留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Femtosecond pulse compression using negative-curvature hollow-core fibers

Tao-ying YU Xue-song LIU D. Pryamikov ANDREY F. Kosolapov ALEXEY Hong-bo ZHANG Zhong-wei FAN

庾韬颖, 刘学松, ANDREYD. Pryamikov, ALEXEYF. Kosolapov, 张鸿博, 樊仲维. 负曲率空芯光纤对飞秒超短脉冲光的压缩研究[J]. 中国光学, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075
引用本文: 庾韬颖, 刘学松, ANDREYD. Pryamikov, ALEXEYF. Kosolapov, 张鸿博, 樊仲维. 负曲率空芯光纤对飞秒超短脉冲光的压缩研究[J]. 中国光学, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075
YU Tao-ying, LIU Xue-song, ANDREY D. Pryamikov, ALEXEY F. Kosolapov, ZHANG Hong-bo, FAN Zhong-wei. Femtosecond pulse compression using negative-curvature hollow-core fibers[J]. Chinese Optics, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075
Citation: YU Tao-ying, LIU Xue-song, ANDREY D. Pryamikov, ALEXEY F. Kosolapov, ZHANG Hong-bo, FAN Zhong-wei. Femtosecond pulse compression using negative-curvature hollow-core fibers[J]. Chinese Optics, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075

负曲率空芯光纤对飞秒超短脉冲光的压缩研究

doi: 10.3788/CO.20191201.0075
基金项目: 

国家自然科学基金 61605215

详细信息
    作者简介:

    庾韬颖(1989-), 男, 山西吕梁人, 博士研究生, 主要从事空芯光纤特性、超短脉冲技术和非线性光学方面的研究。E-mail:

    樊仲维(1965—),男,吉林桦甸人,研究员,博士生导师,主要从事固体激光技术与短脉冲激光技术方面的研究。E-mail:

  • 中图分类号: TP394.1;TH691.9

Femtosecond pulse compression using negative-curvature hollow-core fibers

Funds: 

National Natural Science Foundation of China 61605215

More Information
    Author Bio:

    YU Tao-ying(1989—), male, from Luliang, Shanxi, has a Ph.D. and is mainly engaged in researching the characteristics of hollow-core fibers, ultrashort pulse technology and non-linear optics.E-mail:yutaoying@aoe.ac.cn

    FAN Zhong-wei(1965—), male, from Huadian, Jilin, is a researcher and doctoral tutor who mainly engages in researching solid-state laser technology and short-pulse laser technology. E-mail:fanzhongwei@aoe.ac.cn

    Corresponding author: FAN Zhong-wei.E-mail:fanzhongwei@aoe.ac.cn
  • 摘要: 为了实现对飞秒激光器产生的超短脉冲的进一步压缩,对近年来出现的一种新型负曲率空芯光纤展开了研究,并基于该光纤对800 nm飞秒激光进行了压缩实验。首先介绍了一种圆形玻璃管包层结构的负曲率空芯光纤,通过有限元方法对光纤的损耗特性进行计算,并与实验测试结果进行对比。然后利用广义非线性薛定谔方程对脉冲在光纤中的传输进行了模拟仿真。最后利用该光纤进行了超短脉冲压缩实验,将脉冲宽度为160 fs的钛宝石飞秒激光耦合进一段充高压氩气的圆形玻璃管包层结构的负曲率空芯光纤,通过光纤内反常色散和自相位调制的共同作用,得到84 fs的输出,实现脉冲的压缩,实验结果与仿真计算一致。这种新型的负曲率空芯光纤损伤阈值高、色散、非线性系数小且灵活可调,非常适用于超快领域研究。
  • 图  1  圆形玻璃管空心光纤端面

    Figure  1.  End face of the circular tube hollow-core fiber

    图  2  光纤损耗计算结果

    Figure  2.  Fiber loss calculation results

    图  3  空芯光纤传输损耗测试结果

    Figure  3.  Experimental results of transmittance of the NC-HCF

    图  4  空芯光纤在不同气压下的二阶色散

    Figure  4.  Second-order dispersion of the hollow fiber at different pressures of argon

    图  5  广义非线性薛定谔方程对脉冲在光纤中演变的计算结果. (a)为z=0.5 m时脉冲的频谱分布; (b)为z=0.5 m时脉冲的时域分布; (c)为脉冲在0.5 m长的负曲率空芯光纤中传输时的频域分布; (d)为脉冲在0.5 m长的负曲率空芯光纤中传输时的时域分布

    Figure  5.  The calculated evolution of the ultrafast pulse in the NC-HCF with GNLSE. (a)The spectrum output of 0.5 m NC-HCF; (b)The temporary output of the 0.5 m NC-HCF; (c)The spectrum evolution of the 160 fs pulse propagating along the 0.5 m NC-HCF; (d)The temporary evolution of the 160 fs pulse propagating along the 0.5 m NC-HCF

    图  6  输出脉冲宽度随光纤长度变化

    Figure  6.  Pulse duration evolution varies with fiber length

    图  7  实验光路图

    Figure  7.  Schematic diagram of light path

    图  8  实验与计算的自相关曲线对比

    Figure  8.  Comparison of experimentally measured autocorrelation curves and calculated results

    Figure  9.  Comparison of spectral output obtained from experimental and calculated results

  • [1] PRYAMIKOV A D, BIRIUKOV A S, KOSOLAPOY A F, et al..Demonstration of a waveguide regime for a silica hollow-core microstructured optical fiber with a negative curvature of the core boundary in the spectral region >3.5μm[J].Opt.Express, 2011, 19(2):1441-1448. doi:  10.1364/OE.19.001441
    [2] WANG Y Y, COUNY F, ROBOERS P J, et al..Low loss broadband transmission in optimized core-shape Kagome hollow-core PCF[C].2010 Laser Science to Photonic Applications, San Jose, USA: CLEO, 2010: 1-2.
    [3] JAWORSKI P, YU F, MAIER R R J, et al..Picosecond and nanosecond pulse delivery through a hollow-core negative curvature fiber for micro-machining applications[J].Opt.Express, 2013, 21(19):22742-22753. doi:  10.1364/OE.21.022742
    [4] KOLYADIN A.N, ALAGASHEV G K, PRYAMIKOV A D, et al..Negative curvature hollow-core fibers:dispersion properties and femtosecond pulse delivery[J].Physics Procedia, 2015, 73:59-66. doi:  10.1016/j.phpro.2015.09.122
    [5] MICHIELETTO M, LYNGSE J K, JAKOBSEN C, et al..Hollow-core fibers for high power pulse delivery[J].Opt.Express, 2016, 24(7):7103-7119. doi:  10.1364/OE.24.007103
    [6] POLETTI F.Nested antiresonant nodeless hollow core fiber[J].Opt.Express, 2014, 22(20):23807-23828. doi:  10.1364/OE.22.023807
    [7] HABIB M S, BANG O, BACHE M.Low-loss single-mode hollow-core fiber with anisotropic anti-resonant elements[J].Opt.Express, 2016, 24(8):8429-8436. doi:  10.1364/OE.24.008429
    [8] MENG F C, LIU B W, LI Y F, et al..Low loss hollow-core antiresonant fiber with nested elliptical cladding elements[J].IEEE Photonics Journal, 2017, 9(1):1-11.
    [9] 高寿飞, 汪莹莹, 刘小璐, 等.空芯反谐振光纤及其高功率超短脉冲传输[J].中国激光, 2017, 44(2):0201012.

    GAO SH F, WANG Y Y, LIU X L, et al..Hollow-core anti-resonant fiber and its use for propagation of high power ultrafast pulse[J].Chinese Journal of Lasers, 2017, 44(2):0201012.(in Chinese)
    [10] GEHBARDT M, GAIDA C, HEUERMANN T, et al..Nonlinear pulse compression to 43 W GW-class few-cycle pulses at 2μm wavelength[J].Optics Lett., 2017, 42(20):4179-4182. doi:  10.1364/OL.42.004179
    [11] AZHAR M, WONG G K L, CHANG W, et al..Raman-free nonlinear optical effects in high pressure gas-filled hollow core PCF[J].Opt.Express, 2013, 21(4):4405-4410. doi:  10.1364/OE.21.004405
    [12] GEROME F, DUPRIEZ P, CLOWES J, et al..High power tunable femtosecond soliton source using hollow-core photonic bandgap fiber, and its use for frequency doubling[J].Opt.Express, 2008, 16(4):2381-2386. doi:  10.1364/OE.16.002381
    [13] LU J, HUANG ZH Y, WANG D, et al..Nonlinear compression of picosecond chirped pulse from thin-disk amplifier system through a gas-filled hollow-core fiber[J].Chinese Physics B, 2016, 25(12):124207. doi:  10.1088/1674-1056/25/12/124207
    [14] GEBHARDT M, GAIDA C, STUTZKI F, et al..High average power nonlinear self-compression to few-cycle pulses at 2μm wavelength in antiresonant hollow-core fiber[C].Advanced Solid State Lasers Congress, Nagoya, Japan: ASSL, 2017: ATh3A.6.
    [15] ZURCH M, SOLLAPUR R, KARTASHOV D, et al..Multi-octave supercontinuum driven by soliton explosion in dispersion-designed antiresonant hollow-core fibers[C].Lasers and Electro-Optics, San Jose, USA: CLEO, 2017: 1-2.
    [16] GONZALEZ B N, TORRES G I, ARZATE N, et al..Pulse quality analysis on soliton pulse compression and soliton self-frequency shift in a hollow-core photonic bandgap fiber[J].Opt.Express, 2013, 21(7):9132-9143. doi:  10.1364/OE.21.009132
    [17] LEGSGAARD J, ROBERTS P J.Dispersive pulse compression in hollow-core photonic bandgap fibers[J].Opt.Express, 2008, 16(13):9628-9644. doi:  10.1364/OE.16.009628
    [18] 乔自文, 高炳荣, 陈岐岱, 等.飞秒超快光谱技术及其互补使用[J].中国光学, 2014, 7(4):588-599. http://www.chineseoptics.net.cn/CN/abstract/abstract9168.shtml

    QIAO Z W, GAO B R, CHEN Q D, et al..Ultrafast spectroscopy techniques and their complementary usages[J].Chinese Optics, 2014, 7(4):588-599.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9168.shtml
    [19] EMAURY F, DUTIN C F, SARACENO C J, et al..Beam delivery and pulse compression to sub-50 fs of a mode locked thin-disk laser in a gas-filled Kagome-type HC-PCF fiber[J].Opt.Express, 2013, 21(4):4986-4994. doi:  10.1364/OE.21.004986
    [20] MAK K F, SEIDEL M, PRONIN O, et al..Compressing μJ-level pulses from 250 fs to sub-10 fs at 38-MHz repetition rate using two gas-filled hollow-core photonic crystal fiber stages[J].Opt.Lett., 2015, 40(7):1238-1241. doi:  10.1364/OL.40.001238
    [21] AGRAWAL G P.Nonlinear Fiber Optics[M].Heidelberg:Springer Berlin Heidelberg, 2000.
    [22] DUGUAY M A, KOKUBUN Y, KOCH T L, et al..Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures[J].Appl.Phys.Lett., 2002, 49(18):1592-1594.
    [23] JOHN L.光导在折射率引导光纤、多孔光纤、光子带隙光纤和纳米线中的简要定性解释[J].中国光学, 2014, 7(3):499-508.(in English) http://www.chineseoptics.net.cn/CN/abstract/abstract9155.shtml

    JOHN L.Simple qualitative explanations for light guidance in index-guiding fibres, holey fibres, photonic band-gap fibres and nanowires[J].Chinese Optics, 2014, 7(3):499-508. http://www.chineseoptics.net.cn/CN/abstract/abstract9155.shtml
    [24] POLYANSKIY M N.Refractive index database.https://refractiveindex.info[OL].
    [25] SMITH A V, DO B T.Bulk and surface laser damage of silica by picosecond and nanosecond pulses at 1064 nm[J].Appl.Opt., 2008, 47(26):4812-4832. doi:  10.1364/AO.47.004812
    [26] 王竞, 李健中, 温伟峰, 等.利用自相关方法实现光脉冲时间延迟精确测量[J].中国光学, 2015, 8(2):270-276. http://html.rhhz.net/ZGGX/html/gx20150214.htm

    WANG J, LI J ZH, WEN W F, et al..Precisely measuring for optical pulse time delay using autocorrelation[J].Chinese Optics, 2015, 8(2):270-276.(in Chinese) http://html.rhhz.net/ZGGX/html/gx20150214.htm
    [27] 陈雪坤, 张璐, 吴志勇.空间激光与单模光纤和光子晶体光纤的耦合效率[J].中国光学, 2013, 6(2):208-215. http://www.chineseoptics.net.cn/CN/abstract/abstract8891.shtml

    CHEN X K, ZHANG L, WU ZH Y.Coupling efficiency of free-space laser coupling into single mode fiber and photonic crystal fiber[J].Chinese Optics, 2013, 6(2):208-215.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract8891.shtml
  • [1] Jun-kai SHI, Guo-ming WANG, Rong-yi JI, Wei-hu ZHOU.  Compact dual-wavelength continuous-wave Er-doped fiber laser . 中国光学, 2019, 12(4): 810-819. doi: 10.3788/CO.20191204.0810
    [2] Chi WANG, Bin KUANG, Jian-mei SUN, Jun ZHU, Shu-bo BI, Ying CAI, Ying-jie YU.  Research progress on ultra-small self-focusing optical fiber probe . 中国光学, 2018, 11(6): 875-888. doi: 10.3788/CO.20181106.0875
    [3] Fang-xi SONG, Wei-dong MENG, Yan XIA, Yan CHEN, Xiao-yun PU.  Measuring liquid-phase diffusion coefficient of aqueous sucrose solution using double liquid-core cylindrical lens . 中国光学, 2018, 11(4): 630-643. doi: 10.3788/CO.20181104.0630
    [4] Qiu-shun LI, Lei CAI, Yao-hong MA, Jun-hui YANG, Yan YANG, Qing-jun MENG, Jian-guo SHI.  Research progress of biosensors based on long period fiber grating . 中国光学, 2018, 11(3): 475-502. doi: 10.3788/CO.20181103.0475
    [5] Tian-qi LI, Xiao-jie MAO, Jian LEI, Guo-jiang BI, Dong-sheng JIANG.  Analysis and comparison of solid-state lasers and fiber lasers on the coupling of rod-type photonic crystal fiber . 中国光学, 2018, 11(6): 958-973. doi: 10.3788/CO.20181106.0958
    [6] Chen LI, Razvan STOIAN, Guang-hua CHENG.  Laser-induced periodic surface structures with ultrashort laser pulse . 中国光学, 2018, 11(1): 1-17. doi: 10.3788/CO.20181101.0001
  • 加载中
图(9)
计量
  • 文章访问数:  654
  • HTML全文浏览量:  135
  • PDF下载量:  171
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-03-05
  • 修回日期:  2018-03-16
  • 刊出日期:  2019-02-01

Femtosecond pulse compression using negative-curvature hollow-core fibers

doi: 10.3788/CO.20191201.0075
    基金项目:

    国家自然科学基金 61605215

    作者简介:

    庾韬颖(1989-), 男, 山西吕梁人, 博士研究生, 主要从事空芯光纤特性、超短脉冲技术和非线性光学方面的研究。E-mail:

    樊仲维(1965—),男,吉林桦甸人,研究员,博士生导师,主要从事固体激光技术与短脉冲激光技术方面的研究。E-mail:

    通讯作者: FAN Zhong-wei.E-mail:fanzhongwei@aoe.ac.cn
  • 中图分类号: TP394.1;TH691.9

摘要: 为了实现对飞秒激光器产生的超短脉冲的进一步压缩,对近年来出现的一种新型负曲率空芯光纤展开了研究,并基于该光纤对800 nm飞秒激光进行了压缩实验。首先介绍了一种圆形玻璃管包层结构的负曲率空芯光纤,通过有限元方法对光纤的损耗特性进行计算,并与实验测试结果进行对比。然后利用广义非线性薛定谔方程对脉冲在光纤中的传输进行了模拟仿真。最后利用该光纤进行了超短脉冲压缩实验,将脉冲宽度为160 fs的钛宝石飞秒激光耦合进一段充高压氩气的圆形玻璃管包层结构的负曲率空芯光纤,通过光纤内反常色散和自相位调制的共同作用,得到84 fs的输出,实现脉冲的压缩,实验结果与仿真计算一致。这种新型的负曲率空芯光纤损伤阈值高、色散、非线性系数小且灵活可调,非常适用于超快领域研究。

English Abstract

庾韬颖, 刘学松, ANDREYD. Pryamikov, ALEXEYF. Kosolapov, 张鸿博, 樊仲维. 负曲率空芯光纤对飞秒超短脉冲光的压缩研究[J]. 中国光学, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075
引用本文: 庾韬颖, 刘学松, ANDREYD. Pryamikov, ALEXEYF. Kosolapov, 张鸿博, 樊仲维. 负曲率空芯光纤对飞秒超短脉冲光的压缩研究[J]. 中国光学, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075
YU Tao-ying, LIU Xue-song, ANDREY D. Pryamikov, ALEXEY F. Kosolapov, ZHANG Hong-bo, FAN Zhong-wei. Femtosecond pulse compression using negative-curvature hollow-core fibers[J]. Chinese Optics, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075
Citation: YU Tao-ying, LIU Xue-song, ANDREY D. Pryamikov, ALEXEY F. Kosolapov, ZHANG Hong-bo, FAN Zhong-wei. Femtosecond pulse compression using negative-curvature hollow-core fibers[J]. Chinese Optics, 2019, 12(1): 75-87. doi: 10.3788/CO.20191201.0075
    • Hollow-core microstructured fibers provide excellent media for laser and gas interaction. They have smaller dispersion and nonlinear coefficients and higher damage thresholds than solid fibers. They can be easily adjusted by modifying the used gas types and pressure. Since various parameters of the fiber are controllable, the hollow-core microstructure fiber has been a research hotspot in optics since its introduction. Negative-curvature Hollow-core Fiber(NC-HCF) is a new type of hollow-core microstructured fiber[1] that has emerged in recent years. It is so named for the structural characteristics of the reverse-bending core wall. The earliest appearance of this type of fiber can be traced back to 2010[2] when researchers used a series of theoretical and experimental research[3-5] to conclude that a fiber exhibits low loss characteristics when the curvature of the core wall of the hollow-core Kagome fiber is negative. A variety of new structures have since been proposed, such as nested structures[6], elliptical glass tube structures[7], nested elliptical structures[8], etc.. Compared with Kagome fibers, negative-curvature hollow-core fibers have the advantages of simpler structure, easier fabrication and lower transmission loss, in addition to a wide transmission bandwidth, flexibility and adjustable dispersion and nonlinear coefficients. Therefore, this type of fiber is very suitable for high-energy ultrashort pulse transmission[9], ultrashort pulse compression[10-14], supercontinuum[15], stimulated Raman scattering[16], dispersion wavegeneration[17], etc. The width of the transmission window is sufficient to support compression of pulses to the order of few-cycle.

      In the field of ultrafast applications [18], such as attosecond science, ultrafast chemistry, ultrafast biology, surface science, etc., femtosecond optics are the basis of research so pulse compression technology has always been a research hotspot. The traditional method of compressing pulses is to first broaden the spectrum and then compress the pulse. First, in a nonlinear material, such as a silica fiber or a crystal, the self-phase modulation of the material is used to broaden the spectrum, and then the dispersion compensation component, such as a prism pairs or grating pairs are used. The pulse is then compressed. However, the damage threshold of silica fiber in this scheme is often in the order of MW, which limits the peak power of the pulse. Therefore, a compression method using hollow glass tubes is proposed. In previous studies, hollow glass tubes often have a large inner diameter(~200 μm) to reduce the loss of light during transmission. In such cases, only an injected pulse whose power exceeds GW can effectively perform spectral broadening. For pulses in the order of hundreds of femtoseconds, it is necessary to obtain more than one hundred microjoules of energy to satisfy this condition. With the introduction of new hollow-core fiber, such as Kagome and the negative-curvature hollow-core fiber, it could achieve smaller core diameter and loss of fiber simultaneously. The reduced transmission loss of the fiber allows for the transmission of femtosecond pulses at small core diameters, resulting in extremely high peak power densities and allowing for sufficient spectral broadening of pulses in the MW to GW range. Therefore, anti-resonant hollow-core fibers including Kagome have been extensively studied in pulse compression. In 2016, F. Emaury et al. [19] used Kagome to compress an 860 fs laser generated by a Yb:YAG to 48 fs using the traditional self-phase modulation spectral broadening grating pair dispersion compensation structure. In 2015, K. F. Mak et al. used a soliton self-compression method to compress a 21 fs pulse to 9.1 fs in a Kagome fiber filled with high-pressure Argon[20].

      At present, femtosecond pulses compression with hollow-core fiber is mostly based on Kagome structure[21]. In this paper, a new type of circular tube cladding NC-HCF is used to carry out experimental research on femtosecond pulse compression. We have also tried to extend the application of fiber-based femtosecond pulse compression. A 160 fs Ti:Sapphire laser is used to couple into the negative-curvature hollow-core fiber with high-pressure Argon. The high-order soliton self-compression effect is used to compress the pulse to 84 fs. The numerical simulation is carried out according to the generalized nonlinear Schrödinger equation(GNLSE). The calculated results are consistent with the experimental results.

    • Fig. 1 is a screenshot of the negative-curvature hollow-core fiber end face of the circular tube cladding used in the experiment. The fiber is surrounded by 6 uniformly distributed circular tubes with a core diameter of 34.4 μm and outer diameter of 100 μm. The cladding tube has a diameter of 16.25 μm and a wall thickness of 0.48 μm. Fig. 2 shows the calculation results of the transmission loss of the fiber using the finite element method, where significantly high levels of loss can be seen around 500 nm and around 1 μm. Fig. 3 shows the transmission test results for a 10-meter long fiber. The white light source is coupled into the fiber and the output spectrum of the fiber is measured using a spectrometer with a transmittance of -70 dB at 800 nm. Comparing Fig. 2 and Fig. 3, the high loss wavelength range is presented in the calculated results of Fig. 2. These low transmission levels are also exhibited in the test results shown in Fig. 3. The test results are consistent with the theoretically calculated results. According to the calculation, at 800 nm, the transmission loss of the fiber is as low as 0.046 dB/m.

      图  1  圆形玻璃管空心光纤端面

      Figure 1.  End face of the circular tube hollow-core fiber

      图  2  光纤损耗计算结果

      Figure 2.  Fiber loss calculation results

      图  3  空芯光纤传输损耗测试结果

      Figure 3.  Experimental results of transmittance of the NC-HCF

      The light guiding properties of negative-curvature hollow-core fibers can be explained according to the ARROW theory[22], which is different from the total internal reflection model of the traditional refractive step-index type fiber[23]. The NC-HCF achieves the low loss, nearly fundamental mode transmission characteristics through the anti-resonant condition of the cladding wall thickness and the suppression of the reverse coupling between the core fundamental mode and cladding mode. The high transmission loss of the fiber shown in Fig. 2 can be regarded as the resonance loss of the cladding wall, therefore the wavelength range between the loss bands is the transmission band of the fiber. The loss can be estimated according to formula (1). When the wavelength satisfies the following conditions, the fiber is in high loss states:

      (1)

      Where t is the thickness of the tube and n is the refractive index of the fused silica. The fiber wall thickness used herein is 0.48 μm. When m=1, the resonance wavelength can be calculated using Equation 1 and is found to be 1.008 μm, which is consistent with the results shown in Fig. 2 and Fig. 3.

      The exact transmission characteristics of the fiber need to be calculated according to the finite element method, which requires the refractive index of the gas in the fused silica and fiber at different wavelengths. According to the Sellmeier equation[24], the refractive index distribution of fused silica is:

      (2)

      The Sellmeier coefficients, Bi is0.696 166 3, 0.407 942 6, 0.897 479 4, respectively, and Ci is 4.679 148 26×10-3 μm2, 1.351 206 31×10-2 μm2 and 97.934 002 5 μm2, respectively. The refractive index of the gas filled in the fiber is distributed by wavelength:

      (3)

      Where p0=0.1 MPa and T0=273 K. When calculating the dispersion of the fiber, it is necessary to comprehensively consider the influence of the difference in the refractive index of the filled gas and the fused silica. The propagation constant of the fiber and the dispersion of each order can be approximated using the following formula:

      (4)
      (5)

      The above formula defines that a is the radius of the core and unm=2.045 when the fundamental mode is transmitted in the fiber. For the used fiber structure a=34.4 μm, when the Argon is filled in the fiber. The second-order dispersion of the hollow fiber at different pressures is shown in Fig. 4. As the air pressure increases, the ZDW of the fiber moves toward longer wavelengths. When the air pressure is p=0.8 MPa, the second-order dispersion coefficient at 800 nm is -0.306 783 ps2/km. Adjusting the gas pressure filled in the fiber can significantly change the second-order dispersion of the fiber, especially at positions farther away from the ZDW. For example, with shorter wavelengths, the pressure has a great influence on dispersion. Regarding to the dispersion of the gas-filled fiber, which is affected by the waveguide structure and the gas used, while the nonlinear coefficient is basically only affected by the gas type and the fiber diameter. The waveguide structure does not affect the nonlinear coefficient.

      图  4  空芯光纤在不同气压下的二阶色散

      Figure 4.  Second-order dispersion of the hollow fiber at different pressures of argon

      The nonlinear coefficient is calculated as follows.

      (6)
    • The dispersion and nonlinear coefficients of the fiber are obtained by numerical simulation, and the transmission of the pulse in the fiber is numerically calculated. The GNLSE is used for the simulation calculation.

      (7)

      where A is the pulse envelope, z is the transmission distance, α is the loss of the fiber, and βn is the n-order dispersion of the fiber where only the 2nd and 3rd order dispersions are considered and γ is the nonlinear coefficient. In the right side of the formula, the two variables represent self-phase modulation and self-steepening, respectively. Since the nonlinear medium in this experiment is Ar gas, which is an atomic gas, the influence of stimulated Raman scattering on the pulse can be ignored. The Raman item is ignored in the equation, causing its form to be different from that found in other literature[25]. The temporal waveform of the initial pulse coupled into the fiber is assumed to be hyperbolic secant type. The pulse form is as follows:

      (8)

      P0 is the peak power of the pulse, and C is the chirp parameter. By changing the value of the chirp parameter C, the pulse width 2t0 and the spectral width can be controlled.

      According to the initial conditions described above, the GNLSE is solved using the split-step Fourier algorithm. The corresponding calculated results are shown in Fig. 5. Fig. 5(c) shows the evolution of the pulse spectrum. It is shown that as the transmission distance increases, the spectrum broadens significantly. Since the fiber is filled with inert gas, the nonlinear effect only considers the self-phase modulation and the self-steepening effect. No Raman scattering occurs so the spectrum does not show a significant shift. Fig. 5(a) shows the spectral distribution at z=0.5 m, which clearly demonstrates that the spectrum broadens greatly. Fig. 5(d) shows the temporal evolution with the transmission distance. It is shown that as the transmission distance increases, the pulse width decreases and the peak power also increases. At the same time, as the distance travelled increases, the pulse has a delay, which causes the soliton to slow down. This is a result of third-order dispersion[26]. Fig. 5(b) shows temporal distribution at z=0.5 m. It can be seen that there is obvious splitting of the soliton, which is the combined effect of the third-order dispersion and the self-steepening effect on high-order solitons, causing high-order soliton fission. At this point, it is impossible to evaluate the pulse duration.

      图  5  广义非线性薛定谔方程对脉冲在光纤中演变的计算结果. (a)为z=0.5 m时脉冲的频谱分布; (b)为z=0.5 m时脉冲的时域分布; (c)为脉冲在0.5 m长的负曲率空芯光纤中传输时的频域分布; (d)为脉冲在0.5 m长的负曲率空芯光纤中传输时的时域分布

      Figure 5.  The calculated evolution of the ultrafast pulse in the NC-HCF with GNLSE. (a)The spectrum output of 0.5 m NC-HCF; (b)The temporary output of the 0.5 m NC-HCF; (c)The spectrum evolution of the 160 fs pulse propagating along the 0.5 m NC-HCF; (d)The temporary evolution of the 160 fs pulse propagating along the 0.5 m NC-HCF

      Fig. 6 is a graph showing the output pulse width as a function of the transmission distance. It can be seen that, as the length of the fiber increases, the pulse is compressed gradually. However, according to the calculated results in Fig. 5, when the distance reaches about 0.5 m, soliton splits and the pulse width cannot be evaluated. Therefore, a fiber of 0.4 m in length was used in the experiment.

      图  6  输出脉冲宽度随光纤长度变化

      Figure 6.  Pulse duration evolution varies with fiber length

    • Furthermore, the fiber was used to compress the pulse output of the Ti:Sapphire femtosecond laser. Fig. 7 is a schematic diagram of the experimental device. The light source is a Ti:Sapphire amplifier with an output pulse width of 160 fs. The central wavelength is 800 nm while the spectral width is about 8.19 nm, its repetition frequency is 1 kHz and maximum output power is 460 mW and its spot size is about 7 mm. The HWP is a half-wave plate and the TFP is a polarizing plate. Rotating half-wave plate can continuously adjust the power coupling into the fiber. The ends of the fiber are placed in the air chamber and the fiber is fixed by the V-shaped groove. The focused laser light is then coupled into the fiber in the air chamber. Both L1 and L2 are aspherical lenses(f=50.8 mm) and the spot diameter after focusing is about 33 μm. After measurement, when 1 μJ energy is coupled into a negative-curvature hollow fiber with a length of 40 cm, we can obtain 550-nJ output energy with a coupling efficiency of 55%[27]. After the output beam was collimated with L2, the fiber output was tested using APE′s PulseCheck 50 autocorrelator.

      图  7  实验光路图

      Figure 7.  Schematic diagram of light path

      The soliton effect compression of ultrashort pulse in hollow-core fiber mainly relays on self-phase modulation to broaden the spectrum of a coupled pulse, then uses anomalous dispersion to achieve compression. When the pressure of the Argon is relatively low, the nonlinear coefficient becomes small and no significant pulse compression or spectral broadening can be observed. In order to increase the non-linear coefficient of the medium, the pressure of the chamber is adjusted to 0.8 MPa and the pulse energy coupled into the fiber is adjusted as 6.5 μJ by rotating the half-wave plate. At this time, the coupling efficiency decreases to less than 50% and the output pulse energy becomes approximately 3 μJ. This may be due to the increase of input energy, which causes the fiber to meet the conditions of dispersion wave generation, and the wavelength generated is located in the high loss band of the fiber(below 500 nm), eventually causing energy to be lost. The pulse width output at this time is about 84 fs.

      Under these conditions, the calculated results using split-step Fourier method are consistent with the experimental results. Fig. 8 is a comparison of the experimental measured autocorrelation curve and the calculated result, where the curve 2 is the experimental result and the curve 1 is the calculated result. It can be seen from the comparison that the experimental results are fundamentally consistent with the calculated results.

      图  8  实验与计算的自相关曲线对比

      Figure 8.  Comparison of experimentally measured autocorrelation curves and calculated results

      Fig. 9 shows the comparison of the spectral output. The curve 1 is the data recorded during the experiment while the curve 2 is the calculated result of GNLSE. The experimental and calculated spectral widths are roughly equal, but the curve depicting measured result is higher than the calculated value near 800 nm. This may be caused by a small portion of the residual incident light not being effectively coupled into the core but instead transported through the cladding. This portion of the incident light is quite weak, so the self-phase modulation hardly play a role and cannot effectively form spectral broadening; while the dispersion value of the optical fiber is small, the compression pulse and the residual incident pulse are difficult to completely separate within 40 cm. Besides, the fiber length is relatively short, resulting in that the residual incident pulse cannot be completely lost. It is outputted in overlap with the compressed pulse so the frequency domain is embodied as a slightly higher intensity at approximately 800 nm. There′s a pedestal or sub-pulse near the main compressed pulse in the time domain, which also explains the pre-pulse measured in Fig. 8. In general, the experimental results are consistent with the GNLSE calculations. According to the GNLSE simulation, the GNLSE could be used to guide the pulse compression evolution from hundreds of femtoseconds to tens of femtoseconds in NC-HCF. When the pulse width continues to drop several optical cycles, the basis of the GNLSE and the slow varying envelope approximation fail, causing the Unidirectional Pulse Propagation Equation(UPPE) to be necessary for calculation. In general, negative-curvature hollow-core fibers are excellent medium to compressing the high peak power femtosecond pulse. It could be achieved that compression of the high power and large energy ultrashort pulse within a short NC-HCF. In theory, such a fiber with a bandwidth of several hundred nanometers could support the compression of pulses down to a single optical cycle.

      Figure 9.  Comparison of spectral output obtained from experimental and calculated results

    • In this paper, a type of negative-curvature hollow-core fiber that developed in recent years were investigated. The loss, dispersion, and non-linear characteristics of the fiber were theoretically calculated and tested. In the case of filling 0.8 MPa Argon, the transmission of femtosecond pulses in the fiber was calculated and correspondingly studied using the GNLSE equation. An 800 nm ultrashort pulse of 160 fs was compressed by the soliton self-compression effect, achieving a pulse of 84 fs. The experimental results were consistent with the corresponding theoretical calculations. The characteristics of negative-curvature hollow-core fibers give it great potential in the fields of pulse transmission and compression. By adjusting the gas pressure and gas type which might have a higher nonlinear coefficient, it is thought that the pulse could be compressed down to a few optical cycles.

      ——中文对照版——

    • 空芯微结构光纤为激光与气体相互作用提供了优良的载体, 其相比实芯光纤具有更小的色散和非线性系数以及更高的损坏阈值, 同时通过调节气体的种类、气压等参数可以方便地控制光纤的各项参数。因此空芯微结构光纤自被提出起就一直是光学界的研究热点。负曲率空芯光纤(Negative Curvature Hollow Core Fiber, NC-HCF)是近年来出现的一种新型空芯微结构光纤[1], 因其反向弯曲的纤芯壁的结构特点而得名。该类型光纤最早出现的时间可以追溯到2010年[2], 研究人员发现当空芯Kagome光纤的纤芯壁曲率为负时, 光纤呈现出低损耗特性, 之后针对这一问题开展了一系列的理论和实验研究[3-5], 并提出了多种新型结构, 如嵌套结构[6]、椭圆形玻璃管结构[7]、嵌套椭圆形结构[8]等。相比Kagome光纤, 负曲率空芯光纤除了具有传输带宽宽、色散灵活可调、非线性系数易于改变外, 还具有结构简单, 更容易制作以及传输损耗更低等优点。因此这类光纤非常适用于高能量超短脉冲传输[9], 超短脉冲压缩[10-14]、超连续谱[15]、受激拉曼散射[16]以及色散波[17]产生等。其传输窗口之宽, 足以支撑将脉冲压缩至周期量级。

      在超快应用[18]领域, 诸如阿秒科学、超快化学、超快生物学、表面科学等学科中, 飞秒脉冲是研究的基础, 因此脉冲压缩技术一直以来都是研究热点。传统的压缩脉冲的方法为先展宽光谱后压缩脉冲, 首先在一块非线性材料, 如石英光纤或者晶体中, 利用材料的自相位调制展宽光谱, 再利用色散补偿元件如棱镜对、光栅对等对脉冲进行压缩。然而这种方案中的石英光纤的损伤阈值往往在MW量级, 从而限制了压缩脉冲的峰值功率。因此基于空心玻璃管的压缩方法随之被提出。在之前的研究中, 为了减小光的传输损耗, 空心玻璃管内径往往很大(~200 μm)。这种情况下只有注入脉冲的峰值功率达到GW以上, 才能形成有效的光谱展宽, 对于百飞秒量级的脉冲, 满足此条件需要百微焦以上能量。随着新型空芯光纤结构, 如Kagome、负曲率空芯光纤等的提出。通过合理设计光纤微结构, 在减小纤芯直径的同时, 通过波导结构的设计, 极大地减小光纤的传输损耗, 允许在小芯径条件下传输飞秒脉冲, 获得极高的峰值功率密度, 在MW到GW范围内的脉冲可以获得足够的光谱展宽。因此包括Kagome在内的反谐振空芯光纤在脉冲压缩方面得到了广泛的研究。在传统的自相位调制展宽光谱-光栅对补偿色散结构的基础上, 2016年, F.Emaury等人[19]利用Kagome将Yb: YAG激光器产生的860 fs激光压缩至48 fs。2015年, K.F.Mak等人在充高压Ar的Kagome光纤中, 利用孤子自压缩的方式将21 fs脉冲压缩至9.1 fs[20]

      目前使用空芯光纤压缩飞秒脉冲[21], 多是基于Kagome光纤。本文利用一种新型圆形玻璃管包层的负曲率空芯光纤, 开展飞秒脉冲压缩的实验研究, 探索新结构光纤在飞秒脉冲压缩方向的应用, 拓展基于光纤的飞秒脉冲压缩的方法。利用160 fs的钛宝石激光耦合进充高压氩气的负曲率空芯光纤, 利用高阶孤子自压缩效应将脉冲压缩到84 fs。根据广义非线性薛定谔方程进行了数值模拟, 计算结果与实验结果取得一致。

    • 图 1为本实验采用的圆形玻璃管包层结构的负曲率空芯光纤端面截图, 光纤由6根均匀分布的圆形玻璃管构成, 纤芯直径为34.4 μm, 光纤外径为100 μm, 包层中玻璃管直径为16.25 μm, 壁厚为0.48 μm。图 2为使用有限元方法对光纤的传输损耗进行计算的结果, 其中在500 nm附近和1 μm附近, 可以看到明显的高损耗带。图 3为10 m长光纤的透过率测试结果, 将白光光源耦合到光纤中, 使用光谱仪测试光纤的输出光谱, 其中在800 nm处透过率为-70 dB。对比图 2图 3, 在图 2的计算结果中呈现高损耗的波长范围, 在图 3的测试中也呈现了低透过特性, 测试结果与理论计算结果一致。根据计算在800 nm处, 光纤的传输损耗低达0.046 dB/m。

      负曲率空芯光纤的导光特性可以根据ARROW理论[22]进行解释, 与传统的折射率阶跃型光纤通过全内反射[23]方式传导光场不同, NC-HCF通过包层玻璃管壁厚的反谐振条件以及抑制纤芯基模与包层模式之间反向耦合来维持光纤的低损耗、少模的传输特性。光纤的高损耗区域可以看做是包层玻璃管壁的谐振损耗, 而损耗带之间的波长范围就是光纤的传输带, 损耗带可以根据公式(1)进行推测, 当波长满足下面条件时光纤的损耗极大:

      (1)

      其中, t为玻璃管厚度, n为熔石英的折射率。本文中采用的光纤壁厚为0.48 μm, 根据公式(1)计算, 当m=1时, 谐振波长根据计算为1.008 μm, 这与图 2图 3的结果保持的一致。

      光纤准确的传输特性需要根据有限元方法进行计算, 需要提供熔石英和光纤中气体在不同波长下的折射率。根据Sellmeier方程[24]可知, 熔石英的折射率分布为:

      (2)

      其中, Sellmeier系数为:Bi分别是0.696 166 3、0.407 942 6和0.897 479 4, Ci分别是4.679 148 26×10-3 μm2、1.351 206 31×10-2 μm2和97.934 002 5μm2。光纤中充入气体的折射率随波长的分布则为:

      (3)

      其中, p0=0.1 MPa, T0 =273 K。对光纤的色散进行计算时, 要综合考虑充入气体和熔石英两者折射率不同的影响, 光纤的传播常数和各阶色散可以近似按照下式进行计算:

      (4)
      (5)

      其中, a为纤芯的半径, 而当光纤中传输的为基模时, unm=2.045。按照光纤结构a=34.4 μm, 当光纤中填充的气体为Ar时, 不同气压下的二阶色散计算结果如图 4所示。随着气压的增大光纤的零色散波长(ZDW)向长波长方向移动, 当气压p=0.8 MPa时, 800 nm处二阶色散系数为-0.306 783 ps2/km。调节光纤内充入的气体压力可以显著改变光纤的二阶色散, 尤其在远离零色散波长的位置, 如短波长方向, 气压对色散的影响很大。充气光纤的色散同时受到波导结构和填充气体的影响, 而非线性系数则基本上只受到气体种类和光纤直径的影响, 波导结构对非线性系数不造成影响, 非线性系数计算公式如下。

      (6)
    • 通过数值模拟得到光纤的色散和非线性系数, 对脉冲在光纤中的传输进行数值计算, 采用广义非线性薛定谔方程GNLSE进行模拟计算。

      (7)

      式中, A为脉冲包络, z为传输距离, α为光纤的损耗, βn为光纤的n阶色散, 本文只考虑2阶和3阶色散, γ为非线性系数, 右式中的两项分别代表自相位调制、自陡峭效应。由于本实验的非线性介质是惰性气体Ar, 为原子气体, 故可以不考虑受激拉曼散射对脉冲的影响, 方程中忽略拉曼项, 故形式与其他文献有所区别[25]。耦合进光纤的初始脉冲的时间波形假设为双曲正割型, 脉冲形式如下:

      (8)

      其中, P0是脉冲的峰值功率, C是啁啾参量, 通过改变啁啾参量C的值, 可以改变脉冲宽度2t0和光谱宽度。

      按照前文所述的初始条件, 使用分步傅立叶算法对GNLSE进行求解, 计算结果如图 5所示。图 5(c)为脉冲光谱的演变结果。可见随着传输距离的增加, 光谱发生明显的展宽, 由于光纤中充入的是惰性气体, 非线性效应只考虑自相位调制和自陡峭效应, 并没有拉曼自频移产生, 因此光谱并没有出现明显的偏移。图 5(a)z=0.5 m处的光谱分布, 可以看到光谱得到了极大的展宽。图 5(d)为脉冲时间波形随传输距离的演变结果, 可见随着传输距离的增大, 脉冲宽度随之减小, 峰值功率提高。同时随着传输距离的增大, 脉冲存在延迟现象, 使得孤子慢下来, 这是受三阶色散的影响[26]图 5(b)z=0.5 m处的时间波形, 可以看到存在明显的孤子分裂现象, 这是三阶色散、自陡峭效应对高阶孤子的联合作用, 将高阶孤子分裂成了若干个基阶孤子。此时就无法评估宽度的变化了。

      图 6为输出脉冲宽度随着传输距离变化的曲线, 可见随着光纤长度的增加, 脉冲被压缩到更窄的水平, 但是按照图 5的计算结果, 当到达约0.5 m左右时, 孤子发生了分裂, 无法评估脉冲宽度, 因此在实验中采用了0.4 m长的光纤。

    • 进一步利用该光纤对钛宝石飞秒激光器输出的脉冲进行了压缩实验, 图 7为本实验装置图。光源采用的是光谱物理公司的钛宝石飞秒放大器, 输出的脉冲宽度为160 fs, 中心波长为800 nm, 光谱宽度约为8.19 nm, 重复频率为1 kHz, 最大输出功率为460 mW, 光斑大小约为7 mm。HWP为半波片, TFP为偏振片, 通过旋转半波片可以连续可调地控制耦合进空芯光纤的功率大小。光纤两端密封放置在气室内, 使用V型槽固定光纤, 聚焦的激光通过窗口片进入气室耦合进光纤。L1和L2均为非球面透镜(f=50.8 mm), 聚焦后的光斑直径约为33 μm。经过测量, 将1 μJ能量耦合进长度为40 cm的负曲率空芯光纤中, 输出能量为550 nJ, 耦合效率为55%[27]。在光纤的输出端用L2将输出光束进行准直后使用APE公司的PulseCheck 50型号的自相关仪对光纤输出进行测试。

      基于孤子自压缩的空芯光纤对超短脉冲进行压缩主要依靠气体的自相位调制对耦合脉冲进行光谱展宽, 利用反常色散对光谱展宽后的脉冲进行压缩。当充入系统的氩气的气压比较小的时候, 非线性系数较低, 并未观察到明显的脉冲压缩或者光谱展宽现象。为了增大介质的非线性系数, 增加气室内的压强到0.8 MPa, 调节半波片使耦合进空芯光纤的激光能量大小为6.5 μJ, 此时耦合效率下降不足50%, 输出脉冲能量约为3 μJ。这可能是由于输入能量上升, 导致光纤满足色散波产生的条件, 在光纤的高损耗带范围内(低于500 nm)产生色散波, 以至于损失一部分能量导致的。此时输出的脉冲宽度约为84 fs左右。

      在该条件下, 利用分步傅立叶法求解GNLSE方程对脉冲的演变进行仿真, 计算结果和实验测量的结果基本一致。图 8为用自相关仪测得压缩后的自相关曲线和计算结果的对比, 其中曲线2为实验结果, 曲线1为计算结果。通过对比可以看出实验结果与计算结果基本保持一致。

      图 9为光谱输出的实验结果与计算结果对比图, 曲线1为实验中测得的数据, 曲线2为GNLSE的计算结果, 实验和计算的光谱宽度大致相等, 但是测量曲线中在800 nm附近的值要高于计算值。这极有可能是未耦合进入纤芯而在包层中传输的小部分残余的入射光场所造成的。这部分入射光能量较小, 因此自相位调制比较弱而不能很好地形成光谱展宽; 而光纤的色散值较小, 压缩脉冲和残余的入射脉冲难以在短短40 cm内完全分离; 又因为光纤长度比较短, 残余入射脉冲不能完全损耗掉而与压缩脉冲重叠在一起输出。因此频域上体现为800 nm附近强度略高, 时域上体现为压缩脉冲的基座或子脉冲。这也解释了图 8中测得的自相关曲线中脉冲前沿有预脉冲。总体来说实验结果与GNLSE计算结果一致, 根据GNLSE仿真计算可以指导百飞秒到数十飞秒的超短脉冲在充惰性气体负曲率空芯光纤中的传输。当脉冲宽度继续下降到几个光学周期的程度, GNLSE成立的基础——慢变振幅近似就失效了, 必须采用单向脉冲传输方程(Unidirectional Pulse Propagation Equation, UPPE)来求解。总的来说, 负曲率空芯光纤是一种对飞秒脉冲压缩的优良载体, 可以用较短的光纤实现对大能量、高峰值功率的超短脉冲的压缩, 其宽达几百nm的导通带宽, 理论上可以支撑将脉冲压缩至单个光学周期。

    • 本文研究了近年来兴起的一种圆形玻璃管包层结构负曲率空芯光纤。理论计算并测试了该光纤的损耗、色散、非线性特性。在充入0.8 MPa氩气的情况下, 用GNLSE方程对飞秒脉冲在该光纤中的传输进行了计算和相应的实验研究。160 fs的800 nm的超短脉冲通过孤子自压缩效应压缩到了84 fs, 实验结果和理论计算取得一致。而负曲率空芯光纤的特点决定了其在脉冲传输、压缩等领域有极大的发展潜力。通过调节气体压力、选择充入非线性系数更高的气体, 预计能将脉冲压缩到单个光学周期的水平。

参考文献 (27)

目录

    /

    返回文章
    返回