic signal, an optimized Brillouin comb spectrum with the ability to delay or advance periodic signal without distortion was designed, and the corresponding mathematical expressions were derived. For any periodic signals, the intensity and the position of each frequency component in a comb pump can be obtained conveniently by following the derived equations when the time delay is specified. Compared to the equally-spaced Brillouin comb spectrum with the same number of spectral lines, the optimized Brillouin comb spectrum removes the fluctuation of the extinction ratio during the delay process.
(4) A novel scheme to generate wideband-tunable comb spectrum signal was presented and experimentally demonstrated, where a comb spectrum signal with-50GHz bandwidth and a constant line spacing as large as the Brillouin frequency shift was obtained. The experimental setup of the comb spectrum signal generator is characterized by simple configuration and flexible wavelength. By combining multiple comb spectrum signals, the spectrum width and line spacing of the synthesized signal can be flexibly adjusted. The delay performance of the quasi-optical storage technology with the experimental obtained comb spectrum signal was numerically studied. The results indicate that data stream with high bite rate can be effectively delayed by employing the obtained comb spectrum signal, that the obtained delay-bandwidth product is much larger than1, and the quality of the delayed signal can be effectively improved by reducing the intensity differences among the comb lines.
(5) Aiming at enhancing time delay, the application of a nonlinear optical loop mirror (NOLM) in the SBS-based slow light cascaded system was proposed, and the delay and distortion characteristics of both a single pulse and data stream were investigated. For the single pulse, the NOLM can inhibit pulse broadening effectively in cascaded SBS-based slow light system, such that the number of stage is increased and a larger time delay is obtained. As a fixed relative delay is specified, the amount of pulse broadening of the output pulse can be modified by adjusting the pump power of each stage, and zero-broadening delay according to FWHM width can be realized at some specified parameters. Chirps induced by NOLM are imposed to a compressed pulse, and the chirp in the leading edge of the pulse is a larger than that in the trailing edge, which could be declined by adopting high power pump field. The optimization of the profile of the Brillouin gain spectrum in the cascaded Brillouin slow light system can not only increase time delay, but also improve the output profile of the compressed pulse via the NOLM. For the data stream, although the NOLM can effectively compensate pulse broadening, it increases "1"-level splitting, so the number of stage is limited."1"-level splitting can be greatly reduced by detuning Brillouin gain spectrum away from the signal carrier frequency, which is conducive to the multi-stage cascade to increase time delay.
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