光纤中超高斯型脉冲传输特性的研究
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摘要
本文首先介绍了光纤通信技术的发展和现状及光脉冲在光纤的传输理论,然后对MNLS方程引入超高斯型脉冲的尝试解,并采用变分法,推导出一般情况、无微扰、小损耗微扰、高阶色散微扰、五阶非线性微扰、耦合相互作用微扰等六种不同情况下超高斯型脉冲各参数(振幅A、脉宽a、啁啾b、频率ω、中心位置ξ、相位φ)随传输距离z的演化方程组;在此基础上,讨论了各参数随传输距离z的演化特性,并且得到了无微扰、小损耗微扰、高阶色散微扰、五阶非线性及耦合相互作用微扰五种情况下的参数ω、ξ、a、b的解析解;重点讨论了无微扰、高阶色散微扰、五阶非线性微扰三种情况下,初始啁啾对脉宽的影响及高阶色散系数β和五阶非线性系数γ对脉宽的影响,作出了相应的曲线图形,并得到以下结论:
(1)各种情况下,初始啁啾对光纤中传输的超高斯型脉冲均有影响:初始啁啾b0为负值时,初期脉冲有一窄化过程,且其绝对值越大,脉冲宽度的振荡越慢而振荡幅度越大.脉冲前后沿越锐,脉冲宽度的振荡越慢而振荡幅度越大.
(2)除耦合相互作用外,各种情况下,振幅A和脉宽a满足绝热条件,频率ω、啁啾b和中心位置ξ间存在一约束关系式,脉宽a和啁啾b间也存在一约束关系式。
(3)小损耗只对相位φ产生影响,它导致脉冲峰值功率的衰减;除对ξ无影响外,前后沿锐度m对其他脉冲参数有直接或间接的影响。
(4)高阶色散、五阶非线性和耦合相互作用微扰均会激起啁啾;
(5)高阶色散微扰和脉冲前后沿锐度对参数A、a、b、ω、ξ、φ均有影响。高阶色散使超高斯脉冲展宽。
(6)五阶非线性微扰作用下,五阶非线性、初始啁啾和脉冲前后沿锐度对参数A、a、b、ω、φ均有影响,而五阶非线性对ξ没有影响。五阶非线性使超高斯脉冲压缩。五阶非线性和脉冲前后沿锐度对脉宽的影响可以部分平衡。
(7)耦合相互作用微扰产生的啁啾与高阶色散微扰作用的情况相似,对振幅、脉宽、频率、中心位置、相位的演化规律都有直接的影响,而且破坏了超高斯型脉冲的绝热特性。
In this paper, firstly the origin, development and current research of optical fiber communications are introduced briefly, then, based on the MNLS equation, the answers of super-Gaussian pulse are introduced. The variational method is used to deduce the evolution equations for the parameters [amplitude(A), frequency band width(a), chirp(b), frequency(ω), center position(ξ), phase(ф)] of super-Gaussian pulses in common situation, without perturbation, and situation of the small dielectric loss, the higher-order dispersion, the fifth-order nonlinearity and the influence of the couple-interaction. By these equations, the properties of the parameters are discussed when the distance Z changed and the answers to the evolution equations of the parameters (a,b,ω,ξ) are derived under in the situation of without perturbation. Then the perturbation to the width made by the small dielectric loss, the higher-order dispersion and the fifth-order nonlinearity are mainly discussed, and the curves of the frequency band width (a), the in the situation of without perturbation, the higher-order dispersion and the fifth-order nonlinearity are described. The conclusions are:
(1)The effects of initial chirp exist in all cases while the super-Gaussian pulses transmitting in fibers:initial chirp b0 is negative, there is a narrow pulse in the initial process, and its absolute value is bigger, pulse width's vibration is slower and the oscillation amplitude is greater. The sharper the degree of the pulse`s edge sharpness is, The slower the pulse width's vibration is and the greater the oscillation amplitude is.
(2) In all cases except the coupled interaction, pulse width frequency band width a and amplitude A satisfy the adiabatic condition, frequencyω, chirp b and central positionξsatisfy the constraint relation, and pulse width a and chirp b meet another relationship.
(3) The small dielectric loss effects onф, it leads to the decrease of the power of the pulse;
(4) All of the higher-order dispersion, the fifth-order nonlinearity and the couple interaction can bring about chirp wave;
(5) The higher-order dispersion and the degree of the pulse`s edge sharpness have large effect on A、a、b、ω、ξ、φ,and the higher-order chromatic dispersion causes the super-Gaussian pulse widening
(6)The fifth-order nonlinearity and the chirps and the degree of the pulse`s edge sharpness have effect on A、a、b、ω、φ,but the former has no effect onξ. The fifth-order nonlinearity causes the super-Gaussian pulse compression, and the influence of the fifth-order nonlinearity and the degree of the pulse`s edge sharpness on the pulse-width can counterbalances in part;
(7) The chirp wave brought by the coupled interaction also has direct effect on Ap、ap、bp、ωp、ξp、φp,what’s more, it demolishes the adiabatic property.
(1)各种情况下,初始啁啾对光纤中传输的超高斯型脉冲均有影响:初始啁啾b0为负值时,初期脉冲有一窄化过程,且其绝对值越大,脉冲宽度的振荡越慢而振荡幅度越大.脉冲前后沿越锐,脉冲宽度的振荡越慢而振荡幅度越大.
(2)除耦合相互作用外,各种情况下,振幅A和脉宽a满足绝热条件,频率ω、啁啾b和中心位置ξ间存在一约束关系式,脉宽a和啁啾b间也存在一约束关系式。
(3)小损耗只对相位φ产生影响,它导致脉冲峰值功率的衰减;除对ξ无影响外,前后沿锐度m对其他脉冲参数有直接或间接的影响。
(4)高阶色散、五阶非线性和耦合相互作用微扰均会激起啁啾;
(5)高阶色散微扰和脉冲前后沿锐度对参数A、a、b、ω、ξ、φ均有影响。高阶色散使超高斯脉冲展宽。
(6)五阶非线性微扰作用下,五阶非线性、初始啁啾和脉冲前后沿锐度对参数A、a、b、ω、φ均有影响,而五阶非线性对ξ没有影响。五阶非线性使超高斯脉冲压缩。五阶非线性和脉冲前后沿锐度对脉宽的影响可以部分平衡。
(7)耦合相互作用微扰产生的啁啾与高阶色散微扰作用的情况相似,对振幅、脉宽、频率、中心位置、相位的演化规律都有直接的影响,而且破坏了超高斯型脉冲的绝热特性。
In this paper, firstly the origin, development and current research of optical fiber communications are introduced briefly, then, based on the MNLS equation, the answers of super-Gaussian pulse are introduced. The variational method is used to deduce the evolution equations for the parameters [amplitude(A), frequency band width(a), chirp(b), frequency(ω), center position(ξ), phase(ф)] of super-Gaussian pulses in common situation, without perturbation, and situation of the small dielectric loss, the higher-order dispersion, the fifth-order nonlinearity and the influence of the couple-interaction. By these equations, the properties of the parameters are discussed when the distance Z changed and the answers to the evolution equations of the parameters (a,b,ω,ξ) are derived under in the situation of without perturbation. Then the perturbation to the width made by the small dielectric loss, the higher-order dispersion and the fifth-order nonlinearity are mainly discussed, and the curves of the frequency band width (a), the in the situation of without perturbation, the higher-order dispersion and the fifth-order nonlinearity are described. The conclusions are:
(1)The effects of initial chirp exist in all cases while the super-Gaussian pulses transmitting in fibers:initial chirp b0 is negative, there is a narrow pulse in the initial process, and its absolute value is bigger, pulse width's vibration is slower and the oscillation amplitude is greater. The sharper the degree of the pulse`s edge sharpness is, The slower the pulse width's vibration is and the greater the oscillation amplitude is.
(2) In all cases except the coupled interaction, pulse width frequency band width a and amplitude A satisfy the adiabatic condition, frequencyω, chirp b and central positionξsatisfy the constraint relation, and pulse width a and chirp b meet another relationship.
(3) The small dielectric loss effects onф, it leads to the decrease of the power of the pulse;
(4) All of the higher-order dispersion, the fifth-order nonlinearity and the couple interaction can bring about chirp wave;
(5) The higher-order dispersion and the degree of the pulse`s edge sharpness have large effect on A、a、b、ω、ξ、φ,and the higher-order chromatic dispersion causes the super-Gaussian pulse widening
(6)The fifth-order nonlinearity and the chirps and the degree of the pulse`s edge sharpness have effect on A、a、b、ω、φ,but the former has no effect onξ. The fifth-order nonlinearity causes the super-Gaussian pulse compression, and the influence of the fifth-order nonlinearity and the degree of the pulse`s edge sharpness on the pulse-width can counterbalances in part;
(7) The chirp wave brought by the coupled interaction also has direct effect on Ap、ap、bp、ωp、ξp、φp,what’s more, it demolishes the adiabatic property.
引文
[1]Scoot Russell. Report on waves [J], Pro. Roy. Soc. Edinburgh, 1844,319.
[2]陈陆君,梁昌洪著,孤立子理论及其应用[M],西安电子科技大学出版社,1997.
[3]谷超豪等著,孤立子理论与应用[M],浙江科学技术出版社,1990.
[4]N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett. 1965(15), 240.
[5]杨祥林,温扬敬著,光纤孤子通信理论基础[M],国防工业出版社,2000.
[6]郭柏林,庞小峰著,孤立子[M],科学出版社,1987.
[7]M. J. Ablowitz and P. A. Clarkson, Soliton, Nonlinear Evolution Equation and Inverse Scattering[M], University Press,Cambridge,1991.
[8]V.Zakharov and A.B.Shabat, Sov. Phys. JEPT 1972(5)2,364.
[9]TAYA M,BASHAW M C,FEJER M M, et al.Oberservation of Dark Photovoltaic Spatial Solitons[J]. Phys Rev A,1995,52(4):3095-3100.
[10]SHE W L, LEE K K, LEE W K.Oberservation of two-dimentional Bright Photovoltaic Spatial Solitons[J].Phys Rev Lett,1999,83(16):3182-3185.
[11]杨祥林.光纤通信系统[M].北京:国防工业出版社,2000
[12]Islam M N. Mollenauer L F. Stolen R H and Shang H T. Cross phase modulation in Optical fibers.Opt.Lett.1987, 12(8):625-627
[13]Kodama Y and Hasegawa A,IEEE[J].Quantum Electron,1987,QE-23,5:510
[14]Y.S.Kivshar, B.A.Malomed. Dynamics of Solitons in nearly integrals systems [J].Rev.Mod.Phys,1989,61(4):763-915.
[15]D.R. Nicholson and M.V. Goldman, Damped Nonlinear Schrodinger Equation[J], Physics of Fluids 1976,19(10), 1621-1625.
[16]Kodam Y,Hasegawa A.Generation of asymptotically stable optical solitons and suppression of Gordon-Haus effect[J].Opt.Lett.1992.17(1):31-33
[17]A.Bondeson, M.Lisak and D.Anderson. Soliton Perturbations: A Variational Principle for the Soliton Parameters[J]. Phy Scripta,1979,Vol 20,479-485
[18]D.Anderson,Variational Approach to Nonlinear Pulse Propagation in Optical Fibers[J].Phy Rev A, 1983, Vol 27,3135-3145.
[19]D.Anderson and Lisk M. Bandwidth limits due to mutual pulse interaction in optical soliton communication systems Opt Lett,1986,11(03),174-176
[20]Li Qiliang, Li Qingshan, Lin Libin. Soliton-like pulse timing jitter in dispersion-managed systems[J] Chin.Phys.2006,15, 2306-2314
[21]谢应茂.光纤中光学高斯型脉冲的传输特性研究[J].量子电子学报,2004,21(1):56-59
[22]桑志文,罗开基,王永祥.光纤中小损耗对光学高斯型脉冲传输特性的影响[J].上饶师范学院学报,2005(06):44-47
[23]刘金龙,李海,陈金华等.亚强非局域介质中的超高斯空间光孤子族研究[J].光子学报,2007,36(8):1414～1417
[24]陈守满,石顺祥,董洪舟.有偏压光折变晶体中的高斯孤子[J].物理学报, 2007,56(3):1379-1384
[25]徐铭,吉建华.差分相移键控色散管理孤子多扰动系统的相位抖动[J].光学学报, 2007, 27(5): 781-786
[26]A. Haus. Quantum noise in a solitonlike repeater system[J]. Opt. Soc. Am.B,1991,8(5):1122～1126
[27]Zakharov V.E.,ShabatA.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media[J]. Sov Phys-JETP.1972,34(1),62-69.
[28]Satsuma I,Yajima N. Initial value problems of one-dimensional self modulation of nonlinear waves in dispersive media[J].Supp Prog Theoret Phys(Japan)1974,55,1443-1483
[29]刘庆仪,罗开基.光纤中小损耗对类明孤子传输特性的影响[J].江西科学,2001,19(1):11-13
[30]罗开基,刘庆仪.光纤中三阶色散对类明孤子传输特性的影响[J].量子电子学报,2002,19(2):174-179.
[31]刘庆仪,罗开基.光纤中五阶非线性对类明孤子传输特性的影响[J].激光杂志,2001,22(5):43-44
[32]谢应茂.类明孤子脉冲在色散搭配光纤中传输特性的研究[J].赣南师范学院学报.2001,3,28-30
[33]G.P. Agrawal, Nonlinear fiber optics[M] (Academic Press, San’Diego, Calif. 2002),chap. 2-5.
[34]Hasegawa A.et.Al,Reduction of collision-induced time jitters indispersion-manage soliton transimission systems[J],Opt Lett,1996,12(1):39-41.
[35]Chen Lujun, Liang Changhong.The Theory and Application of Soliton [M]Xi’an:Xidian University Press, 1997.
[36]Sang Minghuang, Luo Kaiji.Behavior of Solition in the Neighborhood of Zero-dispersion Propagation in a Single Model Optical Fiber[J].Journal of Jiangxi Normal University,1995,19(3):226-231.
[37]张书敏,徐文成,罗爱平等.光纤中飞秒基孤子压缩的一种改进性方法[J].光子学报,2001,30(3):280-283.
[38]Guo Fang-jun, Xia Guang-qiong, Ling Xiao-dong. Transmission characteristics of Chirped super-Gaussian optical pulse in the single-mode optical fiber[J].Laser Journal,2007(04)56-57.(in Chinese)
[39]LI QI-Liang, CHEN Xiang-dong, TANG Xiang-hong,etc. Interaction-Induced Timing-Displacement Analysis in a WDM Optical Soliton Transmission System with Dispersion Management[J].CHINESE JOURNAL OF LASERS.2004,31(2):199-204
[40]XU Ming, YANG Xiang-lin, Hu Yu. Timing Jitter in Wacelenth-division-multiplexed Dispersion-Maneged Soliton Conmmuication Systems[J].CHINESE JOURNAL OF LASERS.2002,29(1):47-52.
[41]Zhang Fan, Ye Peida. Timing Jitter in Dispersion-Managed Soliton Systems Controlled in Time and Frequency Domain[J]. ACTA PHOTONICASINICA.2003, 32(2):133-136.
[42]Tai K, Hasegawa A, Tamita A .Observation of modulation instability in optical fibers[J]. Phys. Rev. Lett.1986,56(1):135—138.
[43]A. Biswas. Super-Gaussian soliton in optical fibers[J].Fiber and Integrated Optics,2002,21:115-124.
[44]桑志文,罗开基,桑明煌等.三阶色散对光纤中高斯型脉冲传输特性的影响[J].量子电子学报,2005 ,22(6),946-948
[45]谢应茂.类明孤子在光纤中传输特性的变分研究[J].光学学报,2004, 24(4),452-455
[46]王永祥.高阶微扰对类明孤子传输特性的影响[D],2006
[47]Hasegawa A, Kumar S, Kodama Y. Reduction of collision-induced time jitters in dispersion-managed soliton transmission systems[J].Opt Lett,1996,12(1): 39-41.
[48]A. Hasegawa and Y. Kodama. Soliton in optical communications[M]. Oxford University Press, Oxford, 1995.
[49]Hasegawa A. Optical Soliton in fiber[M].New York: Spring-Verlag, 1989.
[50]谢应茂.单模光纤中光学高斯型脉冲非线性传输特性的变分研究[J].江西科学,2000,18(4):191-192
[51]桑志文,罗开基,桑明煌.五阶非线性对光纤中高斯型脉冲传输特性的影响[J]量子电子学报2007,24(2),122-126
[52]谢应茂.耦合光纤中孤子传输特性的变分研究[J].江西师范大学学报(自然科学版),1992,16(1)
[53]罗开基,刘庆仪,桑明煌.耦合相互作用对光纤中类明孤子传输特性的影响[J].激光杂志,2002,23(6):48-49.
[2]陈陆君,梁昌洪著,孤立子理论及其应用[M],西安电子科技大学出版社,1997.
[3]谷超豪等著,孤立子理论与应用[M],浙江科学技术出版社,1990.
[4]N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett. 1965(15), 240.
[5]杨祥林,温扬敬著,光纤孤子通信理论基础[M],国防工业出版社,2000.
[6]郭柏林,庞小峰著,孤立子[M],科学出版社,1987.
[7]M. J. Ablowitz and P. A. Clarkson, Soliton, Nonlinear Evolution Equation and Inverse Scattering[M], University Press,Cambridge,1991.
[8]V.Zakharov and A.B.Shabat, Sov. Phys. JEPT 1972(5)2,364.
[9]TAYA M,BASHAW M C,FEJER M M, et al.Oberservation of Dark Photovoltaic Spatial Solitons[J]. Phys Rev A,1995,52(4):3095-3100.
[10]SHE W L, LEE K K, LEE W K.Oberservation of two-dimentional Bright Photovoltaic Spatial Solitons[J].Phys Rev Lett,1999,83(16):3182-3185.
[11]杨祥林.光纤通信系统[M].北京:国防工业出版社,2000
[12]Islam M N. Mollenauer L F. Stolen R H and Shang H T. Cross phase modulation in Optical fibers.Opt.Lett.1987, 12(8):625-627
[13]Kodama Y and Hasegawa A,IEEE[J].Quantum Electron,1987,QE-23,5:510
[14]Y.S.Kivshar, B.A.Malomed. Dynamics of Solitons in nearly integrals systems [J].Rev.Mod.Phys,1989,61(4):763-915.
[15]D.R. Nicholson and M.V. Goldman, Damped Nonlinear Schrodinger Equation[J], Physics of Fluids 1976,19(10), 1621-1625.
[16]Kodam Y,Hasegawa A.Generation of asymptotically stable optical solitons and suppression of Gordon-Haus effect[J].Opt.Lett.1992.17(1):31-33
[17]A.Bondeson, M.Lisak and D.Anderson. Soliton Perturbations: A Variational Principle for the Soliton Parameters[J]. Phy Scripta,1979,Vol 20,479-485
[18]D.Anderson,Variational Approach to Nonlinear Pulse Propagation in Optical Fibers[J].Phy Rev A, 1983, Vol 27,3135-3145.
[19]D.Anderson and Lisk M. Bandwidth limits due to mutual pulse interaction in optical soliton communication systems Opt Lett,1986,11(03),174-176
[20]Li Qiliang, Li Qingshan, Lin Libin. Soliton-like pulse timing jitter in dispersion-managed systems[J] Chin.Phys.2006,15, 2306-2314
[21]谢应茂.光纤中光学高斯型脉冲的传输特性研究[J].量子电子学报,2004,21(1):56-59
[22]桑志文,罗开基,王永祥.光纤中小损耗对光学高斯型脉冲传输特性的影响[J].上饶师范学院学报,2005(06):44-47
[23]刘金龙,李海,陈金华等.亚强非局域介质中的超高斯空间光孤子族研究[J].光子学报,2007,36(8):1414～1417
[24]陈守满,石顺祥,董洪舟.有偏压光折变晶体中的高斯孤子[J].物理学报, 2007,56(3):1379-1384
[25]徐铭,吉建华.差分相移键控色散管理孤子多扰动系统的相位抖动[J].光学学报, 2007, 27(5): 781-786
[26]A. Haus. Quantum noise in a solitonlike repeater system[J]. Opt. Soc. Am.B,1991,8(5):1122～1126
[27]Zakharov V.E.,ShabatA.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media[J]. Sov Phys-JETP.1972,34(1),62-69.
[28]Satsuma I,Yajima N. Initial value problems of one-dimensional self modulation of nonlinear waves in dispersive media[J].Supp Prog Theoret Phys(Japan)1974,55,1443-1483
[29]刘庆仪,罗开基.光纤中小损耗对类明孤子传输特性的影响[J].江西科学,2001,19(1):11-13
[30]罗开基,刘庆仪.光纤中三阶色散对类明孤子传输特性的影响[J].量子电子学报,2002,19(2):174-179.
[31]刘庆仪,罗开基.光纤中五阶非线性对类明孤子传输特性的影响[J].激光杂志,2001,22(5):43-44
[32]谢应茂.类明孤子脉冲在色散搭配光纤中传输特性的研究[J].赣南师范学院学报.2001,3,28-30
[33]G.P. Agrawal, Nonlinear fiber optics[M] (Academic Press, San’Diego, Calif. 2002),chap. 2-5.
[34]Hasegawa A.et.Al,Reduction of collision-induced time jitters indispersion-manage soliton transimission systems[J],Opt Lett,1996,12(1):39-41.
[35]Chen Lujun, Liang Changhong.The Theory and Application of Soliton [M]Xi’an:Xidian University Press, 1997.
[36]Sang Minghuang, Luo Kaiji.Behavior of Solition in the Neighborhood of Zero-dispersion Propagation in a Single Model Optical Fiber[J].Journal of Jiangxi Normal University,1995,19(3):226-231.
[37]张书敏,徐文成,罗爱平等.光纤中飞秒基孤子压缩的一种改进性方法[J].光子学报,2001,30(3):280-283.
[38]Guo Fang-jun, Xia Guang-qiong, Ling Xiao-dong. Transmission characteristics of Chirped super-Gaussian optical pulse in the single-mode optical fiber[J].Laser Journal,2007(04)56-57.(in Chinese)
[39]LI QI-Liang, CHEN Xiang-dong, TANG Xiang-hong,etc. Interaction-Induced Timing-Displacement Analysis in a WDM Optical Soliton Transmission System with Dispersion Management[J].CHINESE JOURNAL OF LASERS.2004,31(2):199-204
[40]XU Ming, YANG Xiang-lin, Hu Yu. Timing Jitter in Wacelenth-division-multiplexed Dispersion-Maneged Soliton Conmmuication Systems[J].CHINESE JOURNAL OF LASERS.2002,29(1):47-52.
[41]Zhang Fan, Ye Peida. Timing Jitter in Dispersion-Managed Soliton Systems Controlled in Time and Frequency Domain[J]. ACTA PHOTONICASINICA.2003, 32(2):133-136.
[42]Tai K, Hasegawa A, Tamita A .Observation of modulation instability in optical fibers[J]. Phys. Rev. Lett.1986,56(1):135—138.
[43]A. Biswas. Super-Gaussian soliton in optical fibers[J].Fiber and Integrated Optics,2002,21:115-124.
[44]桑志文,罗开基,桑明煌等.三阶色散对光纤中高斯型脉冲传输特性的影响[J].量子电子学报,2005 ,22(6),946-948
[45]谢应茂.类明孤子在光纤中传输特性的变分研究[J].光学学报,2004, 24(4),452-455
[46]王永祥.高阶微扰对类明孤子传输特性的影响[D],2006
[47]Hasegawa A, Kumar S, Kodama Y. Reduction of collision-induced time jitters in dispersion-managed soliton transmission systems[J].Opt Lett,1996,12(1): 39-41.
[48]A. Hasegawa and Y. Kodama. Soliton in optical communications[M]. Oxford University Press, Oxford, 1995.
[49]Hasegawa A. Optical Soliton in fiber[M].New York: Spring-Verlag, 1989.
[50]谢应茂.单模光纤中光学高斯型脉冲非线性传输特性的变分研究[J].江西科学,2000,18(4):191-192
[51]桑志文,罗开基,桑明煌.五阶非线性对光纤中高斯型脉冲传输特性的影响[J]量子电子学报2007,24(2),122-126
[52]谢应茂.耦合光纤中孤子传输特性的变分研究[J].江西师范大学学报(自然科学版),1992,16(1)
[53]罗开基,刘庆仪,桑明煌.耦合相互作用对光纤中类明孤子传输特性的影响[J].激光杂志,2002,23(6):48-49.