菲波纳契准周期超结构光纤光栅制备与特性研究
|
摘要
本论文的主要工作是设计并制作了菲波纳契准周期超结构光纤光栅并对其特性进行了研究。首先对光纤光栅的发展、种类、制备及其应用作了概括介绍。其次,从麦克斯韦方程组出发,对光纤纤芯与包层的模式的色散关系及电磁场分量的表达式进行了严格的推导。以此为基础,通过耦合模理论推导出了光纤光栅的耦合模方程以及布拉格光纤光栅和长周期光纤光栅的反射率和透射率的解析解。应用光纤光栅耦合模方程及适当的边界条件,推导出了超结构光纤光栅中子光栅和相移部分的传输矩阵。首次用差分方法推导出了在考虑纤芯与包层模式耦合的情况下,计算超结构光纤光栅透射谱的4×4传输矩阵,该方法目前尚未见有文献报道。第三,设计了菲波纳契准周期超结构光纤光栅,并用传输矩阵法对其反射谱和透射谱进行了数值模拟,从理论上验证了其具有六循环及自相似等独特的光学特性。第四,用相位掩模版扫描的方法制备了费氏序数为S3-S10菲波纳契准周期超结构光纤光栅,并通过对实验过程的模拟将参数进行了优化,实验结果与理论数值模拟符合良好。最后,并对该超结构光纤光栅在分布式温度及应变传感领域的应用进行了探讨,同时设计了可应用于密集波分复用系统的广义菲波纳契类准周期超结构光纤光栅滤波器。该器件可以被用作C波段具有分形光谱的光纤滤波器,随机光纤激光器的谐振腔,分布式温度和应变传感器以及密集波分复用滤波器等。据我们所知,关于菲波纳契准周期结构在光纤中的应用尚未见实验报道。
Fiber gratings are fiber devices in which the effective refractive index of the fiber core is periodically modulated. They are now widly used in optical communications and optical sensors because of the advantages such as: compact structure, low insertion loss and low cost. Since K. O. Hill’s first fabrication of UV side writing fiber Bragg grating, the fabrication and application have attracted much attentions.
With the development of fabrication technique of fiber gratings and the increasing demand in the field of optical communination, fiber sensors and high power fiber lasers, superstructure fiber gratings with special characteristics have become the focus in the research of these fields. Various superstructure fiber gratings have been designed and used as EDFA gain-flattener, DWDM filters and multi-characters fiber sensors.
The propagation of optical waves in Fibonacci multilayer has been extensively studied theoretically and experimentally in the last two decades. Constructed by two kinds of layers which are stacked according to the one-dimensional (1D) Fibonacci sequence, the quasi-periodic structure exhibits a spectrum that has a rich self-similar structure including scaling. The transmission spectrum contains narrow resonances separated by numerous pseudo band gaps similar to the band gaps of a photonic crystal. A strongly reduced group velocity, associated with large delay times, is also observed at the band edge of the Fibonacci structure.
However, up to now, the quasi-periodic structure has not been applied to the optical fiber devices due to the limitation of writing technique. In the experimental works reported, the central wavelength of the Fibonacci multilayer located at 700nm or 2000nm, which is outside of the transmission window of optical communication. The input and output of the mulilayer devices must be coupled to fiber during utilization thus have a high insertion loass and the structure is not compact.
In this thesis, we design a new type of Fibonacci quasi-periodic superstructure fiber Bragg grating (SFBG). A phase-shifted section corresponding to A and a uniform section of fiber Bragg grating (FBG) corresponding to B is arranged along the fiber axis according to the Fibonacci generation scheme: Sj=Sj-1Sj-2 (j≧2), with S0=B and S1=A.
Organization of the thesis as follows:
1. In chapter 2, transfer matrices of the fiber grating section and phase shift section were derived from the coupling mode equations. The reflection and transmission spectra of the SFBG with different Fibonacci sequence order were simulated by using the transfer matrix method. For the case ofλ=λ0 andφ=(2m+1)π, I is maximum and the quasiperiodicity is most effective. In addition, the case above has the special feature that the dynamical map of equation Mj has a six-cycle orbit which means Mj=Mj+6 for any j. This implies that the reflectivity of the SFBG has six-cycle property Rf→0→Rf→Rf→4Rf2?(Rf4+1)→Rf→Rf for Sj→Sj+6, where Rf=tanh2(kL1) is the reflectivity of a uniform FBG with length L1.Under such condition, there exists a scale factor which determines the scaling behavior of the reflectivity.
2. In chapter 3, we describe the experimental setup and fabrication procedure of the designed SFBG. The quasi-periodic SFBGs were fabricated in a photosensitive single mode fiber by using a 244nm laser beam. The length and central wavelength of the uniform FBG section were 800μm and 1541.86nm respectively. At the specified positions,π-phase shifts were introduced between FBG sections by moving the phase mask with a computer controlled. The SFBGs from S0 (only 1 FBG section) to S10 (comprising 34 FBG and 55π-phase shift sections) were written into the fiber according to the arrangement of Fibonacci sequence. Both theoretical and experimental results show that the reflectivity of the Fibonacci structure exhibits a six-cycle property when the phase of the phase-shifted section at the central wavelength of FBG is (2m+1)πand the spectra are self-similar including scaling.
3. In chapter 4, the spectral variation of the SFBG with the influence of change of temperature and axial strain was also discussed and the application of the Fibonacce SFBG as distributed fiber grating sensors was proposed. The results show that the reflective spectra of the SFBG have different response to the variation of temperature and axial strain and can be used as distributed fiber sensor for measuring temperature and strain simultaneously. By varing the substitution rules of Fibonacc sequences, we construct a new generalized Fibonacci-class quasi-periodic SFBG, which can be used as DWDM filters in optical communications.
Compared with Fibonacci multilayer, the fabricated SFBG has the advantage of low insertion loss and polarization insensitivity.The complex structure of high order Fibonacci SFBG makes it a good candidate for the cavity that provides feedback for random laser. The Fibonacci quasi-periodic SFBGs can also serve as C-band optical filters with high wavelength selectivity and optical devices for multi-frequency operation.
Fiber gratings are fiber devices in which the effective refractive index of the fiber core is periodically modulated. They are now widly used in optical communications and optical sensors because of the advantages such as: compact structure, low insertion loss and low cost. Since K. O. Hill’s first fabrication of UV side writing fiber Bragg grating, the fabrication and application have attracted much attentions.
With the development of fabrication technique of fiber gratings and the increasing demand in the field of optical communination, fiber sensors and high power fiber lasers, superstructure fiber gratings with special characteristics have become the focus in the research of these fields. Various superstructure fiber gratings have been designed and used as EDFA gain-flattener, DWDM filters and multi-characters fiber sensors.
The propagation of optical waves in Fibonacci multilayer has been extensively studied theoretically and experimentally in the last two decades. Constructed by two kinds of layers which are stacked according to the one-dimensional (1D) Fibonacci sequence, the quasi-periodic structure exhibits a spectrum that has a rich self-similar structure including scaling. The transmission spectrum contains narrow resonances separated by numerous pseudo band gaps similar to the band gaps of a photonic crystal. A strongly reduced group velocity, associated with large delay times, is also observed at the band edge of the Fibonacci structure.
However, up to now, the quasi-periodic structure has not been applied to the optical fiber devices due to the limitation of writing technique. In the experimental works reported, the central wavelength of the Fibonacci multilayer located at 700nm or 2000nm, which is outside of the transmission window of optical communication. The input and output of the mulilayer devices must be coupled to fiber during utilization thus have a high insertion loass and the structure is not compact.
In this thesis, we design a new type of Fibonacci quasi-periodic superstructure fiber Bragg grating (SFBG). A phase-shifted section corresponding to A and a uniform section of fiber Bragg grating (FBG) corresponding to B is arranged along the fiber axis according to the Fibonacci generation scheme: Sj=Sj-1Sj-2 (j≧2), with S0=B and S1=A.
Organization of the thesis as follows:
1. In chapter 2, transfer matrices of the fiber grating section and phase shift section were derived from the coupling mode equations. The reflection and transmission spectra of the SFBG with different Fibonacci sequence order were simulated by using the transfer matrix method. For the case ofλ=λ0 andφ=(2m+1)π, I is maximum and the quasiperiodicity is most effective. In addition, the case above has the special feature that the dynamical map of equation Mj has a six-cycle orbit which means Mj=Mj+6 for any j. This implies that the reflectivity of the SFBG has six-cycle property Rf→0→Rf→Rf→4Rf2?(Rf4+1)→Rf→Rf for Sj→Sj+6, where Rf=tanh2(kL1) is the reflectivity of a uniform FBG with length L1.Under such condition, there exists a scale factor which determines the scaling behavior of the reflectivity.
2. In chapter 3, we describe the experimental setup and fabrication procedure of the designed SFBG. The quasi-periodic SFBGs were fabricated in a photosensitive single mode fiber by using a 244nm laser beam. The length and central wavelength of the uniform FBG section were 800μm and 1541.86nm respectively. At the specified positions,π-phase shifts were introduced between FBG sections by moving the phase mask with a computer controlled. The SFBGs from S0 (only 1 FBG section) to S10 (comprising 34 FBG and 55π-phase shift sections) were written into the fiber according to the arrangement of Fibonacci sequence. Both theoretical and experimental results show that the reflectivity of the Fibonacci structure exhibits a six-cycle property when the phase of the phase-shifted section at the central wavelength of FBG is (2m+1)πand the spectra are self-similar including scaling.
3. In chapter 4, the spectral variation of the SFBG with the influence of change of temperature and axial strain was also discussed and the application of the Fibonacce SFBG as distributed fiber grating sensors was proposed. The results show that the reflective spectra of the SFBG have different response to the variation of temperature and axial strain and can be used as distributed fiber sensor for measuring temperature and strain simultaneously. By varing the substitution rules of Fibonacc sequences, we construct a new generalized Fibonacci-class quasi-periodic SFBG, which can be used as DWDM filters in optical communications.
Compared with Fibonacci multilayer, the fabricated SFBG has the advantage of low insertion loss and polarization insensitivity.The complex structure of high order Fibonacci SFBG makes it a good candidate for the cavity that provides feedback for random laser. The Fibonacci quasi-periodic SFBGs can also serve as C-band optical filters with high wavelength selectivity and optical devices for multi-frequency operation.
引文
[1] K. O. Hill, Y. Fujii, D. C. Johnson, et al. Phostosensityvity in optical fiber waveguedes: Application to reflection filter fabrication [J]. Applied Physics Letters, 1978, 32: 647-649.
[2] B. S. Kawasaki, K. O. Hill, D.C. Johnson, et al. Narrow-band Bragg reflectors in optical fibers [J].Optics Letters, 1978, 3: 66-68.
[3] G. Meltz, W. W. Morey, and W. H. Glenn, Formation of Bragg gratings in optical fibers by a transverse holographic method [J]. Optics. Letters, 1989, 14: 823-825.
[4] K. O. Hill, B. Malo F. Bilodeau, et al. Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask [J]. Applied Physics Letters, 1993, 62: 1035-1037.
[5] K. O. Hill, F. Bilodeau, B. Malo, et al. Chirped in-fiber Bragg gratings for compensation of optical-fiber dispersion [J]. Optics Letters, 1994, 19: 1314 -1316.
[6] J.Albert, K.O. Hill, B. Malo, et al., Apodisation of the spectral response of fibre Bragg gratings using a phase mask with variable diffraction efficiency [J]. Electronics. Letters, 1995, 31: 222-223.
[7] W. H. Loh, M. J. Cole, M. N. Zervas, et al. Complex grating structures with uniform phase masks based on the moving fiber-scanning beam technique [J]. Optics Letters, 1995, 20: 2051-2053.
[8] A. Asseh, H. Storoy, B. E. Sahlgren, et al. A writing technique for long fiber Bragg gratings with complex reflectivity profiles [J]. Journal of Lightwave Technology, 1997, 15: 1419-1423.
[9] K. Raman, Fibre Bragg gratings [M]. Publisher San Diego, Calif.: Academec Press 1999.
[10] B.Poumellic, P. Guenot, I. Riant, et al. UV induced densification during Bragg grating inscription in Ge:SiO2 preforms [J]. Optical Materials, 1995, 4: 441-449.
[11] D. L. Williams, B. J. Ainslie, J. R. Armitage, et al. Enhanced UV photosensitivity in Boron co-doped germanosilicate fibers [J]. Electronics Letters, 1993, 29: 45-47.
[12] L. Dong, J. L. Cruz, L. L. Reekie, et al. Enhanced photosensitivity in Tin-codoped germanosilicate optical fibers [J]. IEEE Photonics Technology Letters, 1995, 7: 1048-1050.
[13] E. M. Dianov, K. M. Golant, R. R. Khrapko, et al. Grating formation in a germanium free silicon oxynitride fibre [J]. Electronics Letters, 1997, 33: 236-238.
[14] G. Brambilla, V. Pruneri, L. Reekie, C. et al. Bragg gratings in ternarySiO_2:SnO_2 :Na_2O optical glass fibers [J]. Optics. Letters, 2000, 25: 1153-1155.
[15] Q. Wang, A. Hidayat, P. Niay, et al. Influence of blanket postexposure on the thermal stability of the spectral characteristics of gratings written in a telecommunication fiber using light at 193 nm [J]. IEEE Photonics Technology Letters, 2000, 18: 1078-1083.
[16] B. O. Guan, H. Y. Tam, X. M. Tao, et al. Highly stable fiber Bragg gratings written in hydrogen-loaded fiber [J]. IEEE Photonics Technology Letters, 2000, 12: 1349-1351.
[17] M.C.Farries, K.Sugden, D.C.J.Reid et al. Very broad reflection bandwidth (44nm) chirped fibre gratings and narrow bandpass filters produced by the use of an amplitude mask [J]. Electronics Letters, 1994, 30:.891-892.
[18] R.Kashyap, P.F.Mckee, R.J.Campbell et al. Novel method of producing all fibre photoinduced chirped gratings [J]. Electronics Letters, 1994, 30: 996-997.
[19] A. M. Vengskar, P. J. Lemaire, J. B. Judkins, et al. Long-period fiber gratings as band-rejiction filters [C]. Techical Digest Confference of Optical Fibre Communication, San Diego, CA, 1995, PD4-2.
[20] A. M. Vengsarkar, P. J. Lemaire, J. B. Judikins, et al. Long-period fibre gratings as band-rejection filters [J]. Journal of Lightwave Technology, 1996, 14: 58-65.
[21] A.M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, et al. Long period fibre grating based gain equalizers [J]. Optics Letters, 1996, 21: 336-338.
[22] M. Harumoto, M. Shigehara, and H. Suganuma, Gain-flattening filter using long-period fibre gratings [J]. IEEE Journal of Lightwave Technoloy, 2002, 20(6): 1027-1033.
[23] B. Ortega, L. Dong, W. F. Liu, et al. High-performance optical fibre polarizers based on long-period gratings in birefringent optical fibre [J]. IEEE Photonics Technology Letters, 1997, 9: 1370-1372.
[24] V. Bhatia and A. M. Vengsarkar, Optical fibre long-period grating sensors [J]. Optics Letters, 1996, 21: 692-694.
[25] V. Bhatia, D. Camphell, and Richard O. Claus, Simultaneous strin and temperature measurement with long-period gratings [J]. Optics Letters, 1997, 22: 648-650.
[26] H. J. Patrick, C. Chang, S. T. Vohra, Long period fibre gratings for structural bend sensing [J]. Electronics Letters, 1998, 34:1773-1775.
[27] H. J. Patrick, A. D. Kersey, F. Bucholtz, et al. Chemical sensor based on long-period fibre grating response to index of refraction [J]. Lasers and Electro-Optics, 1997, 11: 420-421.
[28] B. H. Lee and J. Nishii, Depencence of fringe spacing on the grating separation ina long-period fibre grating pair [J]. Applied Optics, 1999, 38: 3450-3459.
[29] B. H. Lee, Y. J. Kim, Y. Chung, et al. Analytic solution for cascaded long-period fibre gratings [J]. IEICE Transactions Communications, 2001, E84-B: 1247-1254.
[30] D. S. Starodubov, V. Grubsky, and J. Feinberg, All-fiber bandpass filter with adjustable transmission using cladding-mode coupling [J]. IEEE Photonics Technology Letters, 1998, 10: 1590-1592.
[31] Y. C. Jeong, S. Baek, B. H. Lee, All-optical signal grating in cascaded long-period fiber gratings [J]. IEEE Photonics Technology Letters, 2000, 12:.1216-1218.
[32] Y. J. Kim, U. C. Paek, and B. H. Lee, Measurement of refractive-index variation with temperature by use of long-period fibre gratings [J]. Optics Letters, 2002, 27: 1297-1299.
[33] B.H. Lee, and J. Nishii, Self-interference of long-period fibre grating and its application as temperature sensor [J]. Elictronics Letters, 1998, 34: 2059-2060.
[34] M. G. Xu, R. Masskant, M. M. Ohn, et al. Independent tuning of cascaded long period fibre gratings for spectral shaping [J]. Electronics Letters, 1997, 33: 1893-1895.
[35] M. Harumoto, M. Shigehara, M. Kakui, et al. Compact long-period grating module with multi-attenuation peaks [J]. Electronics Letters, 2000, 36: 512-514.
[36] P. D. Greene and H. N. Rourke, Tailoring long period optical fibre gratings for flattening EDFA gain spectra [J]. Electronics Letters, 1999, 35(16): 1373-1374.
[37] I. B. Sohn, J. G. Baek, N. K. Lee, et al. Gain flattened and improved EDFA using micro-bending long-period fibre grating [J]. Electronics Letters, 2002, 38(6): 1324-1325.
[38] E. M. Dianov, S. A. VAsiliev, A. S. Kurkov, et al. In-fibre Mach-Zehnder interferometer based on a pair of long-period gratings [C]. Proceeding of European Conference on Optical Communication, 1996, 65-68.
[39] B. H. Lee and J. Nishii, Bending sensitivityof in-series long-period fiber gratings [J]. Optics Letters, 1998, 23: 1624-1626.
[40] B. O. Guan, A. P. Zhang, X. M. Tao, et al. Step-changed long-period fibre gratings [J]. IEEE Photonics Technology Letters, 2002, 14(5):.657-659.
[41] W. H. Loh, M. J. Cole, M. N. Zervas, et al. Complex grating structures with uniform phase masks based on the moving fibre-scanning beam technique [J]. Optics Letters, 1995, 20: 2051-2053.
[42] J.Canning, M. G. Sceats, Pi-phase-shifted periodic distributed structures in optical fibres by UV post-processing [J]. Electronics Letters, 1994, 30: 1344-1345.
[43] D. Uttamchandani, A. Othonos, Phase shifted Bragg gratings formed in optical fibres by post-fabrication thermal processing [J] Optical. Communications, 1996, 127: 200-204.
[44] Guillaume Tremblay and Yunlong Sheng, Effects of the phase shift split onphase-shifted fiber Bragg gratings [C]. JOAS B, 2006, 23(8): 1511-1516.
[45] Ling Zhao, Lin Li, Aipin Luo, et al. Bandwidth controllable transmission filter based on Moiréfiber Bragg grating [C] Optik-International Journal for Light and Electron Optics, 2002, 113(9): 464-468.
[46] A. M. Gillooly, L. Zhang and I. Bennion, Implementation of a distributed temperature sensor utilizing a chirped Moiréfibre Bragg grating [J]. Optical Communications, 2004, 242(6): 511-515.
[47] Qing Ye, Feng Liu, Ronghui Qu and Zujie Fang, Generation of millimeter–wave in optical pule carrier by using an apodized Moiréfiber grating [J]. Optical Communications, 2006, 266(2): 532-535.
[48] Xiaohui Fang, Muhamad Khawar Islam, pak L. Chu et al. Gigabit soliton generation by means of Moirégrating and figure-8 fibre laser [J]. Optical Communications, 2007, 272(2): 461-466.
[49] W. W. Morey, T. J. Bailey, W. H. Glenn, et al. Fibre fabry-Perot interferometer using side exposed fiber Bragg gratings [C]. OFC1992, San Jose, Paper WA2, February 1992.
[50] G. E. Twon, K. Sugden, J. A. R. Williams, I. Bennion, et al. Wide-band Fabry-Perot like filters in optical fibre [J]. IEEE Photonics Technology Letters, 1995,7: 78-80.
[51] M. G. Shlyagin, P. L. Swart, S. V. Miridonov, Static strain measurement with sub-micro-strain resolution and large dynamic range using a twin-Bragg-grating Fabry-Perot sensor [J]. Optical Engineering, 2002, 41: 1809-1814.
[52] G. A. Ball and W. W. Morey, Compression-tuned single frequency Bragg grating fibre laser [J]. Optics Letters, 1994, 19: 1979-1981.
[53] M. Y. Liu, S. Y. Chou, High-modulation-depth and short-cavity-length silicon Fabry-Perot modulator with two grating Bragg reflector [J]. Applied Physics Letters, 1996, 68: 170-172.
[54] J. Chow, G. Town, B. Eggleton, et al. Multivavelength generation in an Erbium-doped fibre laser using in-fibre comb filters [J]. IEEE Photonics Technology Letters, 1996, 8: 60-62.
[55] M. Ibsen, B. J. Eggleton, M. G. Sceats, et al. Broadly tunable DBR fiber laser using sampled fiber Bragg gratings [J]. Electronics Letters, 1995, 31: 37-38.
[56] J. Hubner, D. Zauner, and M. Kristensen, Low cross talk planar multichannel add-drop multiplexer based on sampled Bragg gratings [C]. Digegest of Optical Fibre Communications Conference 1998(PFC’98), 249-250.
[57] J. Hubner, D. Zauner, and M. Kristensen, Strong sampled Bragg gratings for WDM applications [J]. IEEE Photonics Technology Letters, 1998, 10: 552-554.
[58] W. H. Loh, F. Q. Zhou, and J. J. Pan, Novel designs for sampled grating-based multiplexers-demultiplexers [J]. Optics Letters, 1999, 24: 1457-1459.
[59] F. Quellette, P. A. Krug, T. Stephens, et al. Broadband and WDM dispersioncompensating using chirped sampled fibre Bragg gratings [J]. Electronics Letters, 1995, 31: 899-901.
[60] W. H. Loh, F. Q. Zhou, and J. J. Pan, Sampled fibre grating based-dispersion slope compensator [J]. IEEE Photonics Technology Letters, 1999, 11: 1280-1282.
[61] P. Petropoulos, M. Ibsen, M. N. Zervas, et al. Generation of a 40-GHz pulse stream by pulse multiplication with a sampled fibre Bragg grating [J]. Optics Letters, 2000, 25: 521-523.
[62] A. P. Zhang, B. O. Guan, X. M. Tao, et al. Mode couplings in superstructure fibre Bragg gratings [J]. IEEE Photonics Technology Letters, 2002, 14(4): 489-491.
[63] H. F. Talbot, Facts relating to optical science no. IV [J]. Philosophy Magazine, 1836, 9: 401-407.
[64] J. T. Winthrop and C. R. Worthington, Theopry of Fresnel images. I.Plane periodic objects in monocrotic light [J]. Journal of Optical Society of America, 1965, 55(4): 373-381.
[65] O. Bryngdahl, Image formation using self-imaging techniqued [J]. Journal of Optical Socieaty of America, 1973, 64(4): 416-419.
[66] K. Patorski, The self-imaging phenomenon and its applications [C]. Progress in Optics, E. Wolf, Ed. Amsterdam, the Netherlands: Elsevier Science, 1989, XXVII: 1-108.
[67] P. Latimer and R. F. Crouse, Talbot Effect Reinterpreted [J]. Applied Optics, 1992, 31(1): 80-89.
[68] M. V. Berry and S. Klein, Integer, fractional and fractal Talbot effects [J]. Journal of Modern Optics, 1996, 43(10): 2139-2164.
[69] T. Jannson and J. Jannson, Temporal self-imaging effect in single-mode fiber [J]. Journal of Optical Society of America, 1981, Vol.71, No.11, pp.1373-1376.
[70] K. Tai, A. Tomita, J. L. Jewell,et al. Generation of subpicosecond solitonlike iptical pulses at 0.3 THz repetition rate by induced modulation instability [J]. Applied Physics Letters, 1986, 49(5): 236-238.
[71] A. M. Weiner and D. E. Leaird, Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering [J]. Optics Letters, 1990, 15(1): 51-53.
[72] A. M. Weiner, S. Oudin, D. E. Leaird, et al. Shaping of femtosecond puses using phase-only filters designed by simulated annealing [J]. Journal of Optical Society of America, 1993, 10(5): 1112-1120.
[73] P. Petropoulos, M. Ibsen, M. N. Zervas, et al. Generation of 40-GHz puse stream by pulse multiplication with a sampled fiber Bragg grating [J]. Optics Letters, 1998, 25(8): 521-523.
[74] F. Ouellette, Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides [J]. Optics Letters, 1987, 12(10): 847-849.
[75] F. Oullette, J. F. Cliché, and S. Gagnon, All-fiber devices for chromatic dispersion compensation based on chirped distributede resonant coupling [J]. Journal ofLightwave Technology, 1994, 12(10): 1728-1738.
[76] Y. Nasu and S. Yamashita, Densification of sampled fiber bragg gratings using multiple phase shift (MPS) technique [J]. Journal of Lightwave Technology, 2005, 23(4): 1808-1817.
[77] H. Kogelnik, Filter response of nonuniform almost periodic structure, Bell System Technology Journal, 1976, 55: 109-126.
[78] C. H. Wang, J. Azana and L. R. Chen, Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures [J]. Optics Letters, 2004, 29(14): 1590-1592.
[79] Y. T. Dai, X. F. Chen, High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift [J]. IEEE Photonics Technology Letters, 2005, 17(5): 1040-1042.
[1]光纤光学[M],寥延彪编著,清华大学出版社, 2004.
[2]光纤通信[M],凯泽(美)著,高等教育出版社, 2006.
[3]韦占雄,chirped光纤光栅制作及特性研究[D],长春,吉林大学电子科学与工程学院,2001.
[4]秦莉,长周期光纤光栅制作及特性研究[D],长春,吉林大学电子科学与工程学院,1999.
[5] T. Erdogan, Fiber grating spectra [J]. Journal of Lightwave Technology, 1997, 15: 1278-1294.
[6] T. Erdogan, Cladding-mode resonances in short and long period fiber grating filters [J]. Journal of Optical Society of America A, 1997, 14: 1760-1773.
[1] M. P. van Albada and A. Lagendijk, Observation of weak localization of light in a random medium [J]. Physics Review Letters, 1985, 55: 2692-2695.
[2] L. D. Negro, C. J. Oton, Z. Gaburro, et al. Light transport through the band-edge states of Fibonacci quasicrystals [J]. Physics Review Letters,2003,90(5): 055501.
[3] M. Kohmoto, B. Stherland, and K. Iguchi, Localization in optics: quasiperiodic media [J]. Physics Review Letters, 1987, 58(23): 2436-2438.
[4] W. Gellermann, M. Kohmoto, B. Sutherland et al. Localization of light waves in Fibonacci dielectric multilayers [J]. Physics Review Letters, 1994, 72(5): 633-636.
[5] M. Kohmoto, B. Stherland, and K. Iguchi, Localization in optics: quasiperiodic media,”[J]. Physics Review Letters, 58, 23, 2436-2438
[6] T. Hattori, N. Tsurumachi, S. Kawato, et al. Photonic dispersion relation in a one-dimensional quasicrystal [J]. Physics Review B, 1994, 50(6): 4220-4223
[7] G. W. Chern, L. A. Wang, Transfer-matrix method based on perturbation expansion for periodic and quasi-periodic binary long-period gratings [J]. Journal of Optical Society of America A, 1999, 16(11): 2675-2689
[8] Golmohammadi S,Morawej-farshi MK, Rostami A, et al. Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures [J]. Optics Express, 2007, 15(17):.10520-10532.
[9] M. Kohmoto,J. R. Banavar,Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion [J]. Physics Review B, 1986, 34(2):563-566.
[1] W. Gellermann, M. Kohmoto, B. Sutherland et al. Localization of light waves in Fibonacci dielectric multilayers [J]. Physics Review Letters, 1994, 72(5): 633-636.
[2] L. D. Negro, C. J. Oton, Z. Gaburro, et al. Light transport through the band-edge states of Fibonacci quasicrystals [J]. Physics Review Letters,2003,90(5): 055501.
[3] R. B. Sargent and N. A. O’Bren, Review of thin films in telecommunications applications [C]. Proccedings of Optical Interference Coating (OSA), Banff, Cannada, 2001.
[4] L. R. Chen, H. S. Loka, D. J. F. Cooper. Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moire gratings [J]. Electronics Letters , 1999, 35: 584-585.
[5] J. Chon, A. Zeng, P. Peters, et al. Integrated interleaves technology enables high performance in DWDM systems [C]. Proccedings of National Fiber Optic Enginerring Confference, Baltimore, MD, 2001, 1410-1420.
[2] B. S. Kawasaki, K. O. Hill, D.C. Johnson, et al. Narrow-band Bragg reflectors in optical fibers [J].Optics Letters, 1978, 3: 66-68.
[3] G. Meltz, W. W. Morey, and W. H. Glenn, Formation of Bragg gratings in optical fibers by a transverse holographic method [J]. Optics. Letters, 1989, 14: 823-825.
[4] K. O. Hill, B. Malo F. Bilodeau, et al. Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask [J]. Applied Physics Letters, 1993, 62: 1035-1037.
[5] K. O. Hill, F. Bilodeau, B. Malo, et al. Chirped in-fiber Bragg gratings for compensation of optical-fiber dispersion [J]. Optics Letters, 1994, 19: 1314 -1316.
[6] J.Albert, K.O. Hill, B. Malo, et al., Apodisation of the spectral response of fibre Bragg gratings using a phase mask with variable diffraction efficiency [J]. Electronics. Letters, 1995, 31: 222-223.
[7] W. H. Loh, M. J. Cole, M. N. Zervas, et al. Complex grating structures with uniform phase masks based on the moving fiber-scanning beam technique [J]. Optics Letters, 1995, 20: 2051-2053.
[8] A. Asseh, H. Storoy, B. E. Sahlgren, et al. A writing technique for long fiber Bragg gratings with complex reflectivity profiles [J]. Journal of Lightwave Technology, 1997, 15: 1419-1423.
[9] K. Raman, Fibre Bragg gratings [M]. Publisher San Diego, Calif.: Academec Press 1999.
[10] B.Poumellic, P. Guenot, I. Riant, et al. UV induced densification during Bragg grating inscription in Ge:SiO2 preforms [J]. Optical Materials, 1995, 4: 441-449.
[11] D. L. Williams, B. J. Ainslie, J. R. Armitage, et al. Enhanced UV photosensitivity in Boron co-doped germanosilicate fibers [J]. Electronics Letters, 1993, 29: 45-47.
[12] L. Dong, J. L. Cruz, L. L. Reekie, et al. Enhanced photosensitivity in Tin-codoped germanosilicate optical fibers [J]. IEEE Photonics Technology Letters, 1995, 7: 1048-1050.
[13] E. M. Dianov, K. M. Golant, R. R. Khrapko, et al. Grating formation in a germanium free silicon oxynitride fibre [J]. Electronics Letters, 1997, 33: 236-238.
[14] G. Brambilla, V. Pruneri, L. Reekie, C. et al. Bragg gratings in ternarySiO_2:SnO_2 :Na_2O optical glass fibers [J]. Optics. Letters, 2000, 25: 1153-1155.
[15] Q. Wang, A. Hidayat, P. Niay, et al. Influence of blanket postexposure on the thermal stability of the spectral characteristics of gratings written in a telecommunication fiber using light at 193 nm [J]. IEEE Photonics Technology Letters, 2000, 18: 1078-1083.
[16] B. O. Guan, H. Y. Tam, X. M. Tao, et al. Highly stable fiber Bragg gratings written in hydrogen-loaded fiber [J]. IEEE Photonics Technology Letters, 2000, 12: 1349-1351.
[17] M.C.Farries, K.Sugden, D.C.J.Reid et al. Very broad reflection bandwidth (44nm) chirped fibre gratings and narrow bandpass filters produced by the use of an amplitude mask [J]. Electronics Letters, 1994, 30:.891-892.
[18] R.Kashyap, P.F.Mckee, R.J.Campbell et al. Novel method of producing all fibre photoinduced chirped gratings [J]. Electronics Letters, 1994, 30: 996-997.
[19] A. M. Vengskar, P. J. Lemaire, J. B. Judkins, et al. Long-period fiber gratings as band-rejiction filters [C]. Techical Digest Confference of Optical Fibre Communication, San Diego, CA, 1995, PD4-2.
[20] A. M. Vengsarkar, P. J. Lemaire, J. B. Judikins, et al. Long-period fibre gratings as band-rejection filters [J]. Journal of Lightwave Technology, 1996, 14: 58-65.
[21] A.M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, et al. Long period fibre grating based gain equalizers [J]. Optics Letters, 1996, 21: 336-338.
[22] M. Harumoto, M. Shigehara, and H. Suganuma, Gain-flattening filter using long-period fibre gratings [J]. IEEE Journal of Lightwave Technoloy, 2002, 20(6): 1027-1033.
[23] B. Ortega, L. Dong, W. F. Liu, et al. High-performance optical fibre polarizers based on long-period gratings in birefringent optical fibre [J]. IEEE Photonics Technology Letters, 1997, 9: 1370-1372.
[24] V. Bhatia and A. M. Vengsarkar, Optical fibre long-period grating sensors [J]. Optics Letters, 1996, 21: 692-694.
[25] V. Bhatia, D. Camphell, and Richard O. Claus, Simultaneous strin and temperature measurement with long-period gratings [J]. Optics Letters, 1997, 22: 648-650.
[26] H. J. Patrick, C. Chang, S. T. Vohra, Long period fibre gratings for structural bend sensing [J]. Electronics Letters, 1998, 34:1773-1775.
[27] H. J. Patrick, A. D. Kersey, F. Bucholtz, et al. Chemical sensor based on long-period fibre grating response to index of refraction [J]. Lasers and Electro-Optics, 1997, 11: 420-421.
[28] B. H. Lee and J. Nishii, Depencence of fringe spacing on the grating separation ina long-period fibre grating pair [J]. Applied Optics, 1999, 38: 3450-3459.
[29] B. H. Lee, Y. J. Kim, Y. Chung, et al. Analytic solution for cascaded long-period fibre gratings [J]. IEICE Transactions Communications, 2001, E84-B: 1247-1254.
[30] D. S. Starodubov, V. Grubsky, and J. Feinberg, All-fiber bandpass filter with adjustable transmission using cladding-mode coupling [J]. IEEE Photonics Technology Letters, 1998, 10: 1590-1592.
[31] Y. C. Jeong, S. Baek, B. H. Lee, All-optical signal grating in cascaded long-period fiber gratings [J]. IEEE Photonics Technology Letters, 2000, 12:.1216-1218.
[32] Y. J. Kim, U. C. Paek, and B. H. Lee, Measurement of refractive-index variation with temperature by use of long-period fibre gratings [J]. Optics Letters, 2002, 27: 1297-1299.
[33] B.H. Lee, and J. Nishii, Self-interference of long-period fibre grating and its application as temperature sensor [J]. Elictronics Letters, 1998, 34: 2059-2060.
[34] M. G. Xu, R. Masskant, M. M. Ohn, et al. Independent tuning of cascaded long period fibre gratings for spectral shaping [J]. Electronics Letters, 1997, 33: 1893-1895.
[35] M. Harumoto, M. Shigehara, M. Kakui, et al. Compact long-period grating module with multi-attenuation peaks [J]. Electronics Letters, 2000, 36: 512-514.
[36] P. D. Greene and H. N. Rourke, Tailoring long period optical fibre gratings for flattening EDFA gain spectra [J]. Electronics Letters, 1999, 35(16): 1373-1374.
[37] I. B. Sohn, J. G. Baek, N. K. Lee, et al. Gain flattened and improved EDFA using micro-bending long-period fibre grating [J]. Electronics Letters, 2002, 38(6): 1324-1325.
[38] E. M. Dianov, S. A. VAsiliev, A. S. Kurkov, et al. In-fibre Mach-Zehnder interferometer based on a pair of long-period gratings [C]. Proceeding of European Conference on Optical Communication, 1996, 65-68.
[39] B. H. Lee and J. Nishii, Bending sensitivityof in-series long-period fiber gratings [J]. Optics Letters, 1998, 23: 1624-1626.
[40] B. O. Guan, A. P. Zhang, X. M. Tao, et al. Step-changed long-period fibre gratings [J]. IEEE Photonics Technology Letters, 2002, 14(5):.657-659.
[41] W. H. Loh, M. J. Cole, M. N. Zervas, et al. Complex grating structures with uniform phase masks based on the moving fibre-scanning beam technique [J]. Optics Letters, 1995, 20: 2051-2053.
[42] J.Canning, M. G. Sceats, Pi-phase-shifted periodic distributed structures in optical fibres by UV post-processing [J]. Electronics Letters, 1994, 30: 1344-1345.
[43] D. Uttamchandani, A. Othonos, Phase shifted Bragg gratings formed in optical fibres by post-fabrication thermal processing [J] Optical. Communications, 1996, 127: 200-204.
[44] Guillaume Tremblay and Yunlong Sheng, Effects of the phase shift split onphase-shifted fiber Bragg gratings [C]. JOAS B, 2006, 23(8): 1511-1516.
[45] Ling Zhao, Lin Li, Aipin Luo, et al. Bandwidth controllable transmission filter based on Moiréfiber Bragg grating [C] Optik-International Journal for Light and Electron Optics, 2002, 113(9): 464-468.
[46] A. M. Gillooly, L. Zhang and I. Bennion, Implementation of a distributed temperature sensor utilizing a chirped Moiréfibre Bragg grating [J]. Optical Communications, 2004, 242(6): 511-515.
[47] Qing Ye, Feng Liu, Ronghui Qu and Zujie Fang, Generation of millimeter–wave in optical pule carrier by using an apodized Moiréfiber grating [J]. Optical Communications, 2006, 266(2): 532-535.
[48] Xiaohui Fang, Muhamad Khawar Islam, pak L. Chu et al. Gigabit soliton generation by means of Moirégrating and figure-8 fibre laser [J]. Optical Communications, 2007, 272(2): 461-466.
[49] W. W. Morey, T. J. Bailey, W. H. Glenn, et al. Fibre fabry-Perot interferometer using side exposed fiber Bragg gratings [C]. OFC1992, San Jose, Paper WA2, February 1992.
[50] G. E. Twon, K. Sugden, J. A. R. Williams, I. Bennion, et al. Wide-band Fabry-Perot like filters in optical fibre [J]. IEEE Photonics Technology Letters, 1995,7: 78-80.
[51] M. G. Shlyagin, P. L. Swart, S. V. Miridonov, Static strain measurement with sub-micro-strain resolution and large dynamic range using a twin-Bragg-grating Fabry-Perot sensor [J]. Optical Engineering, 2002, 41: 1809-1814.
[52] G. A. Ball and W. W. Morey, Compression-tuned single frequency Bragg grating fibre laser [J]. Optics Letters, 1994, 19: 1979-1981.
[53] M. Y. Liu, S. Y. Chou, High-modulation-depth and short-cavity-length silicon Fabry-Perot modulator with two grating Bragg reflector [J]. Applied Physics Letters, 1996, 68: 170-172.
[54] J. Chow, G. Town, B. Eggleton, et al. Multivavelength generation in an Erbium-doped fibre laser using in-fibre comb filters [J]. IEEE Photonics Technology Letters, 1996, 8: 60-62.
[55] M. Ibsen, B. J. Eggleton, M. G. Sceats, et al. Broadly tunable DBR fiber laser using sampled fiber Bragg gratings [J]. Electronics Letters, 1995, 31: 37-38.
[56] J. Hubner, D. Zauner, and M. Kristensen, Low cross talk planar multichannel add-drop multiplexer based on sampled Bragg gratings [C]. Digegest of Optical Fibre Communications Conference 1998(PFC’98), 249-250.
[57] J. Hubner, D. Zauner, and M. Kristensen, Strong sampled Bragg gratings for WDM applications [J]. IEEE Photonics Technology Letters, 1998, 10: 552-554.
[58] W. H. Loh, F. Q. Zhou, and J. J. Pan, Novel designs for sampled grating-based multiplexers-demultiplexers [J]. Optics Letters, 1999, 24: 1457-1459.
[59] F. Quellette, P. A. Krug, T. Stephens, et al. Broadband and WDM dispersioncompensating using chirped sampled fibre Bragg gratings [J]. Electronics Letters, 1995, 31: 899-901.
[60] W. H. Loh, F. Q. Zhou, and J. J. Pan, Sampled fibre grating based-dispersion slope compensator [J]. IEEE Photonics Technology Letters, 1999, 11: 1280-1282.
[61] P. Petropoulos, M. Ibsen, M. N. Zervas, et al. Generation of a 40-GHz pulse stream by pulse multiplication with a sampled fibre Bragg grating [J]. Optics Letters, 2000, 25: 521-523.
[62] A. P. Zhang, B. O. Guan, X. M. Tao, et al. Mode couplings in superstructure fibre Bragg gratings [J]. IEEE Photonics Technology Letters, 2002, 14(4): 489-491.
[63] H. F. Talbot, Facts relating to optical science no. IV [J]. Philosophy Magazine, 1836, 9: 401-407.
[64] J. T. Winthrop and C. R. Worthington, Theopry of Fresnel images. I.Plane periodic objects in monocrotic light [J]. Journal of Optical Society of America, 1965, 55(4): 373-381.
[65] O. Bryngdahl, Image formation using self-imaging techniqued [J]. Journal of Optical Socieaty of America, 1973, 64(4): 416-419.
[66] K. Patorski, The self-imaging phenomenon and its applications [C]. Progress in Optics, E. Wolf, Ed. Amsterdam, the Netherlands: Elsevier Science, 1989, XXVII: 1-108.
[67] P. Latimer and R. F. Crouse, Talbot Effect Reinterpreted [J]. Applied Optics, 1992, 31(1): 80-89.
[68] M. V. Berry and S. Klein, Integer, fractional and fractal Talbot effects [J]. Journal of Modern Optics, 1996, 43(10): 2139-2164.
[69] T. Jannson and J. Jannson, Temporal self-imaging effect in single-mode fiber [J]. Journal of Optical Society of America, 1981, Vol.71, No.11, pp.1373-1376.
[70] K. Tai, A. Tomita, J. L. Jewell,et al. Generation of subpicosecond solitonlike iptical pulses at 0.3 THz repetition rate by induced modulation instability [J]. Applied Physics Letters, 1986, 49(5): 236-238.
[71] A. M. Weiner and D. E. Leaird, Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering [J]. Optics Letters, 1990, 15(1): 51-53.
[72] A. M. Weiner, S. Oudin, D. E. Leaird, et al. Shaping of femtosecond puses using phase-only filters designed by simulated annealing [J]. Journal of Optical Society of America, 1993, 10(5): 1112-1120.
[73] P. Petropoulos, M. Ibsen, M. N. Zervas, et al. Generation of 40-GHz puse stream by pulse multiplication with a sampled fiber Bragg grating [J]. Optics Letters, 1998, 25(8): 521-523.
[74] F. Ouellette, Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides [J]. Optics Letters, 1987, 12(10): 847-849.
[75] F. Oullette, J. F. Cliché, and S. Gagnon, All-fiber devices for chromatic dispersion compensation based on chirped distributede resonant coupling [J]. Journal ofLightwave Technology, 1994, 12(10): 1728-1738.
[76] Y. Nasu and S. Yamashita, Densification of sampled fiber bragg gratings using multiple phase shift (MPS) technique [J]. Journal of Lightwave Technology, 2005, 23(4): 1808-1817.
[77] H. Kogelnik, Filter response of nonuniform almost periodic structure, Bell System Technology Journal, 1976, 55: 109-126.
[78] C. H. Wang, J. Azana and L. R. Chen, Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures [J]. Optics Letters, 2004, 29(14): 1590-1592.
[79] Y. T. Dai, X. F. Chen, High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift [J]. IEEE Photonics Technology Letters, 2005, 17(5): 1040-1042.
[1]光纤光学[M],寥延彪编著,清华大学出版社, 2004.
[2]光纤通信[M],凯泽(美)著,高等教育出版社, 2006.
[3]韦占雄,chirped光纤光栅制作及特性研究[D],长春,吉林大学电子科学与工程学院,2001.
[4]秦莉,长周期光纤光栅制作及特性研究[D],长春,吉林大学电子科学与工程学院,1999.
[5] T. Erdogan, Fiber grating spectra [J]. Journal of Lightwave Technology, 1997, 15: 1278-1294.
[6] T. Erdogan, Cladding-mode resonances in short and long period fiber grating filters [J]. Journal of Optical Society of America A, 1997, 14: 1760-1773.
[1] M. P. van Albada and A. Lagendijk, Observation of weak localization of light in a random medium [J]. Physics Review Letters, 1985, 55: 2692-2695.
[2] L. D. Negro, C. J. Oton, Z. Gaburro, et al. Light transport through the band-edge states of Fibonacci quasicrystals [J]. Physics Review Letters,2003,90(5): 055501.
[3] M. Kohmoto, B. Stherland, and K. Iguchi, Localization in optics: quasiperiodic media [J]. Physics Review Letters, 1987, 58(23): 2436-2438.
[4] W. Gellermann, M. Kohmoto, B. Sutherland et al. Localization of light waves in Fibonacci dielectric multilayers [J]. Physics Review Letters, 1994, 72(5): 633-636.
[5] M. Kohmoto, B. Stherland, and K. Iguchi, Localization in optics: quasiperiodic media,”[J]. Physics Review Letters, 58, 23, 2436-2438
[6] T. Hattori, N. Tsurumachi, S. Kawato, et al. Photonic dispersion relation in a one-dimensional quasicrystal [J]. Physics Review B, 1994, 50(6): 4220-4223
[7] G. W. Chern, L. A. Wang, Transfer-matrix method based on perturbation expansion for periodic and quasi-periodic binary long-period gratings [J]. Journal of Optical Society of America A, 1999, 16(11): 2675-2689
[8] Golmohammadi S,Morawej-farshi MK, Rostami A, et al. Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures [J]. Optics Express, 2007, 15(17):.10520-10532.
[9] M. Kohmoto,J. R. Banavar,Quasiperiodic lattice: Electronic properties, phonon properties, and diffusion [J]. Physics Review B, 1986, 34(2):563-566.
[1] W. Gellermann, M. Kohmoto, B. Sutherland et al. Localization of light waves in Fibonacci dielectric multilayers [J]. Physics Review Letters, 1994, 72(5): 633-636.
[2] L. D. Negro, C. J. Oton, Z. Gaburro, et al. Light transport through the band-edge states of Fibonacci quasicrystals [J]. Physics Review Letters,2003,90(5): 055501.
[3] R. B. Sargent and N. A. O’Bren, Review of thin films in telecommunications applications [C]. Proccedings of Optical Interference Coating (OSA), Banff, Cannada, 2001.
[4] L. R. Chen, H. S. Loka, D. J. F. Cooper. Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moire gratings [J]. Electronics Letters , 1999, 35: 584-585.
[5] J. Chon, A. Zeng, P. Peters, et al. Integrated interleaves technology enables high performance in DWDM systems [C]. Proccedings of National Fiber Optic Enginerring Confference, Baltimore, MD, 2001, 1410-1420.