光参量产生及其光谱特性理论研究
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摘要
光参量产生是由抽运光子流和量子噪声在非线性晶体里的综合作用,其下转换光子具有时间、空间、偏振、频率等高度相关特性,具有从抽运光频率到晶格共振频率的宽光谱分布。光参量产生技术的应用研究涉及到光参量振荡和光参量放大、量子通信和光学计量等许多新的科学领域。
本论文主要对光参量产生及其光谱特性进行了系统的理论研究,主要内容及创新工作包括:
1.光参量产生(OPG)基本理论分析:首先系统分析了光参量产生过程的物理机制——三波混频的耦合波方程,并理论推导了归一化的方程表达式和小信号近似解;接着分析了光参量产生的信号源-参量噪声的理论模型,然后详细讨论了基于BBO晶体的光参量产生过程中的相位匹配和相位失配,群速匹配和时间走离效应,并且给出了光参量产生的参量带宽和增益带宽的理论计算模型。
2.基于单晶体高增益体制的光参量超荧光产生的理论分析,具体给出了最佳信号光波长成分的单脉冲能量的的理论计算模型。首先阐述了高增益体制的定义,计算了光参量噪声信号源的光强度;数值模拟了光参量产生过程中的光谱成分和对应的非共线角的变化范围,并且理论计算了群速失配最小时的最佳的光谱成分的变化曲线和最佳的非共线角度的变化曲线;利用小信号输入和高增益放大的光参量放大模型,充分考虑了影响光参量产生的过程的两个干扰源-波长的变化和非共线角度的变化,利用二重积分对光参量产生的能量进行了计算,最终给出了定性和定量的单脉冲能量计算结果。
3.利用波长为0.532μm抽运光脉冲和BBO晶体在Ⅰ类(e→o+o)非共线相位匹配的特征参数,采用放大传递函数理论模拟和分析了基于自发参量下转换产生参量荧光的光谱分布特性,结果表明:对于非简并态,随着抽运光相位匹配角增大荧光单色成分(以波长为0.8μm为例)从晶体输出的角度变大,从而导致荧光空间强度角分布表现为增大趋势,而整个荧光光谱成分分布(以0.7μm-2.1μm为例)是从分散分布逐渐倾向于连续的弱分布的趋势;对于相位匹配角增大到某一范围内时,简并态附近出现荧光光谱具有宽带宽集中分布的特征,采用两种不同的抽运光脉冲(波长分别为0.532μm和0.4μm)进行对比分析发现在不同的抽运光脉冲情况下都存在此特征;关于相位匹配角的变化对于简并态附近光谱成分集中分布区域形状和强弱程度变化的敏感特征,同时采用放大传递函数和光谱成分概率分布函数两种不同理论的数值模拟结果一致,微小的相位匹配角变化导致其荧光光谱分布的显著变化。
Optical parametric generation (OPG) is the combination effects of the pump photon and quantum noise on nonlinear crystal. The photon-pair of the down-conversion are highly correlated in time, space, polarization and frequency. The spectrum of the generated photon is distributed widely from the pump-frequency to the resonance frequency of the lattice. It's shown that the photon-pair has potential application in the region of optical parametric oscillation (OPO), optical parametric amplification, quantum communication and optical metrology etc.
The main contents and innovations are summarized as follows:
1) A theoretical investigation on single BBO based femtosecond optical parametric generation (OPG) is performed. Started from analyzing the physical process of OPG in theory—a three-wave-mixing coupled wave equation, a normalized equation and the small-signal approximate solution are given; following is a discussion on the theoretical model of parametric noise, the signal source for OPG. Sequently the phase matching and mismatching, group velocity matching and temporal walk-off effect in the OPG process based on BBO crystal are detailedly analyzed, with a theoretical model on the OPG parametric bandwidth and gain bandwidth established.
2) The technique of single crystal based high gain OPG has been investigated, with the theoretical computational model of power and bandwidth established. Firstly, the definition of high gain mechanism is demonstrated; secondly, the optical wave component and the possible range of corresponding output noncollinear angle are presented. Since the minimum group velocity mismatch corresponds to the longest walk-off distance, also presented are the variation of the best noncollinear angle and the curves for the ideal optical wave components that have the longest optical parametric interaction; then, the intensity of the signal of OPG and noise from OPG are computed. With the model for small-signal-input and high-gain-output optical parametric amplification adopted and consideration of two disturbing sources in OPG, variation of wavelength and angle variation of the optical vector, the output power of OPG are obtained via double integral. Finally, the quantitative and qualitative power and bandwidth of OPG are presented.
3) With the characteristic parameters for pump pulses at a wavelength of 0.532μm and type-I BBO crystal(e→o+o) working under noncollinear phase matching, the parametric fluorescence distribution generated by spontaneous parametric down conversion is simulated and analyzed via amplification transfer function theory. The result exhibits that for nondegenerate state, the increase of pump phase matching angle leads to the increase of the output angle of the monochromatic component(take the 0.8μm component for instance) in the fluorescence, thus a increasing trend in the spatial intensity angular distribution of the fluorescence and a trend from discrete distribution to continuous weak distribution in the whole fluorescence spectrum distribution(take the 0.7μm -2.1μm for instance); with the increment of phase matching angle toward a certain range, a broadband concentrated fluorescence spectrum distribution shows around degenerate state, then an analytical comparison between two different pump pulses(with wavelength of 0.532μm and 0.4μm) shows that the same distribution exist in terms of different pump wavelengths; Furthermore, via amplification transfer function theory and spectrum component probability distribution function theory respectively, the numerical simulations on the concentrated spectrum distribution profile and the sensitivity of intensity variation induced by the variation of phase matching angle near degeneracy has reached an unanimous result that a tiny change of phase matching angle leads to an apparent change in the fluorescence spectrum distribution.
本论文主要对光参量产生及其光谱特性进行了系统的理论研究,主要内容及创新工作包括:
1.光参量产生(OPG)基本理论分析:首先系统分析了光参量产生过程的物理机制——三波混频的耦合波方程,并理论推导了归一化的方程表达式和小信号近似解;接着分析了光参量产生的信号源-参量噪声的理论模型,然后详细讨论了基于BBO晶体的光参量产生过程中的相位匹配和相位失配,群速匹配和时间走离效应,并且给出了光参量产生的参量带宽和增益带宽的理论计算模型。
2.基于单晶体高增益体制的光参量超荧光产生的理论分析,具体给出了最佳信号光波长成分的单脉冲能量的的理论计算模型。首先阐述了高增益体制的定义,计算了光参量噪声信号源的光强度;数值模拟了光参量产生过程中的光谱成分和对应的非共线角的变化范围,并且理论计算了群速失配最小时的最佳的光谱成分的变化曲线和最佳的非共线角度的变化曲线;利用小信号输入和高增益放大的光参量放大模型,充分考虑了影响光参量产生的过程的两个干扰源-波长的变化和非共线角度的变化,利用二重积分对光参量产生的能量进行了计算,最终给出了定性和定量的单脉冲能量计算结果。
3.利用波长为0.532μm抽运光脉冲和BBO晶体在Ⅰ类(e→o+o)非共线相位匹配的特征参数,采用放大传递函数理论模拟和分析了基于自发参量下转换产生参量荧光的光谱分布特性,结果表明:对于非简并态,随着抽运光相位匹配角增大荧光单色成分(以波长为0.8μm为例)从晶体输出的角度变大,从而导致荧光空间强度角分布表现为增大趋势,而整个荧光光谱成分分布(以0.7μm-2.1μm为例)是从分散分布逐渐倾向于连续的弱分布的趋势;对于相位匹配角增大到某一范围内时,简并态附近出现荧光光谱具有宽带宽集中分布的特征,采用两种不同的抽运光脉冲(波长分别为0.532μm和0.4μm)进行对比分析发现在不同的抽运光脉冲情况下都存在此特征;关于相位匹配角的变化对于简并态附近光谱成分集中分布区域形状和强弱程度变化的敏感特征,同时采用放大传递函数和光谱成分概率分布函数两种不同理论的数值模拟结果一致,微小的相位匹配角变化导致其荧光光谱分布的显著变化。
Optical parametric generation (OPG) is the combination effects of the pump photon and quantum noise on nonlinear crystal. The photon-pair of the down-conversion are highly correlated in time, space, polarization and frequency. The spectrum of the generated photon is distributed widely from the pump-frequency to the resonance frequency of the lattice. It's shown that the photon-pair has potential application in the region of optical parametric oscillation (OPO), optical parametric amplification, quantum communication and optical metrology etc.
The main contents and innovations are summarized as follows:
1) A theoretical investigation on single BBO based femtosecond optical parametric generation (OPG) is performed. Started from analyzing the physical process of OPG in theory—a three-wave-mixing coupled wave equation, a normalized equation and the small-signal approximate solution are given; following is a discussion on the theoretical model of parametric noise, the signal source for OPG. Sequently the phase matching and mismatching, group velocity matching and temporal walk-off effect in the OPG process based on BBO crystal are detailedly analyzed, with a theoretical model on the OPG parametric bandwidth and gain bandwidth established.
2) The technique of single crystal based high gain OPG has been investigated, with the theoretical computational model of power and bandwidth established. Firstly, the definition of high gain mechanism is demonstrated; secondly, the optical wave component and the possible range of corresponding output noncollinear angle are presented. Since the minimum group velocity mismatch corresponds to the longest walk-off distance, also presented are the variation of the best noncollinear angle and the curves for the ideal optical wave components that have the longest optical parametric interaction; then, the intensity of the signal of OPG and noise from OPG are computed. With the model for small-signal-input and high-gain-output optical parametric amplification adopted and consideration of two disturbing sources in OPG, variation of wavelength and angle variation of the optical vector, the output power of OPG are obtained via double integral. Finally, the quantitative and qualitative power and bandwidth of OPG are presented.
3) With the characteristic parameters for pump pulses at a wavelength of 0.532μm and type-I BBO crystal(e→o+o) working under noncollinear phase matching, the parametric fluorescence distribution generated by spontaneous parametric down conversion is simulated and analyzed via amplification transfer function theory. The result exhibits that for nondegenerate state, the increase of pump phase matching angle leads to the increase of the output angle of the monochromatic component(take the 0.8μm component for instance) in the fluorescence, thus a increasing trend in the spatial intensity angular distribution of the fluorescence and a trend from discrete distribution to continuous weak distribution in the whole fluorescence spectrum distribution(take the 0.7μm -2.1μm for instance); with the increment of phase matching angle toward a certain range, a broadband concentrated fluorescence spectrum distribution shows around degenerate state, then an analytical comparison between two different pump pulses(with wavelength of 0.532μm and 0.4μm) shows that the same distribution exist in terms of different pump wavelengths; Furthermore, via amplification transfer function theory and spectrum component probability distribution function theory respectively, the numerical simulations on the concentrated spectrum distribution profile and the sensitivity of intensity variation induced by the variation of phase matching angle near degeneracy has reached an unanimous result that a tiny change of phase matching angle leads to an apparent change in the fluorescence spectrum distribution.
引文
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[19]S.Acco,P.Blau,and A.A.Arie "Output power and spectrum of optical parametric generator in the superfluorescent regime" Opt.Lett 2008 33 1264
[20]M.C.Lefort,B.Afeyan,and M.M.Fejer "Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers",J.Opt.Soc.Am.B 2008 25(9)
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[1]石顺祥,陈国夫,赵卫,刘继芳.非线性光学.西安:西安电子科技大学出版社,2003.147-148
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[6]R.L.Ryer and S.E.Harris,"Power and bandwidth of spontaneous parametric emission" Phy.Rev.1968 168,1064-1068
[7]刘军,魏晓峰,黄小军,陈慰宗,袁晓东,王晓东,曾小明,郭仪,吕志伟, “BBO,LBO,KDP晶体光参量啁啾脉冲放大特性的比较研究,”强激光与粒子束,2003,15(6),555-558
[8]夏江帆,魏志义,张杰,“BBO晶体中非共线参量过程的带宽与增益特性研究,” 物理学报,2000,49(2),256-261
[9]冷雨欣,金石琦,彭家晖,杨晓东,徐至展,“BBO晶体Ⅰ型非共线相位匹配参量放大研究,”中国激光,2001,28(11),977-980.
[10]L.H.Jun,Z.Wei,Y.Y.Long,W.H.Ying,W.Y.Shan,C.G.Fu,"Matching of both group-velocity and pulse-front for ultrabroadband three-wave-mixing with noncollinear angularly dispersed geometry," Applied Physics B 2006,82,585-594
[11]L.H.Jun,Z.Wei,W.H.Ying,L.X.Li,W.Y.Shan,"Ultra-broadband optical parametric chirped-pulse amplification by matching of both group-velocity and pulse-front," Optics Communications,2005 261,163-168
[12]Z.Wei,L.H.Jun,W.Y.Shan,W.H.Ying,C.Zhao,C.G.Fu,"Pulse-front matched ultra-broadband optical parametric chirped pulse amplifier for sub-12fs pulse," Chinese Physics,2005 14(2),359-365
[13]刘红军,陈国夫,赵卫,王屹山,王涛,赵尚弘,“三波非共线作用参变过程的相位匹配研究,”光学学报,2002,129-133.
[14]刘红军,赵卫,王红英,李小莉,王屹山,“相位失配补偿的超宽带OPCPA,”第五届全国夜视技术交流会暨2005年全国瞬态光学与光子技术交流会会议论文集,2005,370-376.
[15]S.Y.Beak and Y.H.Kim "Spectral properities of entangled photon pairs generated via frequency-degenerate type-Ⅰ spontaneous parametric down-conversion" Phys.Rev.A 2008 77 043807
[16]A.Penzkofer,H.J.Lehmeier "Theoretical investigation of noncollinear phase-matched parametric four-photon amplification of ultrashort light pulses in isotropic media" Optical and Quantum Electronics 1993 25 815
[17]P.D.Trapnani,A.Andreoni,C.Solcia et al "Matching of group velocities in three-wave parametric interaction with femtosecond pulses and application to traveling-wave generations",J.Opt.Soc.Am.B 1995 12 2237-2244
[18]R.Danielius,A.Piskarskas,and A.Stabinis "Traveling-wave parametric generation of widely tunable,highly coherent femtosecsond light pulses" J.Opt.Soc.Am.B 1993 10 2222-2232
[19]C.Manzoni,G.Cirmi,and D.Brida et al "Optical-parametric-generation process driven by femtosecond pulses:Timing and carrier-envelope phase properties"Phy.Rev.A 2009 79 033818
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[22]刘红军,陈国夫,赵卫,王屹山,“三波混频光参量放大器中带宽的研究,”中国激光,2002,29(8),680-686.
[1]T.G.Giallorenzi and C.L.Tang "Quantum Theory of Spontaneous Parametric Scattering of Intense Light",Phys.Rev.1968 166 225
[2]D.A.Kleinman "Theory of Optical parametric Nois",Phys.Rev.1968 174 1027
[3]C.L.Tang Quantum electronics:A treatise.Volume 1-Nonlinear Optics.Part A.(A76-42001 21-74) New York,1975 Academic Press,Inc.,419)
[4]S.Acco,P.Blau,and A.A.Arie "Output power and spectrum of optical parametric generator in the superfluorescent regime" Opt.Lett 2008 33 1264
[5]W.D.Kulatilaka,T.N.Anderson,T.L.Bougher,and R.P.Lucht,"Development of injection-seeded,pulsed optical parametric generator/oscillator systems for high-resolution spectroscopy," Appl.Phys.B,2005 80,669-680
[6]V.Petrov,F.Seifert,and F.Noack,"High repetition rate traveling wave optical parametric generator producing nearly bandwidth limited 50 fs infrared light pulses," Appt.Phy.Lett.1994 66,268-270
[7]F.Devaux,E.Lantz,"Ultrahith-speed imaging by parametric image amplification"Opt.Commun 1995 114 295
[8]F.Devaux and E.Lantz "Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal," Eur.Phys.J.D 2000,8117
[9]R.L.Ryer and S.E.Harris,"Power and bandwidth of spontaneous parametric emission" Phy.Rev.1968 168,1064-1068
[10]V.Krylov and A.Kalintsev et.al "Noncollinear parametric generation in LiIO_3 and β-barium borate by frequency-doubled femtosecond Ti:sapphire laser pulses",Opt.Lett,1995 20(2)
[11]P.D.Trapnani,A.Andreoni,C.Solcia et al "Matching of group velocities in three-wave parametric interaction with femtosecond pulses and application to traveling-wave generations",J.Opt.Soc.Am.B 1995 12 2237-2244
[12]P.D.Trapnani,A.Andreoni,G.P.Banfi et al "Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation" Phys.Rev.A 1995 513164
[13]M.Jing,Z.R.Bing,L.Bin et al "Group velocity self-matching in noncollinear optical parametric generation with a type-Ⅰ phase-matched BBO crystal",Acta.Phys.Sin.2005 54 4765(in chinese)[马晶,章若冰,刘博等“BBO I类相位匹配非共线参量产生中的群速自匹配”物理学报 2005 54 4765]
[14]黄小军,张树葵,袁晓东,王晓东,唐军,曾小明,魏晓峰,“光参量啁啾脉冲放大增益特性研究,”强激光与粒子束,2002,14(4),516-520
[15]H.Yoshida,E.Ishii,R.Kodama,H.Fujita,Y.Kitagawa,Y.Izawa,and T.Yamanaka,"High-power and high-contrast optical parametric chirped pulse amplification in β-BaB_2O_4 crystal," Opt.Lett.2003 15(4),257-259
[16]I.N.Ross,P.Matousek,G.H.C.New,and K.Osvay,"Analysis and optimization of optical parametric chirped pulse amplification," J.Opt.Soc.Am.B,2002 19(12),2945-2956
[17]刘红军,陈国夫,赵卫,王屹山,“三波混频光参量放大器中带宽的研究,”中国激光,2002 29(8),680-686
[18]石顺祥,陈国夫,赵卫,刘继芳.非线性光学.西安:西安电子科技大学出版社,2003.389-390.
[19]S.Acco,P.Blau,and A.A.Arie "Output power and spectrum of optical parametric generator in the superfluorescent regime" Opt.Lett 2008 33 1264
[20]M.C.Lefort,B.Afeyan,and M.M.Fejer "Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers",J.Opt.Soc.Am.B 2008 25(9)
[1]T.G.Giallorenzi and C.L.Tang "Quantum Theory of Spontaneous Parametric Scattering of Intense Light",Phys.Rev.1968 166 225
[2]D.A.Kleinman"Theory of Optical parametric Nois",Phys.Rev.1968 174 1027
[3]C.L.Tang Quantum electronics:A treatise.Volume 1-Nonlinear Optics.Part A.(A76-42001 21-74) New York,1975 Academic Press,Inc.,419)
[4]W.Louisell,A.Yariv,A.E.Siegman "Quantum Fluctuations and Noise in Parametric Processes.I." Phys.Rev.1961 124 1646
[5]D.Magde and H.Mahr "Study in ammonium dihydrogen phosphate of spontaneous parametric interaction tunable from 4400 to 16000(?)" Phys.Rev.Lett.1967 18 905
[6]S.Haris,M.K.Oshman,R.L.Byer "Obeservation of tunable optical parametric fluorescence" Phys.Rev.Lett.1967 18 732
[7]J.E.Pearson,A.Yariv and U.Ganiel "Observation of parametric Fluorescence an Oscillation in the infrared" Appl.Opt.1973 12 1165
[8]P.D.Trapani,A.Andreoni,G.P.Banfi et al "Group-velocity self-matching of femtosecond pulses in noncollinear parametric generation" Phys.Rev.A 1995 51 3164
[9]F.Devaux and E.Lantz "Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal," Eur.Phys.J.D 2000(8)117
[10]J.Ma,R.B.Zhang,B.Liu et al "Group velocity self-matching in noncollinear optical parametric generation with a type-Ⅰ phase-matched BBO crystal",Acta Phys.Sin.2005 54 4765(in chinese)[马晶,章若冰,刘博等“BBO I类相位匹配非共线参量产生中的群速自匹配”物理学报 2005 54 4765]
[11]M.N.Hou,H.J.Liu,W.Zhao et al "Tunable parametric fluorescence using a single crystal",Acta phys.sin.2007 56 5872(in chinese)[侯米娜,刘红军,赵卫等“基于单晶体的可调谐参量超荧光的产生”物理学报 2007 54 5872]
[12]S.Acco,P.Blau,and A.Arie "Output power and spectrum of optical parametric generator in the superfluorescent regime" Opt.Lett.2008 33 1264
[13]D.Bouwmeester,J.W.Pan,K.Mattle et al Phil.Trans.R.Soc.Lond.A 1998356 1733
[14]M.D.Angelo,M.V.Chekhova,Y.Shih "Two-Photon Diffraction and Quantum Lithography" Phys.Rev.Lett.2001 87,013602
[15]A.R.Altman,K.G.Koprulu,E.Corndorf,et al "Quantum Imaging of Nonlocal Spatial Correlations Induced by Orbital Angular Momentum" Phys.Rev.Lett.2005,94,123601
[16]X.J.Jia,X.L.Su,Q.Pan et al "Experimental generation of two EPR entangled states with classical coherence",Acta Phys.Sin.2005 54 2717(in chinese)[贾晓军,苏晓龙,潘庆等“具有经典相干性的两组EPR纠缠态光场的实验产生”物理学报 2005 54 2717]
[17]S.Y.Beak and Y.H.Kim 2008 "Spectral properities of entangled photon pairs generated via frequency-degenerate type-Ⅰ spontaneous parametric down-conversion" Phys.Rev.A 77 043807
[18]H.J.Liu,W.Zhao,Y.Yang et al "Matching of both group-velocity and pulse-front for ultrabroadband three-wave-mixing with noncollinear angularly dispersed geometry" Appl.Phys.B 2006 82 585
[19]H.J.Liu,G.F.Chen,W.Zhao et al "Phase matching analysis of noncollinear optical parametric process in nonlinear anisotropic crystals" Opt.Commun.2001197 507
[20]A.Penzkofer,H.J.Lehmeier "Theoretical investigation of noncollinear phase-matched parametric four-photon amplification of ultrashort light pulses in isotropic media" Optical and Quantum Electronics 1993 25 815
[21]J.F.Xia,Z.Y.Wei,J.Zhang "Bandwidth and gain of BBO in noncollinear optical parametric process" Acta Phys.Sin.2000 49 0256(in chinese)[夏江帆,魏志义,张杰物理学报 2000 49 0256]
[22]D.N.Schimpf,J.Rothhardt,J.Limpert et al "Theoretical analysis of the gain bandwidth for noncollinear parametric amplication of ultrafast pulses" J.Opt.Soc.Am.B 2007 24,2837
[23]F.Devaux and E.Lantz "Parametric amplification of a polychromatic image" J.Opt.Soc.Am.B 1995 12,2245
[24]W.P.Grice and I.A.Walmsley "Spectral infromation and distinguishability in type-Ⅱ down-conversion with a broadband pump Phys.Rev A 1997 56 1627
[25]M.H.Rubin "Tanseverse correlation in optical spontaneous parametric down-convesion" Phys.Rev.A 1996 54,5349
[26]Y.H.Kim and W.P.Grice "Measurement of the spectral properties of the two-photon state generated via type-Ⅱ spontaneous parametric down-conversion" Opt.Lett 2005 30 908
[27]Z.G.Lu,H.J.Liu,F.Jing et al "Theoretical analysis of spectral properties of parametric fluorescence via spontaneous parametric down-conversion",Acta.Physica.Sinica 2009 58(7) 卢宗贵,刘红军,赵卫等,“基于自发参量下转换产生参量荧光的光谱分布特性理论分析”物理学报 2009 58(7)