基于采样光纤光栅的多通道光学滤波器
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摘要
随着光通信产业的发展,光纤光栅作为一种新型的无源器件由于其本身防爆、抗电磁干扰、抗辐射、耐高温、体积小、重量轻、灵活方便等特点可以作为光通信系统和光传感系统的基本元件越来越得到人们的重视。
采样光纤光栅由于其实现多个窄带通道,特别适用于波分复用(WDM)系统、多波长滤波器和光码分多址系统。啁啾采样Bragg光纤光栅由于在产生多通道、色散补偿方面的特性而受到人们的关注。然而当采样光纤光栅发生任意啁啾时(光栅周期啁啾,采样周期周期或者两者同时啁啾),最大反射峰的位置会发生偏移,这对我们设计多通道滤波器的效果将会产生很大影响,通常的方法是进行传输矩阵的方法,但是进行矩阵模拟运算花费时间长,而且最大峰值的位置需要放大取点,很不方便。我们提出了一种基于傅里叶变换的方法计算任意啁啾采样光纤光栅最大反射峰通道的理论和方法。通过对啁啾采样光纤光栅进行建模,运用傅里叶变换,得到了任意啁啾采样光纤光栅的数值解析表达式。运用该解析表达式,可精确计算任意啁啾采样光纤光栅最大反射峰值位置,并且得出啁啾光纤光栅的通道波长位置,不仅与光栅的啁啾系数有关,而且于光栅的总长度有关,并用模拟矩阵法证明其预测是正确的,该解析表达式加深了对复杂采样光栅内部结构的认识和明确了各种参数对光栅反射通道的影响。
随着对波长信道数目需求的增长,寻求一种制造容易,且能产生频域宽、隔离度好多通道滤波技术,一直是设计者追求的目标。在实际使用是,通常使用两种采样光纤光栅。一种是振幅型采样光纤光栅,一种是相位采样光纤光栅。传统的振幅型采样光纤光栅的最大缺点是反射光谱范围与反射光谱能量之间的平衡,光谱的频域范围是和光栅长度占空比系数成反比。光谱的反射通道要求越多,则光栅长度的占空比越小,但是若光栅长度很小,光谱反射通道的能量效率会降低。近来,得到了能够实现多通道的采样光纤光栅中的Talbot效应。利用Talbot效应,通过改变光栅的啁啾系数,可以实现任意通道密度(自由光谱范围)的光谱,而传统的采样光纤光栅只能通过改变采样周期来实现自由光谱范围的改变。传统振幅型采样光纤光栅为了得到良好的反射通道,在Talbot条件下,duty cycle依然很小,因此反射通道能量效率依然很低。相位采样光纤光栅以其高的能量利用率、平坦的反射通道的独特优势引起光学研究者的极大兴趣。然而制作相位采样光纤光栅是一件很困难、很昂贵的事。虽然,相位采样光纤光栅在Talbot条件下,可以用较少的相位采样点得到高通道数的反射光谱,但制作依然很困难。所以,我们提出了一种可以有效产生高通道数的全占空比(duty cycle=1),新颖的振幅型采样光纤光栅结构。这种结构整合了振幅采样光纤光栅(容易制作、易实现),相位采样光纤光栅(能量效率高、光栅长度短)和Talbot效应(多通道高效率、任意调节自由光谱范围)的特点。在光栅长度一定的情况下,通道能量效率可以和相位采样光纤光栅相比,直接运用高斯光束并使用高斯函数的性质得到了高均匀性,高隔离度,高计数的反射通道输出。
With the fast development of optical communications industry, fiber Bragg gratings, as a novel type of passive fiber components in optical communication systems and the optical sensing system, are attracting more and more attentions due to its superior characteristics of explosion-proof, immue of electromagnetic interference, anti-radiation, surviving in high temperature, small size, light weight, and all-fiber flexibility.
Chirped and sampled fiber Bragg gratings are taking attention by its capabilities of generating multi-channel and dispersion compensation. It was found that the multichannel reflection peaks shift from the corresponding uniform sampled FBG when either the grating period or the sampling function or both is chirped. The amount of the shifts were usually obtained numerically using the T-matrix calculation. In view of the importance of the accurate prediction or determination of the wavelength shift, (subsequently, the precise wavelength position of each channel) due to the chirp introduced in the grating parameters, there is a need to develop an analytical, rather than a numerical tool, to characterize the channel wavelength. In this paper, we present an analytical expression for the sampled FBGs with arbitrary chirps in sampling function or grating period or combination of both using Fourier theory. The relationship among the wavelength of each channel, the chirp coefficient of the sampling function and the grating period, and the length of the grating is explicitly given. The calculated results based on the analytical expression are examined with the conventional numerical results, which are found to be in excellent agreement. This analytical tool can provide insight into the designs of more-complex sampled grating structures and into ways to tailor the parameters properly to obtain a specific performance.
As the increasing requirement of the wavelength channel numbers, finding a simple and flexible manufacturing method for multi-channel fiber optical filters with wide wavelength range and clear isolation is always the goal of designers. Two types of sampled fiber Bragg gratings are most frequently employed in practice, i.e., amplitude sampled fiber Bragg grating (ASFBG) and phase-only sampled fiber Bragg grating (PSFBG). The main drawback of the conventional ASFBG is the trade-off between the spectral range and the channel energy efficiency according to Fourier transform in which the spectral range in frequency domain is inversely proportional to the duty cycle in each sampling period. The more the output channel, the smaller the duty cycle, which directly results in the very low energy efficiency when an ASFBG is employed in a conventional way since a large portion of the fiber is absent of the grating. Recently, it has been shown that the multi-channel generation can be implemented by exploiting Talbot effect in sampled and chirped FBGs, in which the channel density (or free spectral range, FSR) can be effectively multiplied by changing the chirp coefficient with no need to change the sampling period as the case in conventional SFBGs. However, when we examine the structure of an ASFBG used under condition of Talbot effect, it is found that the duty cycle of each sampling period must also be kept small in order to obtain clean multi-channel outputs, which also results in low energy efficiency and the practical application is thus very limited. The most attractive feature of phase-only sampled FBGs (PSFBGs) is the high energy efficiency. The Talbot effect in PSFBGs for multi-channel generation has also been proposed to enhance the energy efficiency with a limited fiber length. It is shown that, under the Talbot condition, the PSFBGs using less phase transitions is capable of generating superior high-count DWDM channels with high energy efficiency. Nonetheless, the manufacturing difficulty of PSFBGs still remians. In this paper, we propose a novel amplitude sampled FBG structure that has a full duty cycle (=1) for efficient generation of broadband high-count channels operated under spectral Talbot effect. This structure integrates advantages of amplitude sampled FBGs (easy and straightforward making), phase-only sampled FBGs (high energy efficiency and short fiber length) and Talbot effect (inherit high efficiency in high-count channel output and arbitrily FSR tuning). It is shown that the energy efficiency of the structure is comparable to that of the PSFBGs with the same fiber length. The direct use of a simple Gaussian beam profile or combination of Gaussian profile yields high uniformity, high isolation and high-count channel outputs.
采样光纤光栅由于其实现多个窄带通道,特别适用于波分复用(WDM)系统、多波长滤波器和光码分多址系统。啁啾采样Bragg光纤光栅由于在产生多通道、色散补偿方面的特性而受到人们的关注。然而当采样光纤光栅发生任意啁啾时(光栅周期啁啾,采样周期周期或者两者同时啁啾),最大反射峰的位置会发生偏移,这对我们设计多通道滤波器的效果将会产生很大影响,通常的方法是进行传输矩阵的方法,但是进行矩阵模拟运算花费时间长,而且最大峰值的位置需要放大取点,很不方便。我们提出了一种基于傅里叶变换的方法计算任意啁啾采样光纤光栅最大反射峰通道的理论和方法。通过对啁啾采样光纤光栅进行建模,运用傅里叶变换,得到了任意啁啾采样光纤光栅的数值解析表达式。运用该解析表达式,可精确计算任意啁啾采样光纤光栅最大反射峰值位置,并且得出啁啾光纤光栅的通道波长位置,不仅与光栅的啁啾系数有关,而且于光栅的总长度有关,并用模拟矩阵法证明其预测是正确的,该解析表达式加深了对复杂采样光栅内部结构的认识和明确了各种参数对光栅反射通道的影响。
随着对波长信道数目需求的增长,寻求一种制造容易,且能产生频域宽、隔离度好多通道滤波技术,一直是设计者追求的目标。在实际使用是,通常使用两种采样光纤光栅。一种是振幅型采样光纤光栅,一种是相位采样光纤光栅。传统的振幅型采样光纤光栅的最大缺点是反射光谱范围与反射光谱能量之间的平衡,光谱的频域范围是和光栅长度占空比系数成反比。光谱的反射通道要求越多,则光栅长度的占空比越小,但是若光栅长度很小,光谱反射通道的能量效率会降低。近来,得到了能够实现多通道的采样光纤光栅中的Talbot效应。利用Talbot效应,通过改变光栅的啁啾系数,可以实现任意通道密度(自由光谱范围)的光谱,而传统的采样光纤光栅只能通过改变采样周期来实现自由光谱范围的改变。传统振幅型采样光纤光栅为了得到良好的反射通道,在Talbot条件下,duty cycle依然很小,因此反射通道能量效率依然很低。相位采样光纤光栅以其高的能量利用率、平坦的反射通道的独特优势引起光学研究者的极大兴趣。然而制作相位采样光纤光栅是一件很困难、很昂贵的事。虽然,相位采样光纤光栅在Talbot条件下,可以用较少的相位采样点得到高通道数的反射光谱,但制作依然很困难。所以,我们提出了一种可以有效产生高通道数的全占空比(duty cycle=1),新颖的振幅型采样光纤光栅结构。这种结构整合了振幅采样光纤光栅(容易制作、易实现),相位采样光纤光栅(能量效率高、光栅长度短)和Talbot效应(多通道高效率、任意调节自由光谱范围)的特点。在光栅长度一定的情况下,通道能量效率可以和相位采样光纤光栅相比,直接运用高斯光束并使用高斯函数的性质得到了高均匀性,高隔离度,高计数的反射通道输出。
With the fast development of optical communications industry, fiber Bragg gratings, as a novel type of passive fiber components in optical communication systems and the optical sensing system, are attracting more and more attentions due to its superior characteristics of explosion-proof, immue of electromagnetic interference, anti-radiation, surviving in high temperature, small size, light weight, and all-fiber flexibility.
Chirped and sampled fiber Bragg gratings are taking attention by its capabilities of generating multi-channel and dispersion compensation. It was found that the multichannel reflection peaks shift from the corresponding uniform sampled FBG when either the grating period or the sampling function or both is chirped. The amount of the shifts were usually obtained numerically using the T-matrix calculation. In view of the importance of the accurate prediction or determination of the wavelength shift, (subsequently, the precise wavelength position of each channel) due to the chirp introduced in the grating parameters, there is a need to develop an analytical, rather than a numerical tool, to characterize the channel wavelength. In this paper, we present an analytical expression for the sampled FBGs with arbitrary chirps in sampling function or grating period or combination of both using Fourier theory. The relationship among the wavelength of each channel, the chirp coefficient of the sampling function and the grating period, and the length of the grating is explicitly given. The calculated results based on the analytical expression are examined with the conventional numerical results, which are found to be in excellent agreement. This analytical tool can provide insight into the designs of more-complex sampled grating structures and into ways to tailor the parameters properly to obtain a specific performance.
As the increasing requirement of the wavelength channel numbers, finding a simple and flexible manufacturing method for multi-channel fiber optical filters with wide wavelength range and clear isolation is always the goal of designers. Two types of sampled fiber Bragg gratings are most frequently employed in practice, i.e., amplitude sampled fiber Bragg grating (ASFBG) and phase-only sampled fiber Bragg grating (PSFBG). The main drawback of the conventional ASFBG is the trade-off between the spectral range and the channel energy efficiency according to Fourier transform in which the spectral range in frequency domain is inversely proportional to the duty cycle in each sampling period. The more the output channel, the smaller the duty cycle, which directly results in the very low energy efficiency when an ASFBG is employed in a conventional way since a large portion of the fiber is absent of the grating. Recently, it has been shown that the multi-channel generation can be implemented by exploiting Talbot effect in sampled and chirped FBGs, in which the channel density (or free spectral range, FSR) can be effectively multiplied by changing the chirp coefficient with no need to change the sampling period as the case in conventional SFBGs. However, when we examine the structure of an ASFBG used under condition of Talbot effect, it is found that the duty cycle of each sampling period must also be kept small in order to obtain clean multi-channel outputs, which also results in low energy efficiency and the practical application is thus very limited. The most attractive feature of phase-only sampled FBGs (PSFBGs) is the high energy efficiency. The Talbot effect in PSFBGs for multi-channel generation has also been proposed to enhance the energy efficiency with a limited fiber length. It is shown that, under the Talbot condition, the PSFBGs using less phase transitions is capable of generating superior high-count DWDM channels with high energy efficiency. Nonetheless, the manufacturing difficulty of PSFBGs still remians. In this paper, we propose a novel amplitude sampled FBG structure that has a full duty cycle (=1) for efficient generation of broadband high-count channels operated under spectral Talbot effect. This structure integrates advantages of amplitude sampled FBGs (easy and straightforward making), phase-only sampled FBGs (high energy efficiency and short fiber length) and Talbot effect (inherit high efficiency in high-count channel output and arbitrily FSR tuning). It is shown that the energy efficiency of the structure is comparable to that of the PSFBGs with the same fiber length. The direct use of a simple Gaussian beam profile or combination of Gaussian profile yields high uniformity, high isolation and high-count channel outputs.
引文
[1]. K. O. Hill, Fujii Y, Johnson D.C., and B. S. Kawasaki,“Photo sensitivity in optical fiber waveguides: Application to reflection filter fabrication,”Applied Physics Letters, 1978, 32(10), 647-649.
[2]. G. Meltz, W. W. Morey, and W. H. Glenn,“Formation of Bragg gratings in optical fibers by a transverse holographic method,”Opt. Lett., 1989, 14, 823-825.
[3]. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert,“Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,”Appl. Phys. Lett. 1993, 62, 1035-1037.
[4]. Ashish. M. Vengsarkar, Paul. J. Lemaire, J. B. Judkins, B. Bhatia, T. Erdogan, J. E. Sipe,“Long-period fiber gratings as band-rejection filters,”J. lightwave technol.1996, 14 (1), 58-65.
[5]. Fran?ois. Ouellette,“Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,”Optics Letters, 1987, 12, 847-849.
[6]. J¨org H¨ubner, Dan Zauner, and Martin Kristensen,“Strong Sampled Bragg Gratings for WDM Applications,”IEEE Photonics Technology Letters, 1998, 10, 552-554.
[7]. R Zengerle, O Leminger,“Phase-shifted Bragg-grating filters with improved transmissioncharacteristics,”Journal of Lightwave Technology, 1995, 13, 354-2358.
[8]. T. Erdogan, J. E. Sipe,“Tilted fiber phase gratings,”J. Opt. Soc. Am. A. 1996, 13, 296-313.
[9]. D. D. Davis, T. K. Gaylord, E. N. Glytsis et all.“CO2 laser-induced long-period fibre gratings: spectral characteristics cladding modes and polarization independence,”Electron. Lett. 1998, 34(14), 1416-1417.
[10]. C. Wang, J. Aza?a, and L. R. Chen,“Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,”IEEE Photon. Technol. Lett. 2004, 16, 1867–1869.
[11]. L. Xia, X. Li, X. Chen, and S. Xie,“A novel dispersion compensating fiber Bragggrating with a large chirp parameter and period sampled distribution,”Opt. Commun. 2003, 227, 311-315.
[12]. Li S., Chan K.T.,“Electrical wavelength-tunable actively mode-lock fiber ring laser with a linearly chirped fiber Bragg grating,”IEEE Photonics technology Letters, 1998, 10(6), 799-801.
[13].赵同刚,任建华,赵荣华,“光纤光栅外腔半导体激光器的理论和实验分析,”光电子·激光,2004,15(10),1186-1189.
[14].徐庆扬,陈少武,“光纤光栅外腔半导体激光器改进模型分析,”中国激光,2005,32(2),156-160.
[15]. S. M. Lord, G. Switzer and M. A. Krainak.“Usig fiber gratings to stabilize laser diode wavelength under modulation for atmospheric lidar transmitters,”Electronics Letters, 1996, 32, 561-563.
[16]. F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton,“Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,”Electron. Lett. 1995, 11, 899–901.
[17]. X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, and S.-Z. Xie,“Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,”IEEE Photon. Technol. Lett. 2000, 12, 1013–1015.
[18]. A. Yariv.“coupled-mode theory for guided-wave optics,”IEEE J. Quantum Electron., 1973, QE-9, 919-933.
[19]. R. Kashyap, Fiber Bragg Grating (Academic, San Diego, 1999).
[20]. S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures,“Bragg intragraing structural sensing,”Applied Optics, 1995, 34, 5003-5009.
[21]. B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette,“Long periodic superstructure Bragg gratings in optical fibres,”Electron. Lett. 1994, 30, 1620-1622.
[22]. M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming,“Sinc-sampled Fiber Bragg Gratings for Identical Multiple Wavelength operation,”IEEE Photonics Technol.Lett. 1998, 10, 842 -844.
[23]. N. Yusuke and Y. Shinji,“Densification of sampled fiber Bragg gratings using multiple phase shift (MPS) technique,”J. Lightw. Technol. 2005, 23, 1808–1817.
[24]. W. H. Loh, F. Q. Zhou, and J. J. Pan, Sampled Fiber Grating based-dispersion slope compensator, IEEE Photonics Technol. Lett. 1999, 11, 1280-1282.
[25]. M. S. Kumar and A. Bekal,“Performance evaluation of SSFBG based optical CDMA systems employing golden sequences,”Opt. Fiber Technol. 2005, 11, 56–68.
[26]. X. H. Zou, W. Pan, B. Luo, W. L. Zhang, and M.Y. Wang,“Accurate Analytical Expression for Reflection-Peak Wavelengths of Sampled Bragg Grating,”IEEE Photonics Technol. Lett. 2006, 18, 529-531.
[27]. C. H. Wang, L. R. Chen, and P. W. E. Smith,“Analysis of chirped-sampled and sampled-chirped fiber Bragg gratings,”Appl. Opt. 2002, 41, 1654-1660.
[28]. X. J. Zhu, Y. L. Lu, G. J. Zhang, C. H. Wang, and M. F. Zhao,“Analytical determination of reflection-peak wavelengths of chirped sampled fiber Bragg gratings,”Appl. Opt. 2008, 47, 1135-1140.
[29]. Yitang Dai, Xiangfei Chen, Ximing Xu, Chongcheng Fan, and Shizhong Xie,“High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,”IEEE Photo. Technol. Lett. 2005, 17, 1040-1042.
[30]. W. H. Loh, F. Q. Zhou, and J. J. Pan,“Novel designs for sampled grating-based multiplexers-demultiplexers,”Opt. Lett., 1999, 24, 1457-1459.
[31]. J. M. Castro, J. E. Castillo, R. Kostuk, C. M. Greiner, D. Iazikov, T. W. Mossberg, and D. F. Geraghty,“Interleaved sampled Bragg gratings with concatenated spectrum,”IEEE Photon. Technol. Lett. 2006, 18, 1615-1617.
[32]. H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg,“Phase-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,”J. Lightwave technol., 2003, 21, 2074-2083.
[33]. J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback,“Dammann fiber Bragg gratings and phase-only sampling for highchannel counts,”IEEE Photon. Technol. Lett. 2002, 14, 1309-1311.
[34]. J. E. Rothenberg, H. Li, Y. Sheng, J. Popelek, J. Zweiback,“Phase-only sampled 45 channel fiber Bragg grating written with a diffraction-compensated phase mask,”Opt. Lett., 31, 2006, 1199-1201.
[35]. C. H. Wang, J. Aza?a, and L. R. Chen,“Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures,”Opt. Lett. 2004, 29, 1590-1592.
[36]. C. H. Wang, J. Aza?a, and L. R. Chen,“Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,”IEEE Photon. Technol. Lett. 2004, 16, 1867–1869.
[37]. J. Aza?a, C. H. Wang, and L. R. Chen,“Spectral self-imaging phenomena in sampled Bragg gratings,”J. Opt. Soc. Am. B, 2005, 22, 1829-1841.
[38]. Julien Magné, Philippe Giaccari, Sophie LaRochelle, JoséAza?a, and Lawrence R. Chen,“All-fiber comb filter with tunable free spectral range ,”Opt. Lett., 2005, 12, 2062-2064.
[39]. Y. Lu, X. Zhu, C. Wang, and G. Zhang,“Broadband high-channel-count phase-only sampled fiber Bragg gratings based on spectral Talbot effect,”Opt. Express. 2008, 16, 15584-15594.
[2]. G. Meltz, W. W. Morey, and W. H. Glenn,“Formation of Bragg gratings in optical fibers by a transverse holographic method,”Opt. Lett., 1989, 14, 823-825.
[3]. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert,“Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,”Appl. Phys. Lett. 1993, 62, 1035-1037.
[4]. Ashish. M. Vengsarkar, Paul. J. Lemaire, J. B. Judkins, B. Bhatia, T. Erdogan, J. E. Sipe,“Long-period fiber gratings as band-rejection filters,”J. lightwave technol.1996, 14 (1), 58-65.
[5]. Fran?ois. Ouellette,“Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,”Optics Letters, 1987, 12, 847-849.
[6]. J¨org H¨ubner, Dan Zauner, and Martin Kristensen,“Strong Sampled Bragg Gratings for WDM Applications,”IEEE Photonics Technology Letters, 1998, 10, 552-554.
[7]. R Zengerle, O Leminger,“Phase-shifted Bragg-grating filters with improved transmissioncharacteristics,”Journal of Lightwave Technology, 1995, 13, 354-2358.
[8]. T. Erdogan, J. E. Sipe,“Tilted fiber phase gratings,”J. Opt. Soc. Am. A. 1996, 13, 296-313.
[9]. D. D. Davis, T. K. Gaylord, E. N. Glytsis et all.“CO2 laser-induced long-period fibre gratings: spectral characteristics cladding modes and polarization independence,”Electron. Lett. 1998, 34(14), 1416-1417.
[10]. C. Wang, J. Aza?a, and L. R. Chen,“Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,”IEEE Photon. Technol. Lett. 2004, 16, 1867–1869.
[11]. L. Xia, X. Li, X. Chen, and S. Xie,“A novel dispersion compensating fiber Bragggrating with a large chirp parameter and period sampled distribution,”Opt. Commun. 2003, 227, 311-315.
[12]. Li S., Chan K.T.,“Electrical wavelength-tunable actively mode-lock fiber ring laser with a linearly chirped fiber Bragg grating,”IEEE Photonics technology Letters, 1998, 10(6), 799-801.
[13].赵同刚,任建华,赵荣华,“光纤光栅外腔半导体激光器的理论和实验分析,”光电子·激光,2004,15(10),1186-1189.
[14].徐庆扬,陈少武,“光纤光栅外腔半导体激光器改进模型分析,”中国激光,2005,32(2),156-160.
[15]. S. M. Lord, G. Switzer and M. A. Krainak.“Usig fiber gratings to stabilize laser diode wavelength under modulation for atmospheric lidar transmitters,”Electronics Letters, 1996, 32, 561-563.
[16]. F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton,“Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,”Electron. Lett. 1995, 11, 899–901.
[17]. X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, and S.-Z. Xie,“Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,”IEEE Photon. Technol. Lett. 2000, 12, 1013–1015.
[18]. A. Yariv.“coupled-mode theory for guided-wave optics,”IEEE J. Quantum Electron., 1973, QE-9, 919-933.
[19]. R. Kashyap, Fiber Bragg Grating (Academic, San Diego, 1999).
[20]. S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures,“Bragg intragraing structural sensing,”Applied Optics, 1995, 34, 5003-5009.
[21]. B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette,“Long periodic superstructure Bragg gratings in optical fibres,”Electron. Lett. 1994, 30, 1620-1622.
[22]. M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming,“Sinc-sampled Fiber Bragg Gratings for Identical Multiple Wavelength operation,”IEEE Photonics Technol.Lett. 1998, 10, 842 -844.
[23]. N. Yusuke and Y. Shinji,“Densification of sampled fiber Bragg gratings using multiple phase shift (MPS) technique,”J. Lightw. Technol. 2005, 23, 1808–1817.
[24]. W. H. Loh, F. Q. Zhou, and J. J. Pan, Sampled Fiber Grating based-dispersion slope compensator, IEEE Photonics Technol. Lett. 1999, 11, 1280-1282.
[25]. M. S. Kumar and A. Bekal,“Performance evaluation of SSFBG based optical CDMA systems employing golden sequences,”Opt. Fiber Technol. 2005, 11, 56–68.
[26]. X. H. Zou, W. Pan, B. Luo, W. L. Zhang, and M.Y. Wang,“Accurate Analytical Expression for Reflection-Peak Wavelengths of Sampled Bragg Grating,”IEEE Photonics Technol. Lett. 2006, 18, 529-531.
[27]. C. H. Wang, L. R. Chen, and P. W. E. Smith,“Analysis of chirped-sampled and sampled-chirped fiber Bragg gratings,”Appl. Opt. 2002, 41, 1654-1660.
[28]. X. J. Zhu, Y. L. Lu, G. J. Zhang, C. H. Wang, and M. F. Zhao,“Analytical determination of reflection-peak wavelengths of chirped sampled fiber Bragg gratings,”Appl. Opt. 2008, 47, 1135-1140.
[29]. Yitang Dai, Xiangfei Chen, Ximing Xu, Chongcheng Fan, and Shizhong Xie,“High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,”IEEE Photo. Technol. Lett. 2005, 17, 1040-1042.
[30]. W. H. Loh, F. Q. Zhou, and J. J. Pan,“Novel designs for sampled grating-based multiplexers-demultiplexers,”Opt. Lett., 1999, 24, 1457-1459.
[31]. J. M. Castro, J. E. Castillo, R. Kostuk, C. M. Greiner, D. Iazikov, T. W. Mossberg, and D. F. Geraghty,“Interleaved sampled Bragg gratings with concatenated spectrum,”IEEE Photon. Technol. Lett. 2006, 18, 1615-1617.
[32]. H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg,“Phase-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,”J. Lightwave technol., 2003, 21, 2074-2083.
[33]. J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback,“Dammann fiber Bragg gratings and phase-only sampling for highchannel counts,”IEEE Photon. Technol. Lett. 2002, 14, 1309-1311.
[34]. J. E. Rothenberg, H. Li, Y. Sheng, J. Popelek, J. Zweiback,“Phase-only sampled 45 channel fiber Bragg grating written with a diffraction-compensated phase mask,”Opt. Lett., 31, 2006, 1199-1201.
[35]. C. H. Wang, J. Aza?a, and L. R. Chen,“Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures,”Opt. Lett. 2004, 29, 1590-1592.
[36]. C. H. Wang, J. Aza?a, and L. R. Chen,“Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,”IEEE Photon. Technol. Lett. 2004, 16, 1867–1869.
[37]. J. Aza?a, C. H. Wang, and L. R. Chen,“Spectral self-imaging phenomena in sampled Bragg gratings,”J. Opt. Soc. Am. B, 2005, 22, 1829-1841.
[38]. Julien Magné, Philippe Giaccari, Sophie LaRochelle, JoséAza?a, and Lawrence R. Chen,“All-fiber comb filter with tunable free spectral range ,”Opt. Lett., 2005, 12, 2062-2064.
[39]. Y. Lu, X. Zhu, C. Wang, and G. Zhang,“Broadband high-channel-count phase-only sampled fiber Bragg gratings based on spectral Talbot effect,”Opt. Express. 2008, 16, 15584-15594.