基于光子晶体光纤的超短脉冲展宽器设计
|
摘要
高能激光器在国民经济、国防建设和科学研究等众多领域有着非常重大的应用,因此各种类型的高能激光器不断涌现。常用高能激光器设计技术主要有啁啾脉冲放大技术(CPA)和光参量啁啾脉冲放大技术(OPCPA)。在这两种技术中,对光脉冲进行展宽和压缩技术最为关键。本文理论分析了基于光子晶体光纤的超短脉冲展宽器设计。由于光子晶体光纤结构可以灵活设计,通过改变空气孔半径、间距、介质材料和空气孔排列方式等可以获得不同的色散值、非线性系数、双折射和有效模场面积等,为许多光功能器件提供了新的设计途径。
本文首先简单介绍了光子晶体光纤和脉冲展宽器的国内外研究现状,以及光子晶体光纤一些突出特性,如无限单模传输、色散可调节、高双折射和有效模场面积可调等性质。重点分析了矢量有效折射率分析模型,通过该理论模型分析了光子晶体光纤包层有效折射率的计算方法。通过计算推导出光子晶体光纤包层空间填充模的特征值方程,可以由二阶、三阶色散计算公式对应的色散值。由包层空间填充模特征值方程计算出包层的有效折射率,然后通过采用与折射率阶跃光纤一样的数值孔径法求出光子晶体光纤的非线性系数,并且分析了光子晶体光纤非线性系数与空气孔半径和间距的变化关系。
本文以超短脉冲展宽器为设计目标,采用光子晶体光纤作为设计方案,可以对超短脉冲的10000倍以上展宽。通过对一般展宽器设计要求的分析,可以知道作为展宽器设计的光子晶体光纤在800nm波长处的二阶色散值要高而且平坦。经过理论计算后表明在光子晶体光纤空气孔半径等于0.265μm和空气孔间距等于1.27μm时,在800nm波长处存在平坦的二阶色散值。该光子晶体光纤的二阶色散约等于35.72ps2/km,三阶色散约等于0.0002ps3/km以及非线性系数约等于36.4W-1·km-1,色散平坦宽度约为300nm。通过理论计算和分析得出结论：采用1000m长优化设计的光子晶体光纤可以实现对超短光脉冲进行展宽,展宽因子可以达到10000倍以上。由于光子晶体光纤的各种优越特性,该展宽器设计方案将有一定的参考意义和现实意义。
All types of ultra-high peak-power laser systems are emerging, because they have more and more important applications in the fields of national economy, military and scientific research. The Large-ratio stretching of the ultra-short pulse seed laser and recompression technology are the key techniques for chirped pulse amplification (CPA) or optical parametric chirped pulse amplification (OPCPA) of ultrahigh peak-power laser systems. In this paper, we use photonic crystal fiber (PCF) to design large-ratio stretcher for ultra-short pulses. Because of the PCF's design with flexibility of changing the radius and lattice pitch of air-holes, dielectric materials and arrangement of air holes, it can easily get different dispersion values, nonlinear coefficients, birefringence and effective mode areas, etc. Therefore, PCF provides a new design approach for many optical devices.
In the paper, we briefly introduce the research situation of PCF and pulse stretcher at home and abroad. PCF have been shown desirable characteristics such as endlessly single mode, adjustable dispersion, high birefringence and adjustable effective mode field area, etc. The cladding effective index of PCF can be calculated through vector effective index method. Through theoretical analysis and calculation, we obtain the characteristic equation of cladding space-filling mode and the formula of second-order and third-order dispersion. The effective refractive index of cladding can be obtained by the characteristic equation of cladding space-filling mode. And then use numerical aperture to calculate nonlinear coefficient as step-index fibers. The relationship of nonlinear coefficient of PCF with the radius and lattice pitch of air holes is also analyzed.
In this paper, we propose a PCF structure that can be used as the ultra-short pulse stretcher with stretching ratio of more then 10,000. From analysis of the stretcher's requirements, PCF should have high and flattened second-order dispersion value at the wavelength of 800nm. Through theoretical analysis and simulation, with the air hole radius of 0.265μm and lattice pitch of 1.27μm, the PCF can provide more than 300-nm working wavelength range with flattened dispersion suitable for most ultra-short pulse laser sources around 800nm. And the second-order dispersion is 35.72 ps2/km, third-order dispersion 0.0002 ps3/km and nonlinear coefficient 36.4W-1.km-1. Results indicate that more than 10,000 stretching ratio is achievable for ultra-short pulses with pulse width less than 100fs. Such approach may be more practical in the near future due to its all-fiber nature.
本文首先简单介绍了光子晶体光纤和脉冲展宽器的国内外研究现状,以及光子晶体光纤一些突出特性,如无限单模传输、色散可调节、高双折射和有效模场面积可调等性质。重点分析了矢量有效折射率分析模型,通过该理论模型分析了光子晶体光纤包层有效折射率的计算方法。通过计算推导出光子晶体光纤包层空间填充模的特征值方程,可以由二阶、三阶色散计算公式对应的色散值。由包层空间填充模特征值方程计算出包层的有效折射率,然后通过采用与折射率阶跃光纤一样的数值孔径法求出光子晶体光纤的非线性系数,并且分析了光子晶体光纤非线性系数与空气孔半径和间距的变化关系。
本文以超短脉冲展宽器为设计目标,采用光子晶体光纤作为设计方案,可以对超短脉冲的10000倍以上展宽。通过对一般展宽器设计要求的分析,可以知道作为展宽器设计的光子晶体光纤在800nm波长处的二阶色散值要高而且平坦。经过理论计算后表明在光子晶体光纤空气孔半径等于0.265μm和空气孔间距等于1.27μm时,在800nm波长处存在平坦的二阶色散值。该光子晶体光纤的二阶色散约等于35.72ps2/km,三阶色散约等于0.0002ps3/km以及非线性系数约等于36.4W-1·km-1,色散平坦宽度约为300nm。通过理论计算和分析得出结论：采用1000m长优化设计的光子晶体光纤可以实现对超短光脉冲进行展宽,展宽因子可以达到10000倍以上。由于光子晶体光纤的各种优越特性,该展宽器设计方案将有一定的参考意义和现实意义。
All types of ultra-high peak-power laser systems are emerging, because they have more and more important applications in the fields of national economy, military and scientific research. The Large-ratio stretching of the ultra-short pulse seed laser and recompression technology are the key techniques for chirped pulse amplification (CPA) or optical parametric chirped pulse amplification (OPCPA) of ultrahigh peak-power laser systems. In this paper, we use photonic crystal fiber (PCF) to design large-ratio stretcher for ultra-short pulses. Because of the PCF's design with flexibility of changing the radius and lattice pitch of air-holes, dielectric materials and arrangement of air holes, it can easily get different dispersion values, nonlinear coefficients, birefringence and effective mode areas, etc. Therefore, PCF provides a new design approach for many optical devices.
In the paper, we briefly introduce the research situation of PCF and pulse stretcher at home and abroad. PCF have been shown desirable characteristics such as endlessly single mode, adjustable dispersion, high birefringence and adjustable effective mode field area, etc. The cladding effective index of PCF can be calculated through vector effective index method. Through theoretical analysis and calculation, we obtain the characteristic equation of cladding space-filling mode and the formula of second-order and third-order dispersion. The effective refractive index of cladding can be obtained by the characteristic equation of cladding space-filling mode. And then use numerical aperture to calculate nonlinear coefficient as step-index fibers. The relationship of nonlinear coefficient of PCF with the radius and lattice pitch of air holes is also analyzed.
In this paper, we propose a PCF structure that can be used as the ultra-short pulse stretcher with stretching ratio of more then 10,000. From analysis of the stretcher's requirements, PCF should have high and flattened second-order dispersion value at the wavelength of 800nm. Through theoretical analysis and simulation, with the air hole radius of 0.265μm and lattice pitch of 1.27μm, the PCF can provide more than 300-nm working wavelength range with flattened dispersion suitable for most ultra-short pulse laser sources around 800nm. And the second-order dispersion is 35.72 ps2/km, third-order dispersion 0.0002 ps3/km and nonlinear coefficient 36.4W-1.km-1. Results indicate that more than 10,000 stretching ratio is achievable for ultra-short pulses with pulse width less than 100fs. Such approach may be more practical in the near future due to its all-fiber nature.
引文
[1]P. Maine, D. Strickland, P. Bado, M. Pessot and G. Mourou. Generation of ultrahigh peak power pulses by chirped pulse amplification [J]. IEEE J. Quantum Electron., 1988, QE-24 (2):398-403.
[2]D. Du, J. Squier, S. Kane, G. Korn, G. Mourou. Terawatt Ti:sapphire laser with a spherical reflective-optic pulse expander [J]. Opt. Lett.,1995,20(20):2114-2116.
[3]K. Kim, S. Lee, and P. Delfyett.1.4kW high peak power generation from an all semiconductor mode-locked master oscillator power amplifier system based on eXtreme Chirped Pulse Amplification(X-CPA). Opt. Express,2005,13(12):4600-4606.
[4]J. Rothhardt, S. Hadrich, E. Seise, M. Krebs, F. Tavella, et al. High average and peak power few-cycle laser pulses delivered by fiber pumped OPCPA system [J]. Opt. Express,2010,18(12):12719-12726.
[5]G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker and L. F. Dimauro. Aberration-free stretcher design for ultrashort-pulse amplification [J]. Opt. Lett.,1996, 21(6):414-416.
[6]I. N. Ross, P. Matousek, M. Towrie, A. J. Langley and J. L. Collier. The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers [J]. Opt. Comm.,1997,144(1-3):125-133.
[7]P. St. J. Russell, J. C. knight, T. A. Birks,et al. Recent progress in photonic crystal fiber [C].OFC,2000,3:98-100.
[8]P. Russell. Photonic Crystal Fibers [J]. Science,2003,299(1):358-362.
[9]S. G. Li, L. Hou, et al.Super continuum Generation in Holey Micro-structure Fibers with Random Cladding Distribution by Femto second Lase Pulses [J]. Chin. Phys. Lett.,2003,20(8):1300-1302.
[10]T. A. Birks, J. C. Knight, P. S. J. Russell. Endlessly Single-Mode Photonic Crystal Fiber [J]. Opt. Lett.,1997,22(13):961-963.
[11]B. A. Ortigosa, J. C. Knight, W. J. Wadsworth, et al. Highly birefringent photonic crystal fibers [J]. Opt. Lett.,2000,25(18):1325-1327.
[12]S. Kim and C. Kee. Dispersion properties of dual-core photonic-quasicrystal fiber [J]. Opt. Express.,2009,17(18):15885-15890.
[13]A. Huttunen and P. Torma. Optimization of dual-core and microstructure fiber geometries for dispersion compensation and large mode area [J]. Opt. Express,2005, 13(2):627-635.
[14]K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka and M. Fujita. Optical properties of a low-loss polarization-maintaining photonic crystal fiber [J]. Opt. Express,2001, 9(13):676-680.
[15]W. Wadsworth, R. Percival, G. Bouwmans, J. Knight and P. Russell. High power air-clad photonic crystal fibre laser [J]. Opt. Express,2003, 11(1):48-53.
[16]T. Ritari, J. Tuominen, H. Ludvigsen, J. Petersen, T. Sorensen, et al. Gas sensing using air-guiding photonic bandgap fibers [J]. Opt. Express,2004,12(17):4080-4087.
[17]J. Broeng, S. E. Barkou, et al. Photonic crystal fiber:a new class of optical waveguides [J]. Opt. Fiber. Technol.,1999,5:305-330.
[18]J. Broeng, S. E. Barkou, T. Sφndergaard and A. Bjarklev. Analysis of air-guiding photonic bandgap fibers [J]. Opt. Lett.,2000,25(2):96-98.
[19]J. C. Knight and D. V. Skryabin. Nonlinear waveguide optics and photonic crystal fibers [J]. Opt. Express,2007,15(23):15365-15376.
[20]E. Yblonovitch. Inhibited Spontaneous Emission in Solid-State Physics and Electronics [J]. Phys. Rev. Lett.,1987,58:2059-2062.
[21]S. John. Strong localization of photons in certain disordered dielectric superlattices [J]. Phys. Rev. Lett.,1987,58:2486-2489.
[22]J. C. Knight, T. A. Birks, P. St. Russell, et al. All-silica single-mode optical fiber with Photonic crystal cladding [J]. Opt. Lett.,1996,21:1547-1548.
[23]T. M. Monro, P. J. Bennet, et al. Holey fibers with random cladding distributions [J]. Opt. Lett.,2000,25:206-208.
[24]M. Lehtonen, G. Genty, H. Ludvigsen, et al. Super continuum generation in highly birefringent photonic crystal fiber [J]. Appl. Phy. Lett.,2003,82:2197-2199.
[25]S. Kim, C.Kee and C. G. Lee. Modified rectangular lattice photonic crystal fibers with high birefringence and negative dispersion [J]. Opt. Express,2009,17(10):7952-7957.
[26]M. N. M. Nasir, Z. Yusoff, et al. Widely tunable multi-wavelength Brillouin-erbium fiber laser utilizing low SBS threshold photonic crystal fiber [J]. Opt. Express,2009, 17(15):12829-12834.
[27]M. Chen and R. Yu. Analysis of Photonic Bandgaps in Modified Honeycomb Structures [J]. IEEE Photon. Technol. Lett.,2004,16(3):819-821.
[28]M. Chen and R. Yu. Square-Structured Photonic Bandgap Fibers [J]. Opt. Comm., 2004,235:63-67.
[29]M. Hu, C. Wang, L. Chai and A. Zheltikov. Frequency-tunable anti-Stokes line emission by eigenmodes of a birefringent microstructure fiber [J]. Opt. Express,2004, 12(9):1932-1937.
[30]Y. Li, M. Hu, C. Wang and A. M. Zheltikov. Perturbative and phase-transition-type modification of mode field profiles and dispersion of photonic-crystal fibers by arrays of nanosize air-hole defects [J]. Opt. Express,2006,14(22):10878-10886.
[31]Z. Wang, G. Kai, Y. Liu, J. Liu, C. Zhang, T. Sun, et al. Coupling and decoupling of dual-core photonic bandgap fibers [J]. Opt. Lett.,2005,30(19):2542-2544.
[32]Z. Wang, Y. Liu, G. Kai, et al. Directional couplers operated by resonant coupling in all-solid photonic bandgap fibers [J]. Opt. Express,2007,15(14):8925-8930.
[33]L. Zhang and C. Yang. Polarization splitter based on photonic crystal fibers [J]. Opt. Express,2003,11(9):1015-1020.
[34]H. Yan, C. Gu, C. Yang, J. Liu, G. Jin, J. Zhang, et al. Hollow core photonic crystal fiber surface-enhanced Raman probe [J]. Appl. Phys. Lett.,2006,89(204101):1-3.
[35]N. Yi, L. Zhang, S. Jia and J. Peng. Dispersion of square solid-core photonic bandgap fibers [J]. Opt. Express,2004,12(13):2825-2830.
[36]L. Xiao, W. Jin, M. S. Demokan. Photonic crystal fibers confining light by both index-guiding and bandgap-guiding:hybrid PCFs [J]. Opt. Express,2007,15(24): 15637-15647.
[37]P. Li, J. Zhao, X. Zhang. Nonlinear coupling in triangular triple-core photonic crystal fibers [J]. Opt. Express,2010,18(26):26828-26833.
[38]E. Treacy. Optical pulse compression with diffraction gratings [J]. IEEE J. Quantum Electron.,1969,5(9):454-458.
[39]B. E. Lemoff and C. P. J. Barty. Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses [J]. Opt. Lett.,1993,18(19):1651-1653.
[40]O. E. Martinez.3000 Times grating compressor with positive group velocity dispersion: Application to fiber compensation in 1.3-1.6μm region [J]. IEEE J. Quantum Electron., 1987, QE-23(1):59-64.
[41]J. P. Chambaret, C. L. Blanc, G. Cheriaux, P. Curley, et al. Generation of 25-TW,32-fs pulses at 10 Hz [J]. Opt. Lett.,1996,21(23):1921-1923.
[42]B. C. Stuart, M. D. Perry, J. Miller, G. Tietbohl, S. Herman, et al.125-TW Ti: sapphire/Nd:glass laser system [J]. Opt. Lett.,1997,22(4):242-244.
[43]P. S. Banks, M. D. Perry, et al. Novel all-reflective stretcher for chirped-pulse amplification of ultrashort pulses [J]. IEEE J. Quantum Electron.,2000,36(3): 268-274.
[44]R. Khare, P. K. Shukla, G. K. Mishra, et al. A novel confocal optical pulse stretcher for laser pulses [J]. Opt. Comm.,2009,282:3850-3853.
[45]L. Gruner-Nielsen, D. Jakobsen, et al. A stretcher fiber for use in fs chirped pulse Yb amplifiers [J]. Opt. Express,2010,18(4):3768-3773.
[46]张树葵,文国庆,周丕璋等.钛宝石飞秒激光的啁啾脉冲再生放大[J].强激光与粒子束,1996,8(4)：500-506.
[47]魏志义,张杰等.高效率太瓦级飞秒掺钛蓝宝石激光装置[J].中国科学,2000,30(11)：1046-1050.
[48]田金荣,孙敬华,魏志义等Offner展宽器高倍率展宽脉冲的理论与实验研究[J].物理学报,2005,54(3)：1200-1207.
[49]王逍,朱启华,林东晖等.高展宽量八通展宽器的设计制作[J].中国激光,2006,33(7)：895-898.
[50]胡婉约,王二玉,李文雪,丁良恩.适用于亚10 fs的共心衍射无像差展宽器[J].光学学报,2007,27(1)：181-186.
[51]G. P. Agrawal. Nonlinear Fiber Optics [M]. Third edition, Academic Press,2001.
[52]G. K. Wong, A. Y. Chen, S. Ha, et al. Characterization of Chromatic Dispersion in Photonic Crystal Fibers Using Scalar Modulation Instability [J]. Opt. Express,2005, 13(21):8662-8670.
[53]J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, et al. Anomalous Dispersion in Photonic Crystal Fiber [J]. Photon. Technol. Lett.,2000,12(7):807-809.
[54]J. C. Travers, J. M. Stone, A. B. Rulkov, et al. Optical pulse compression in dispersion decreasing photonic crystal fiber [J]. Opt. Express,2007,15(20):13203-13211.
[55]A. Podlipensky, P. Szarniak, N. Y. Joly, C. G. Poulton, and P. St. J. Russell. Bound soliton pairs in photonic crystal fiber [J]. Opt. Express,2007,15(4):1653-1662.
[56]T. P. Hansen, J. Broeng, S. E. B. Libori, et al. Highly birefringent index-guiding photonic crystal fibers [J]. IEEE Photon. Technol. Lett.,2001,13(6):588-590.
[57]W. Belardi, G. Bouwmans, L. Provino, M. Douay. Form-Induced Birefringence in Elliptical Hollow Photonic Crystal Fiber With Large Mode Area [J]. IEEE J. Quantum Electron.,2005,41(12):1558-1564.
[58]T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legre, et al. Experimental study of polarization properties of highly birefringent photonic crystal fibers [J]. Opt. Express, 2004,12(24):5931-5939.
[59]K. Saitoh, T. Fujisawa, T. Kirihara and M. Koshiba. Approximate empirical relations for nonlinear photonic crystal fibers [J]. Opt. Express,2006,14(14):6572-6582.
[60]K. Saitoh and M. KoshibaHighly. nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window [J]. Opt. Express,2004, 12(10):2027-2032.
[61]T. M. Monro, D. J. Richardson, et al. Holey Optical Fibers:An Efficient Modal Model [J]. J. Lightwave Technol.,1999,17(6):1093-1102.
[62]J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro. Properties of photonic crystal fiber and the effective index model [J]. J. Opt. Soc. Am. A.,1998, 15(3):748-752.
[63]M. Dems, R. Kotynski, and K. Panajotov. PlaneWave Admittance Method-a novel approach for determining the electromagnetic modes in photonic structures [J]. Opt. Express,2005,13(9):3196-3207.
[64]S. Guo, S. Albin. Simple planewave implementation for photonic crystal calculations [J]. Opt. Express,2003,11(2):167-175.
[65]T. P. White, B. T. Kuhlmey, R. C. McPhedran, et al. Multipole method for microstructured optical fibers. I. Formulation [J]. J. Opt. Soc. Am. B.,2002,19(10): 2322:2330.
[66]B. T. Kuhlmey, T. P. White, G. Renversez, et al. Multipole method for microstructured optical fibers. II. Implementation and results [J]. J. Opt. Soc. Am. B.,2002,19(10): 2331:2340.
[67]C. A. D. Francisco, B. V. Borges, M. A. Romero. A semivectorial iterative finite-difference method to model photonic crystal fibers [C]. IMOC,2001,1:407-409.
[68]Z. Zhu and T. Brown. Full-vectorial finite-difference analysis of microstructured optical fibers [J]. Opt. Express,2002,10(17):853-864.
[69]C. P. Yu and H. C. Chang. Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers [J]. Opt. Express,2004,12(25):6165-6177.
[70]M. A. R. Franco, H. T. Hattori, F. Sircilli, A. Passaro, N. M. Abe. Finite element analysis of photonic crystal fibers [C]. IMOC,2001,1:5-7.
[71]M. Koshiba, K. Saitoh. Numerical verification of degeneracy in hexagonal Photonic crystal fibers [J]. IEEE Photon. Technol. Lett.,2001,13(12):1313-1315.
[72]M. Midrio, M. P. Singh, and C. G. Someda. The space filling mode of holey fibers:an analytical vectorial solution [J]. J. Lightwave Technol.,2000,18(7):1031-1037.
[73]N. A. Mortensen. Effective area of photonic crystal fibers [J]. Opt. Express,2002, 10(7):341-348.
[74]K. Saitoh and M. Koshiba. Empirical relations for simple design of photonic crystal fibers [J]. Opt. Express,2005,13(1):267-274.
[75]L. Farr, J. C. Knight, B. J. Mangan and P. J. Roberts. Low loss photonic crystal fiber [C]. ECOC (Copenhagen,2002). Post-deadline paper PD13.
[76]L. Kuznetsova and F. W. Wise. Scaling of femtosecond Yb-doped fiber amplifiers to tens of microjoule pulse energy via nonlinear chirped pulse amplification [J]. Opt. Lett., 2007,32(18):2671-2673.
[2]D. Du, J. Squier, S. Kane, G. Korn, G. Mourou. Terawatt Ti:sapphire laser with a spherical reflective-optic pulse expander [J]. Opt. Lett.,1995,20(20):2114-2116.
[3]K. Kim, S. Lee, and P. Delfyett.1.4kW high peak power generation from an all semiconductor mode-locked master oscillator power amplifier system based on eXtreme Chirped Pulse Amplification(X-CPA). Opt. Express,2005,13(12):4600-4606.
[4]J. Rothhardt, S. Hadrich, E. Seise, M. Krebs, F. Tavella, et al. High average and peak power few-cycle laser pulses delivered by fiber pumped OPCPA system [J]. Opt. Express,2010,18(12):12719-12726.
[5]G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker and L. F. Dimauro. Aberration-free stretcher design for ultrashort-pulse amplification [J]. Opt. Lett.,1996, 21(6):414-416.
[6]I. N. Ross, P. Matousek, M. Towrie, A. J. Langley and J. L. Collier. The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers [J]. Opt. Comm.,1997,144(1-3):125-133.
[7]P. St. J. Russell, J. C. knight, T. A. Birks,et al. Recent progress in photonic crystal fiber [C].OFC,2000,3:98-100.
[8]P. Russell. Photonic Crystal Fibers [J]. Science,2003,299(1):358-362.
[9]S. G. Li, L. Hou, et al.Super continuum Generation in Holey Micro-structure Fibers with Random Cladding Distribution by Femto second Lase Pulses [J]. Chin. Phys. Lett.,2003,20(8):1300-1302.
[10]T. A. Birks, J. C. Knight, P. S. J. Russell. Endlessly Single-Mode Photonic Crystal Fiber [J]. Opt. Lett.,1997,22(13):961-963.
[11]B. A. Ortigosa, J. C. Knight, W. J. Wadsworth, et al. Highly birefringent photonic crystal fibers [J]. Opt. Lett.,2000,25(18):1325-1327.
[12]S. Kim and C. Kee. Dispersion properties of dual-core photonic-quasicrystal fiber [J]. Opt. Express.,2009,17(18):15885-15890.
[13]A. Huttunen and P. Torma. Optimization of dual-core and microstructure fiber geometries for dispersion compensation and large mode area [J]. Opt. Express,2005, 13(2):627-635.
[14]K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka and M. Fujita. Optical properties of a low-loss polarization-maintaining photonic crystal fiber [J]. Opt. Express,2001, 9(13):676-680.
[15]W. Wadsworth, R. Percival, G. Bouwmans, J. Knight and P. Russell. High power air-clad photonic crystal fibre laser [J]. Opt. Express,2003, 11(1):48-53.
[16]T. Ritari, J. Tuominen, H. Ludvigsen, J. Petersen, T. Sorensen, et al. Gas sensing using air-guiding photonic bandgap fibers [J]. Opt. Express,2004,12(17):4080-4087.
[17]J. Broeng, S. E. Barkou, et al. Photonic crystal fiber:a new class of optical waveguides [J]. Opt. Fiber. Technol.,1999,5:305-330.
[18]J. Broeng, S. E. Barkou, T. Sφndergaard and A. Bjarklev. Analysis of air-guiding photonic bandgap fibers [J]. Opt. Lett.,2000,25(2):96-98.
[19]J. C. Knight and D. V. Skryabin. Nonlinear waveguide optics and photonic crystal fibers [J]. Opt. Express,2007,15(23):15365-15376.
[20]E. Yblonovitch. Inhibited Spontaneous Emission in Solid-State Physics and Electronics [J]. Phys. Rev. Lett.,1987,58:2059-2062.
[21]S. John. Strong localization of photons in certain disordered dielectric superlattices [J]. Phys. Rev. Lett.,1987,58:2486-2489.
[22]J. C. Knight, T. A. Birks, P. St. Russell, et al. All-silica single-mode optical fiber with Photonic crystal cladding [J]. Opt. Lett.,1996,21:1547-1548.
[23]T. M. Monro, P. J. Bennet, et al. Holey fibers with random cladding distributions [J]. Opt. Lett.,2000,25:206-208.
[24]M. Lehtonen, G. Genty, H. Ludvigsen, et al. Super continuum generation in highly birefringent photonic crystal fiber [J]. Appl. Phy. Lett.,2003,82:2197-2199.
[25]S. Kim, C.Kee and C. G. Lee. Modified rectangular lattice photonic crystal fibers with high birefringence and negative dispersion [J]. Opt. Express,2009,17(10):7952-7957.
[26]M. N. M. Nasir, Z. Yusoff, et al. Widely tunable multi-wavelength Brillouin-erbium fiber laser utilizing low SBS threshold photonic crystal fiber [J]. Opt. Express,2009, 17(15):12829-12834.
[27]M. Chen and R. Yu. Analysis of Photonic Bandgaps in Modified Honeycomb Structures [J]. IEEE Photon. Technol. Lett.,2004,16(3):819-821.
[28]M. Chen and R. Yu. Square-Structured Photonic Bandgap Fibers [J]. Opt. Comm., 2004,235:63-67.
[29]M. Hu, C. Wang, L. Chai and A. Zheltikov. Frequency-tunable anti-Stokes line emission by eigenmodes of a birefringent microstructure fiber [J]. Opt. Express,2004, 12(9):1932-1937.
[30]Y. Li, M. Hu, C. Wang and A. M. Zheltikov. Perturbative and phase-transition-type modification of mode field profiles and dispersion of photonic-crystal fibers by arrays of nanosize air-hole defects [J]. Opt. Express,2006,14(22):10878-10886.
[31]Z. Wang, G. Kai, Y. Liu, J. Liu, C. Zhang, T. Sun, et al. Coupling and decoupling of dual-core photonic bandgap fibers [J]. Opt. Lett.,2005,30(19):2542-2544.
[32]Z. Wang, Y. Liu, G. Kai, et al. Directional couplers operated by resonant coupling in all-solid photonic bandgap fibers [J]. Opt. Express,2007,15(14):8925-8930.
[33]L. Zhang and C. Yang. Polarization splitter based on photonic crystal fibers [J]. Opt. Express,2003,11(9):1015-1020.
[34]H. Yan, C. Gu, C. Yang, J. Liu, G. Jin, J. Zhang, et al. Hollow core photonic crystal fiber surface-enhanced Raman probe [J]. Appl. Phys. Lett.,2006,89(204101):1-3.
[35]N. Yi, L. Zhang, S. Jia and J. Peng. Dispersion of square solid-core photonic bandgap fibers [J]. Opt. Express,2004,12(13):2825-2830.
[36]L. Xiao, W. Jin, M. S. Demokan. Photonic crystal fibers confining light by both index-guiding and bandgap-guiding:hybrid PCFs [J]. Opt. Express,2007,15(24): 15637-15647.
[37]P. Li, J. Zhao, X. Zhang. Nonlinear coupling in triangular triple-core photonic crystal fibers [J]. Opt. Express,2010,18(26):26828-26833.
[38]E. Treacy. Optical pulse compression with diffraction gratings [J]. IEEE J. Quantum Electron.,1969,5(9):454-458.
[39]B. E. Lemoff and C. P. J. Barty. Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses [J]. Opt. Lett.,1993,18(19):1651-1653.
[40]O. E. Martinez.3000 Times grating compressor with positive group velocity dispersion: Application to fiber compensation in 1.3-1.6μm region [J]. IEEE J. Quantum Electron., 1987, QE-23(1):59-64.
[41]J. P. Chambaret, C. L. Blanc, G. Cheriaux, P. Curley, et al. Generation of 25-TW,32-fs pulses at 10 Hz [J]. Opt. Lett.,1996,21(23):1921-1923.
[42]B. C. Stuart, M. D. Perry, J. Miller, G. Tietbohl, S. Herman, et al.125-TW Ti: sapphire/Nd:glass laser system [J]. Opt. Lett.,1997,22(4):242-244.
[43]P. S. Banks, M. D. Perry, et al. Novel all-reflective stretcher for chirped-pulse amplification of ultrashort pulses [J]. IEEE J. Quantum Electron.,2000,36(3): 268-274.
[44]R. Khare, P. K. Shukla, G. K. Mishra, et al. A novel confocal optical pulse stretcher for laser pulses [J]. Opt. Comm.,2009,282:3850-3853.
[45]L. Gruner-Nielsen, D. Jakobsen, et al. A stretcher fiber for use in fs chirped pulse Yb amplifiers [J]. Opt. Express,2010,18(4):3768-3773.
[46]张树葵,文国庆,周丕璋等.钛宝石飞秒激光的啁啾脉冲再生放大[J].强激光与粒子束,1996,8(4)：500-506.
[47]魏志义,张杰等.高效率太瓦级飞秒掺钛蓝宝石激光装置[J].中国科学,2000,30(11)：1046-1050.
[48]田金荣,孙敬华,魏志义等Offner展宽器高倍率展宽脉冲的理论与实验研究[J].物理学报,2005,54(3)：1200-1207.
[49]王逍,朱启华,林东晖等.高展宽量八通展宽器的设计制作[J].中国激光,2006,33(7)：895-898.
[50]胡婉约,王二玉,李文雪,丁良恩.适用于亚10 fs的共心衍射无像差展宽器[J].光学学报,2007,27(1)：181-186.
[51]G. P. Agrawal. Nonlinear Fiber Optics [M]. Third edition, Academic Press,2001.
[52]G. K. Wong, A. Y. Chen, S. Ha, et al. Characterization of Chromatic Dispersion in Photonic Crystal Fibers Using Scalar Modulation Instability [J]. Opt. Express,2005, 13(21):8662-8670.
[53]J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, et al. Anomalous Dispersion in Photonic Crystal Fiber [J]. Photon. Technol. Lett.,2000,12(7):807-809.
[54]J. C. Travers, J. M. Stone, A. B. Rulkov, et al. Optical pulse compression in dispersion decreasing photonic crystal fiber [J]. Opt. Express,2007,15(20):13203-13211.
[55]A. Podlipensky, P. Szarniak, N. Y. Joly, C. G. Poulton, and P. St. J. Russell. Bound soliton pairs in photonic crystal fiber [J]. Opt. Express,2007,15(4):1653-1662.
[56]T. P. Hansen, J. Broeng, S. E. B. Libori, et al. Highly birefringent index-guiding photonic crystal fibers [J]. IEEE Photon. Technol. Lett.,2001,13(6):588-590.
[57]W. Belardi, G. Bouwmans, L. Provino, M. Douay. Form-Induced Birefringence in Elliptical Hollow Photonic Crystal Fiber With Large Mode Area [J]. IEEE J. Quantum Electron.,2005,41(12):1558-1564.
[58]T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legre, et al. Experimental study of polarization properties of highly birefringent photonic crystal fibers [J]. Opt. Express, 2004,12(24):5931-5939.
[59]K. Saitoh, T. Fujisawa, T. Kirihara and M. Koshiba. Approximate empirical relations for nonlinear photonic crystal fibers [J]. Opt. Express,2006,14(14):6572-6582.
[60]K. Saitoh and M. KoshibaHighly. nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window [J]. Opt. Express,2004, 12(10):2027-2032.
[61]T. M. Monro, D. J. Richardson, et al. Holey Optical Fibers:An Efficient Modal Model [J]. J. Lightwave Technol.,1999,17(6):1093-1102.
[62]J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro. Properties of photonic crystal fiber and the effective index model [J]. J. Opt. Soc. Am. A.,1998, 15(3):748-752.
[63]M. Dems, R. Kotynski, and K. Panajotov. PlaneWave Admittance Method-a novel approach for determining the electromagnetic modes in photonic structures [J]. Opt. Express,2005,13(9):3196-3207.
[64]S. Guo, S. Albin. Simple planewave implementation for photonic crystal calculations [J]. Opt. Express,2003,11(2):167-175.
[65]T. P. White, B. T. Kuhlmey, R. C. McPhedran, et al. Multipole method for microstructured optical fibers. I. Formulation [J]. J. Opt. Soc. Am. B.,2002,19(10): 2322:2330.
[66]B. T. Kuhlmey, T. P. White, G. Renversez, et al. Multipole method for microstructured optical fibers. II. Implementation and results [J]. J. Opt. Soc. Am. B.,2002,19(10): 2331:2340.
[67]C. A. D. Francisco, B. V. Borges, M. A. Romero. A semivectorial iterative finite-difference method to model photonic crystal fibers [C]. IMOC,2001,1:407-409.
[68]Z. Zhu and T. Brown. Full-vectorial finite-difference analysis of microstructured optical fibers [J]. Opt. Express,2002,10(17):853-864.
[69]C. P. Yu and H. C. Chang. Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers [J]. Opt. Express,2004,12(25):6165-6177.
[70]M. A. R. Franco, H. T. Hattori, F. Sircilli, A. Passaro, N. M. Abe. Finite element analysis of photonic crystal fibers [C]. IMOC,2001,1:5-7.
[71]M. Koshiba, K. Saitoh. Numerical verification of degeneracy in hexagonal Photonic crystal fibers [J]. IEEE Photon. Technol. Lett.,2001,13(12):1313-1315.
[72]M. Midrio, M. P. Singh, and C. G. Someda. The space filling mode of holey fibers:an analytical vectorial solution [J]. J. Lightwave Technol.,2000,18(7):1031-1037.
[73]N. A. Mortensen. Effective area of photonic crystal fibers [J]. Opt. Express,2002, 10(7):341-348.
[74]K. Saitoh and M. Koshiba. Empirical relations for simple design of photonic crystal fibers [J]. Opt. Express,2005,13(1):267-274.
[75]L. Farr, J. C. Knight, B. J. Mangan and P. J. Roberts. Low loss photonic crystal fiber [C]. ECOC (Copenhagen,2002). Post-deadline paper PD13.
[76]L. Kuznetsova and F. W. Wise. Scaling of femtosecond Yb-doped fiber amplifiers to tens of microjoule pulse energy via nonlinear chirped pulse amplification [J]. Opt. Lett., 2007,32(18):2671-2673.