超短脉冲Ⅰ型倍频特性的研究
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摘要
超短脉冲倍频是获得短波长超短脉冲激光行之有效的方法。由于超短脉冲具有较宽的光谱范围及较高功率密度,倍频转换效率和谐波脉冲波形将受到许多因素的影响。为了提高转换效率和改善脉冲光束质量,有必要对相关的各种物理因素进行研究。
本文研究了飞秒脉冲在BBO晶体中的I型倍频特性。首先,根据麦克斯韦方程组建立了超短脉冲I型倍频过程的物理模型,其中考虑了空间离散、衍射、群速失配、群速度色散、三阶非线性效应等多种物理因素。介绍了BBO晶体的物理光学性质以及一般的数值求解算法,并通过对耦合波方程组进行归一化处理并且编写了相应的数值模拟程序。其次,模拟了飞秒脉冲的I型匹配倍频过程;详细分析了高转换效率下各个因素如晶体长度、脉宽、脉冲能量、束腰半径在单独或组合情况下对倍频脉冲波形、空间近场分布(在晶体出射面上)及转换效率的影响。最后,用初始角度失谐和基频脉冲啁啾两种方法来补偿倍频过程中产生的相位失配,提高了倍频转换效率。在此基础上,设计了超短脉冲三倍频群速度补偿方案,方案采用了晶体双折射群速度补偿、以及极化旋转技术。分析发现,各种因素对倍频过程有不同的影响,且倍频脉冲时间波形和空间近场分布十分相似。啁啾补偿方法相对来说能较好地补偿倍频过程中的相位失配,从而为实际应用提供了一定参考。
Frequency doubling of ultra-short pulses is an effective method to obtain short-wavelength ultra-short pulses. Conversion efficiency and pulse wave-forms will be affected by many factors due to the wide spectrum range and high intensity density of ultra-short pulses. To increase conversion efficiency and improve beam quality, it is necessary to study various physical factors involved.
Properties of frequency doubling of femtosecond pulses in type-I phase-matched BBO crystal are investigated in this thesis. First, a physical model on the frequency doubling of ultra-short pulses in type-I phase-matching case has been built up on the basis of Maxwell's equations, where various physical factors such as spatial walk-off, diffraction, group velocity mismatch(GVM), dispersion (GVD) and third order nonlinear effect are considered. Physical and optical properties of BBO and general numerical solving methods are introduced, these coupling equations are normalized and a final numerical simulation program is programmed. Second, the frequency doubling process of femtosecond pulses in type-I phase-matching case is simulated, where the influence on conversion efficiency, pulse waveforms and spatial near-field distribution (in the exit plane of crystal) of harmonic pulses with different physic factors by pulse width, energy and beam radius is studied in detail in high conversion efficiency case. At last, two methods of initial angular mismatching and pulse chirping are used to compensate phase matches in frequency doubling processes, which really increases conversion efficiency. Based on phase mismatch compensation, a scheme of group velocity compensation in frequency tripling is designed by compensation principle of birefringence and polarization rotation. It is found that different factors have different decent influences on frequency doubling processes; where the pulse spatial distributions are quite similar to temporal waveforms. The chirping method is better in compensation for phase mismatch comparatively, thus can provide a practical reference in application.
本文研究了飞秒脉冲在BBO晶体中的I型倍频特性。首先,根据麦克斯韦方程组建立了超短脉冲I型倍频过程的物理模型,其中考虑了空间离散、衍射、群速失配、群速度色散、三阶非线性效应等多种物理因素。介绍了BBO晶体的物理光学性质以及一般的数值求解算法,并通过对耦合波方程组进行归一化处理并且编写了相应的数值模拟程序。其次,模拟了飞秒脉冲的I型匹配倍频过程;详细分析了高转换效率下各个因素如晶体长度、脉宽、脉冲能量、束腰半径在单独或组合情况下对倍频脉冲波形、空间近场分布(在晶体出射面上)及转换效率的影响。最后,用初始角度失谐和基频脉冲啁啾两种方法来补偿倍频过程中产生的相位失配,提高了倍频转换效率。在此基础上,设计了超短脉冲三倍频群速度补偿方案,方案采用了晶体双折射群速度补偿、以及极化旋转技术。分析发现,各种因素对倍频过程有不同的影响,且倍频脉冲时间波形和空间近场分布十分相似。啁啾补偿方法相对来说能较好地补偿倍频过程中的相位失配,从而为实际应用提供了一定参考。
Frequency doubling of ultra-short pulses is an effective method to obtain short-wavelength ultra-short pulses. Conversion efficiency and pulse wave-forms will be affected by many factors due to the wide spectrum range and high intensity density of ultra-short pulses. To increase conversion efficiency and improve beam quality, it is necessary to study various physical factors involved.
Properties of frequency doubling of femtosecond pulses in type-I phase-matched BBO crystal are investigated in this thesis. First, a physical model on the frequency doubling of ultra-short pulses in type-I phase-matching case has been built up on the basis of Maxwell's equations, where various physical factors such as spatial walk-off, diffraction, group velocity mismatch(GVM), dispersion (GVD) and third order nonlinear effect are considered. Physical and optical properties of BBO and general numerical solving methods are introduced, these coupling equations are normalized and a final numerical simulation program is programmed. Second, the frequency doubling process of femtosecond pulses in type-I phase-matching case is simulated, where the influence on conversion efficiency, pulse waveforms and spatial near-field distribution (in the exit plane of crystal) of harmonic pulses with different physic factors by pulse width, energy and beam radius is studied in detail in high conversion efficiency case. At last, two methods of initial angular mismatching and pulse chirping are used to compensate phase matches in frequency doubling processes, which really increases conversion efficiency. Based on phase mismatch compensation, a scheme of group velocity compensation in frequency tripling is designed by compensation principle of birefringence and polarization rotation. It is found that different factors have different decent influences on frequency doubling processes; where the pulse spatial distributions are quite similar to temporal waveforms. The chirping method is better in compensation for phase mismatch comparatively, thus can provide a practical reference in application.
引文
[1]王玉英.超短脉冲激光器及应用[J].光机电信息,2006,3:21-28.
[2] GOVIND P A.Nonlinear Fiber Optics[M].3.Sinagpore:Elsevier Pte Ltd,2005:1-25.
[3] JUN Y,CUNDIFF S T.Femtosecond Optical Frequency Comb:Principle, Operation and Applications[M].Berlin:Springer Science and Business Media, Inc.,2005:54-75.
[4]周建英,曾健华,李俊韬.超短激光脉冲传输特性的量子相干操控与应用[J].科学通报,2008,53(1):23-30.
[5]王水才,贺俊芳,彭菊芳.超快微光分子光谱探测技术研究[J].光子学报,2004,33(7):871-875.
[6] MAINE P,STRICKLAND D,BADO P.Generation of High Peak Power Pulses by Chirped Pulse Amplification[J].IEEE J. Quantum. Electron,1988,24(2):398-403.
[7] MARTINEZ O E.Design of High-power Ultrashort Pulse Amplifiers by Expansion and Recompression of Ultrashort Optical Pulse[J].Opt. Lett.,1993,18:1651-1656.
[8] IIDAY F ?,K?RTNER F X.Cavity-enhanced Optical Parametric Chirped-pulse Amplification[J].Opt. Lett.,2006,31(5):637-639.
[9] DUBIETIS A,JONUSAUKAS G.Powerful Femtosecond Generation by Chirped and Stretched Pulse Parametric Amplification in BBO Crystal[J].Opt. Commun,1992,88(4-6):437-440.
[10]孟绍贤.超强激光场物理学[J].物理学进展,1999,19(3):237-267.
[11]盛政明,张杰.强场物理新进展----强激光在等离子体中加速电子的新机制[J].2003,32(1):17-18.
[12] PERRY M D . Intense High-energy Proton Beams from Petwatt Laser Irradiation of Solids[J].Phy. Rev. Lett.,2000,85(14):2945-2948.
[13] USMAN K.S.Femtosecond Pulse Synthesis by Efficient Second-harmonic Generation in Engineered Quasi Phase Matching Gratings[J].OSA.,2007:7448-7456.
[14]张伟力.全固化飞秒激光器进展[J].光电子·激光,1999,10(3):282-285.
[15]侯洵.瞬态光学及其进展[J].河南大学学报(自然科学版),2002,32(1):1-6.
[16]邹其徽.超短脉冲光束的传输特性和光谱异常行为的研究[D].四川大学:博士论文,2006:1-7.
[17]侯洵.超短脉冲激光及其应用.空军工程大学学报[J],2000,1(1):1-5.
[18] WORKMAN J,MAKSIMCHUK A,etal.Control of Bright Picosecond X-ray Emission from Intense Subpicosecond Laser-plasma Interactions[J].Phys. Rev. Lett.,1995,75(12):2324-2327.
[19] MACKLIN J J,KMETEC J D.Higher Order Harmonic Generation Using Femtosecond Pulses[J].Phy. Rev. Lett,1993,70(6):766-769.
[20] STRICKLAND D,MOUROU G.Compression of Amplified Chirped Optical Pulses[J].Opt. Commun.,1985,56(3):219-221.
[21] MUCKE O D,SIDOROV D,etal.Scalable Yb-MOPA-driven Carrier-envelope Phase-stable Few-cycle Parametric Amplifier at 1.5μm [J].Opt. Lett..2009,34:118-120.
[22]魏志义,张杰,夏江帆,等.高效率太瓦级飞秒掺钛蓝宝石激光装置[J].中国科学(A),2000,30(11):1046-1050.
[23] BALTUSKA A,FUJI T,KOBAYASHI T.Visible Pulse Compression to 4fs by Optical Parametric Amplification and Programmable Dispersion Control[J].Opt. Lett.,2002,27(5):306-308.
[24]石顺祥.非线性光学[M].西安:电子科技大学出版社,2003:1-3,113-144.
[25]钱士雄,王恭明.非线性光学-原理与进展[M].上海:复旦大学出版社,2001:1-13,53-79.
[26] ARMSTRONG J A.Interactions Between Light Waves in A Nonlinear Dielectric[J].Phys. Rev.,1962,127(6):1918-1939.
[27] CRAXTON R S.High Efficiency Frequency Tripling Scheme for High-Power Nd: Glass[J].IEEE J Q E,1981,17(9):1771-1782.
[28] EIMERL D,AUERBACH J M,MILONNI P W.Paraxial Wave Theory of Second and Third Harmonic Generation in Uniaxial Crystals in Narrowband Pump Fields[J].Journal of Modern Optics,1995,42(5):1037-1067.
[29] AUERBACH J M ,EIMERL D , MILAM D . Perturbation Theory for Electric-field Amplitude and Phase Ripple Transfer in Frequency Doubling andTripling[J].Applied Optics,1997,36(3):606-612.
[30] SKELDON M D,CRAXTON R S,KESSLER T J.Efficient Harmonic Generation with A Broad-Band Laser[J].IEEE J Q E,1992,28(5):1389-1399.
[31] AUERBACH J M , MILAM D , BARKER C E , et al . Frequency Conversion Modeling with Spatially and Temporally Varying Beam[C].SPIE,1995,2633:230-241.
[32] BANKS P S,FEIT M D,PERRY M D.High-Intensity Third-harmonic Generation[J].Opt. Soc. Am. B,2002,19(1):102-118.
[33] CHIEN C Y,KORN G,COE J S,et al.Highly Efficient Second-harmonic Generation of Ultraintense Nd: glass Laser Pulses[J].Optics Letters,1995,20(4):353-355
[34] KRYLOV V,REBANE A,KALINTSEV A G,et al.Second-harmonic Generation of Amplified Femtosecond Ti: Sapphire Laser Pulses[J].Optics Letters.,1995,20(2):198-200.
[35] TAMAKI Y,OBARA M,MIDORIKAWA K.Second-Harmonic Generation from Intense 100fs Ti:Sapphire Laser Pulses in Potassium Dihydrogen Phosphate Cesium Lithium Borate andβ-barium Metaborate[J].Japanese Journal of Applied Physics,1998,37(9A):4801-4805.
[36] QUENEUILLE J,DRUON F,MAKSIMCHUK A,etal.Second-harmonic Generation and Wave-front Correction of A Terawatt Laser System[J].Optics Letters,2000,25(7):508-510.
[37] AOYAMA M,ZHANG T J.Noncollinear Second-Harmonic Generation with Compensation of Phase Mismatch by Controlling Frequency Chirp and Tilted Pulse Fronts of Femtosecond Laser Pulses[J].Jpn. Appl. Phys.,2000,39(6):3394-3399.
[38] ZHANG T J,KOICHI Y K.Numerical Analysis of Type I Third-Harmonic Generation through Third-Order and Cascaded Second-Order Nonlinear Optical Processes[J].Jpn. Appl. Phys.,2000,39:91-95.
[39] DUBIETIS A,TAMO?AUSKAS G.Femtosecond Third-harmonic Pulse Generation by Mixing of Pulses with Different Duration[J] . Optics. Commucations,2000,186(1-3):211-217.
[40] ILDAR A B.Limitation of Second-harmonic Generation of FemtosecodTi:apphire Laser Pulses[J].Opt. Soc. Am. B,2004,21(2):318-322.
[41]刁煦,李琨,张彬.高强度超短脉冲单块BBO晶体的三倍频研究[J].光电工程,2008,35(4):115-119.
[42]韩耀锋,杨爱粉,宁自立.超短激光脉冲二倍频理论分析[J].应用光学,2007,28(4):468-471.
[43]徐晗.超短脉冲激光在二阶非线性介质中的时空调制及其应用[D].华东师范大学:博士论文,2006:15-28.
[44]胡淼.BBO晶体四倍频的紫外激光器研究[D].浙江大学:博士学位论文,2008:13-28.
[45] DAVID N N.Nonlinear Optical Crystals:A Complete Survey[M].Berlin:Springer Science+Business Media,2005:5-14.
[46] HUANG J J,CHANG Y Q,etal.Proposal of High Quality Walk-off Compensated Sum Frequency Generation of Ultra-short Pulses . Optics Communications,2008,281:5244-5248.
[2] GOVIND P A.Nonlinear Fiber Optics[M].3.Sinagpore:Elsevier Pte Ltd,2005:1-25.
[3] JUN Y,CUNDIFF S T.Femtosecond Optical Frequency Comb:Principle, Operation and Applications[M].Berlin:Springer Science and Business Media, Inc.,2005:54-75.
[4]周建英,曾健华,李俊韬.超短激光脉冲传输特性的量子相干操控与应用[J].科学通报,2008,53(1):23-30.
[5]王水才,贺俊芳,彭菊芳.超快微光分子光谱探测技术研究[J].光子学报,2004,33(7):871-875.
[6] MAINE P,STRICKLAND D,BADO P.Generation of High Peak Power Pulses by Chirped Pulse Amplification[J].IEEE J. Quantum. Electron,1988,24(2):398-403.
[7] MARTINEZ O E.Design of High-power Ultrashort Pulse Amplifiers by Expansion and Recompression of Ultrashort Optical Pulse[J].Opt. Lett.,1993,18:1651-1656.
[8] IIDAY F ?,K?RTNER F X.Cavity-enhanced Optical Parametric Chirped-pulse Amplification[J].Opt. Lett.,2006,31(5):637-639.
[9] DUBIETIS A,JONUSAUKAS G.Powerful Femtosecond Generation by Chirped and Stretched Pulse Parametric Amplification in BBO Crystal[J].Opt. Commun,1992,88(4-6):437-440.
[10]孟绍贤.超强激光场物理学[J].物理学进展,1999,19(3):237-267.
[11]盛政明,张杰.强场物理新进展----强激光在等离子体中加速电子的新机制[J].2003,32(1):17-18.
[12] PERRY M D . Intense High-energy Proton Beams from Petwatt Laser Irradiation of Solids[J].Phy. Rev. Lett.,2000,85(14):2945-2948.
[13] USMAN K.S.Femtosecond Pulse Synthesis by Efficient Second-harmonic Generation in Engineered Quasi Phase Matching Gratings[J].OSA.,2007:7448-7456.
[14]张伟力.全固化飞秒激光器进展[J].光电子·激光,1999,10(3):282-285.
[15]侯洵.瞬态光学及其进展[J].河南大学学报(自然科学版),2002,32(1):1-6.
[16]邹其徽.超短脉冲光束的传输特性和光谱异常行为的研究[D].四川大学:博士论文,2006:1-7.
[17]侯洵.超短脉冲激光及其应用.空军工程大学学报[J],2000,1(1):1-5.
[18] WORKMAN J,MAKSIMCHUK A,etal.Control of Bright Picosecond X-ray Emission from Intense Subpicosecond Laser-plasma Interactions[J].Phys. Rev. Lett.,1995,75(12):2324-2327.
[19] MACKLIN J J,KMETEC J D.Higher Order Harmonic Generation Using Femtosecond Pulses[J].Phy. Rev. Lett,1993,70(6):766-769.
[20] STRICKLAND D,MOUROU G.Compression of Amplified Chirped Optical Pulses[J].Opt. Commun.,1985,56(3):219-221.
[21] MUCKE O D,SIDOROV D,etal.Scalable Yb-MOPA-driven Carrier-envelope Phase-stable Few-cycle Parametric Amplifier at 1.5μm [J].Opt. Lett..2009,34:118-120.
[22]魏志义,张杰,夏江帆,等.高效率太瓦级飞秒掺钛蓝宝石激光装置[J].中国科学(A),2000,30(11):1046-1050.
[23] BALTUSKA A,FUJI T,KOBAYASHI T.Visible Pulse Compression to 4fs by Optical Parametric Amplification and Programmable Dispersion Control[J].Opt. Lett.,2002,27(5):306-308.
[24]石顺祥.非线性光学[M].西安:电子科技大学出版社,2003:1-3,113-144.
[25]钱士雄,王恭明.非线性光学-原理与进展[M].上海:复旦大学出版社,2001:1-13,53-79.
[26] ARMSTRONG J A.Interactions Between Light Waves in A Nonlinear Dielectric[J].Phys. Rev.,1962,127(6):1918-1939.
[27] CRAXTON R S.High Efficiency Frequency Tripling Scheme for High-Power Nd: Glass[J].IEEE J Q E,1981,17(9):1771-1782.
[28] EIMERL D,AUERBACH J M,MILONNI P W.Paraxial Wave Theory of Second and Third Harmonic Generation in Uniaxial Crystals in Narrowband Pump Fields[J].Journal of Modern Optics,1995,42(5):1037-1067.
[29] AUERBACH J M ,EIMERL D , MILAM D . Perturbation Theory for Electric-field Amplitude and Phase Ripple Transfer in Frequency Doubling andTripling[J].Applied Optics,1997,36(3):606-612.
[30] SKELDON M D,CRAXTON R S,KESSLER T J.Efficient Harmonic Generation with A Broad-Band Laser[J].IEEE J Q E,1992,28(5):1389-1399.
[31] AUERBACH J M , MILAM D , BARKER C E , et al . Frequency Conversion Modeling with Spatially and Temporally Varying Beam[C].SPIE,1995,2633:230-241.
[32] BANKS P S,FEIT M D,PERRY M D.High-Intensity Third-harmonic Generation[J].Opt. Soc. Am. B,2002,19(1):102-118.
[33] CHIEN C Y,KORN G,COE J S,et al.Highly Efficient Second-harmonic Generation of Ultraintense Nd: glass Laser Pulses[J].Optics Letters,1995,20(4):353-355
[34] KRYLOV V,REBANE A,KALINTSEV A G,et al.Second-harmonic Generation of Amplified Femtosecond Ti: Sapphire Laser Pulses[J].Optics Letters.,1995,20(2):198-200.
[35] TAMAKI Y,OBARA M,MIDORIKAWA K.Second-Harmonic Generation from Intense 100fs Ti:Sapphire Laser Pulses in Potassium Dihydrogen Phosphate Cesium Lithium Borate andβ-barium Metaborate[J].Japanese Journal of Applied Physics,1998,37(9A):4801-4805.
[36] QUENEUILLE J,DRUON F,MAKSIMCHUK A,etal.Second-harmonic Generation and Wave-front Correction of A Terawatt Laser System[J].Optics Letters,2000,25(7):508-510.
[37] AOYAMA M,ZHANG T J.Noncollinear Second-Harmonic Generation with Compensation of Phase Mismatch by Controlling Frequency Chirp and Tilted Pulse Fronts of Femtosecond Laser Pulses[J].Jpn. Appl. Phys.,2000,39(6):3394-3399.
[38] ZHANG T J,KOICHI Y K.Numerical Analysis of Type I Third-Harmonic Generation through Third-Order and Cascaded Second-Order Nonlinear Optical Processes[J].Jpn. Appl. Phys.,2000,39:91-95.
[39] DUBIETIS A,TAMO?AUSKAS G.Femtosecond Third-harmonic Pulse Generation by Mixing of Pulses with Different Duration[J] . Optics. Commucations,2000,186(1-3):211-217.
[40] ILDAR A B.Limitation of Second-harmonic Generation of FemtosecodTi:apphire Laser Pulses[J].Opt. Soc. Am. B,2004,21(2):318-322.
[41]刁煦,李琨,张彬.高强度超短脉冲单块BBO晶体的三倍频研究[J].光电工程,2008,35(4):115-119.
[42]韩耀锋,杨爱粉,宁自立.超短激光脉冲二倍频理论分析[J].应用光学,2007,28(4):468-471.
[43]徐晗.超短脉冲激光在二阶非线性介质中的时空调制及其应用[D].华东师范大学:博士论文,2006:15-28.
[44]胡淼.BBO晶体四倍频的紫外激光器研究[D].浙江大学:博士学位论文,2008:13-28.
[45] DAVID N N.Nonlinear Optical Crystals:A Complete Survey[M].Berlin:Springer Science+Business Media,2005:5-14.
[46] HUANG J J,CHANG Y Q,etal.Proposal of High Quality Walk-off Compensated Sum Frequency Generation of Ultra-short Pulses . Optics Communications,2008,281:5244-5248.