随机激光器的偏振依赖特性与阈值特性的理论研究
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摘要
随机激光器是利用增益无序介质中的受激辐射原理所形成的一种新型的激光器,它是目前激光物理界的一个研究热点,具有广泛的应用前景。从随机激光现象被实验所证实到现在的10多年里,研究工作者们进行了大量的实验和理论研究。本文的主要内容包括:
(1)综述了随机激光器的概念及其特点,以及当前随机激光器的各种实验现象和理论模型。
(2)介绍了时域有限差分法(Finite Difference Time Domain, FDTD)的基本原理和思想方法,以及对稳定性条件、PML吸收边界条件的设定、激励源设置等问题的分析和处理。
(3)研究了一维随机激活介质中激光模式的输出强度与抽运速率之间的关系,对准态模式的局域化程度进行了讨论,并分析了局域化程度对于模式阈值大小的影响作用。
(4)研究了具有不同颗粒数目的一维随机介质中的准态模阈值特性,并分析了随机激光器模式的阈值随散射颗粒个数的增多而降低的原因。.
(5)采用激光时域理论模型分别对TE偏振与TM偏振的二维随机激光器进行了性质分析,考察了在同一随机构型下不同偏振态在频率、辐射强度、辐射谱线宽度以及阈值大小等方面的区别,表明了TM模比TE模具有更小的抽运阈值;同时还发现了在各向异性介质中,随着颗粒光轴方向的无序性的增大,阈值有减小的趋势。
Random laser, which is a new-type laser, is based on the lasing phenomenon in the amplifying disordered media. It has been a hot subject in laser physics and it presents an important value in application. Since random laser phenomenon was explained by experiments about 10 years before, researchers have done lots of experimental and theoretical work on it.
The main contents of this thesis are summarized as follows:
(1) A summary of the concept and characteristic of random lasers is given, and some theoretical models and experimental results at present are expatiated.
(2) The principle and thoughtway of Finite Difference Time Domain (FDTD) method is introduced , and then, we analyze the conditions of stability、Perfectly Matched Layer (PML) boundary conditions and the setting of excitation sources.
(3) The output intensity of a lasing mode varying with the pumping rate is simulated for a one-dimensional random active medium, and the mode’s localization extent is also discussed. Subsequently, the influence of the localization extent on the pumping threshold of quasi-state modes is also analyzed.
(4) The quasi-state’threshold in one-dimensional random media which has different number of particles for scattering is investigated, and we also analyzed the reason why the value of the pumping threshold of random lasers’quasi-state modes will decrease when the number of particles is increased.
(5) Based on the time dependent theory of random lasers, the characteristic of the two-dimensional random laser for both transverse electric and transverse magnetic polarization fashions is analyzed, and we investigate the difference between the two polarization fashions in the same random pattern , such as the modes’frequency、the intensity of radiation、the width of the spectrum、the value of the pumping threshold and so on. The phenomenon that TM modes have a lower value of the pumping threshold than TE modes is found. Finally, we indicated that, as the increase of the orientational disorder of particles’optical axes in the anisotropic media, the laser threshold would decrease.
(1)综述了随机激光器的概念及其特点,以及当前随机激光器的各种实验现象和理论模型。
(2)介绍了时域有限差分法(Finite Difference Time Domain, FDTD)的基本原理和思想方法,以及对稳定性条件、PML吸收边界条件的设定、激励源设置等问题的分析和处理。
(3)研究了一维随机激活介质中激光模式的输出强度与抽运速率之间的关系,对准态模式的局域化程度进行了讨论,并分析了局域化程度对于模式阈值大小的影响作用。
(4)研究了具有不同颗粒数目的一维随机介质中的准态模阈值特性,并分析了随机激光器模式的阈值随散射颗粒个数的增多而降低的原因。.
(5)采用激光时域理论模型分别对TE偏振与TM偏振的二维随机激光器进行了性质分析,考察了在同一随机构型下不同偏振态在频率、辐射强度、辐射谱线宽度以及阈值大小等方面的区别,表明了TM模比TE模具有更小的抽运阈值;同时还发现了在各向异性介质中,随着颗粒光轴方向的无序性的增大,阈值有减小的趋势。
Random laser, which is a new-type laser, is based on the lasing phenomenon in the amplifying disordered media. It has been a hot subject in laser physics and it presents an important value in application. Since random laser phenomenon was explained by experiments about 10 years before, researchers have done lots of experimental and theoretical work on it.
The main contents of this thesis are summarized as follows:
(1) A summary of the concept and characteristic of random lasers is given, and some theoretical models and experimental results at present are expatiated.
(2) The principle and thoughtway of Finite Difference Time Domain (FDTD) method is introduced , and then, we analyze the conditions of stability、Perfectly Matched Layer (PML) boundary conditions and the setting of excitation sources.
(3) The output intensity of a lasing mode varying with the pumping rate is simulated for a one-dimensional random active medium, and the mode’s localization extent is also discussed. Subsequently, the influence of the localization extent on the pumping threshold of quasi-state modes is also analyzed.
(4) The quasi-state’threshold in one-dimensional random media which has different number of particles for scattering is investigated, and we also analyzed the reason why the value of the pumping threshold of random lasers’quasi-state modes will decrease when the number of particles is increased.
(5) Based on the time dependent theory of random lasers, the characteristic of the two-dimensional random laser for both transverse electric and transverse magnetic polarization fashions is analyzed, and we investigate the difference between the two polarization fashions in the same random pattern , such as the modes’frequency、the intensity of radiation、the width of the spectrum、the value of the pumping threshold and so on. The phenomenon that TM modes have a lower value of the pumping threshold than TE modes is found. Finally, we indicated that, as the increase of the orientational disorder of particles’optical axes in the anisotropic media, the laser threshold would decrease.
引文
[1]周炳琨,高以智,陈倜嵘等.激光原理. (第四版).北京:国防工业出版社, 2002. 9~22
[2] D. Rafizadeh, J. P. Zhang, S. C. Hagness et al. Waveguide-coupled AlGaAs/ GaAs microcavity ring and disk resonator with high finesse and 21.6-nm free spectral range. Optics Lett, 1997, 22 (16): 1244~1246
[3] F. C. Blom, D.R.van Dijk, H. J. W. M. Hoekstra et al. Experimental study of integrated-optics microcavity resonators: Toward an all-optical switching device. Applied Physics Lett, 1997, 71(6): 747~749
[4] Yamamoto, R. Slusher. Optical process in microcavities. Phys Today, 1993, 46(10): 66~77
[5] H. Cao. Lasing in random media. Wave in Random Media, 2003, 13:1~39
[6] V. M. Alpalkov, M. E. Raikh, B. Shapiro. Random resonator and prelocalizated mode in disorder dielectric films, Phys. Rev. Lett., 2002, l89: 016802
[7]刘劲松,王春,吕健滔等.随机激光器的准态模理论.中国激光(增刊), 2004 31(4): 26~28
[8] X. Y. Jiang, C. M. Soukoulis. Time dependent theory for random lasers. Phys. Rev. Lett., 2000, 85(1): 70~73
[9] C. Vanneste, P. Sebbah. Selective of localized modes in active random media. Phys. Rev. Lett., 2001, 87: 183903
[10] H. Cao, Y. G. Zhao, H. C. Ong et al. Far-field characteristics of random lasers. Phys.Rev. B, 1999, 59: 15107~15111
[11] V. S. Letokhov. Generation of light a scattering medium with negative resonance absorption. Sov. Phys., 1968, 26(8): 835~840
[12] N. M. Lawandy, R. M. Sslschandran, A.S.Lgomes et al. Laser action in strongly scattering media. Nature, 1994, 368: 436~43
[13] N. M. Lawandy, D. S. Wiersma, A. Lagendijk. Random laser. Nature, 1995, 373: 203~204
[14] H. Cao, Y. G. Zhao, S. T. Ho et al. Random Laser Action in Semiconductor Powder. Phys. Rev. Lett.,1999, 82(11): 2278~2281
[15] H. Cao, J. Y. Xu, D. Z. Zhang et al. Spatial Confinement of Laser Light in Active Random Media. Phys. Rev. Lett., 2000, 84 (24): 5584~5587
[16] H. Cao, J. Y. Xu, E. W. Seelig et al. Microlaser made of disorder media. Appl. Phys. Lett., 2000, 76(21): 2997~2999
[17] H. Cao, Y. Ling, J. Y. Xu et al. Photon statistics of lasers with resonant feedback. Phys. Rev. Lett., 2001, 86: 4524~4527
[18] G. A. Berg, M. Kempe, A. Z. Genack. Dynamics of stimulate emission from random media. Phys. Rev.E , 1997, 56: 6118~6124
[19] C. M. Soukoulis, X. Y. Jiang, J. Y. Xu et al. Dynamic response and relaxation oscillations in random lasers. Phys. Rev. B, 2002, 65: 041103~041107
[20] P. W. Anderson. Absence of diffusion in certain random lattices. Phys. Rev., 1958, 109: 1492~1505
[21] Yu. Zyuzin. Transmission fluctuations and spectral rigidity of lasing states in a random amplifying medium. Phys. Rev .E, 1995, 51: 5274~5278
[22] Deng, D. S. Wiersma. Coherent backscattering of light from random media with inhomogeneous gain coefficient. Phys. Rev. B, 1997, 56: 178~181
[23] V. Tutov, A. A. Maradudin, T. A. Leskova. Scattering of light from an amplifying medium bounded by a randomly rough surface. Phys. Rev. B, 1999, 60: 12692~12704
[24] D. S. Wiersma, M. P. van Albada, Ad Lagendijk. Coherent Backscattering of Light fromAmplifying Random Media. Phys. Rev. Lett,. 1995, 75: 1739~1742
[25] P. C. de Oliveira, A. E. Perkins, N. M. Lawandy. Coherent backscattering from high-gain scattering media. Opt. Lett, 1996, 21: 1685~1687
[26] G. Zacharakis, N. A. Papadogiannis, T. G. Papzoglou. Random lasing following two-photon excitation of highly scattering gain media. Appl. Phys. Lett., 2002, 81: 2511~2513
[27] B. Liu, A. Yamilov, Y. Ling et al. Dynamic nonlinear effect on lasing in a random medium. Phys. Rev. Lett., 2003, 91: 063903
[28] D. S. Wiersma, S. Cavalieri. A temperature-tunable random laser. Nature, 2001, 414: 708~709
[29] D. S. Wiersma, M. Colocci, R. Righini. Temperature-control light diffusion in random media. Phys. Rev. A, 2001, 64: 144208
[30]葛德彪,闫玉波.电磁波有限使用差分法. (第一版).西安:西安电子科技大学出版社, 2002. 8~89
[31]王长清,祝西里.电磁场计算中的有限使用差分方法. (第一版).北京:北京大学出版社, 1994. 1~90
[32]高本庆.时域有限差分法. (第一版).北京:国防工业出版社, 1995. 1~106
[33] J. P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves. J. Computational Physics, 1994, 114(1): 185~200
[34] J. P. Berenger. Perfectly matched layer for FDTD solution of wave-structure interaction problems. IEEE Trans. Antennas and Propagation, 1996, 51(1): 110~117
[35] J. P. Berenger. A perfectly matched layer for free-space simulations in finite-difference comuter codes. Annales des telecommunications, 1996, 51(1): 36~46
[36] M. Qiu, S. He. Numerical method for computing defect modes in two-dimensional photonic crystals with dielectric or metallic inclusions. Phys. Rev. B., 2000, 61(19): 2871~2876
[37] S. C. Hagness, R. M. Joseph, A. Taflove. Subpicosecond electrodynamics of distributed Bragg reflector microlasers: results from finite difference time domain simulations. Radio Science, 1996, 31(4): 931~941
[38] P. Sebbah, C. Vanneste. Random laser in the localized regime. Phys. Rev. B, 2002, 66(14): 4202
[39]王可嘉,王宏,刘劲松.随机激光器的最新进展.激光与光电子学进展, 2003, 40(2): 51~54
[40] A. L. Burin, M. A. Ratner, H. Cao et al. Model for a random laser. Phys. Rev. Lett, 2001, 87(21): 5503
[41] H. Cao, J. Y. Xu, Y. Ling et al. Mode repulsion and mode coupling in random lasers. Phys. Rev. B., 2003, 67(16): 1101
[42]刘劲松,刘海,王春等.二维随机介质中准态模的频谱时间演化特性.物理学报, 2005, 53: 3117~3121
[43]刘海,刘劲松,王春.不同分布区域的散射颗粒对二维随机激光器腔内各模式的影响.光学与光电子技术, 2006, 4(1): 34~37
[44]刘劲松,王宏.随机激光器中准态模式的阈值与其局域化程度的关系.物理学报,2004, 53(12): 4224~4227
[45] Ito. T, Tomita. M. Polarization-dependent laser action in a two-dimensional random medium. Phys. Rev. E, 2002, 66: 027601
[46]郁道银,谈恒英.工程光学. (第一版).北京:机械工业出版社, 2003. 179~287
[2] D. Rafizadeh, J. P. Zhang, S. C. Hagness et al. Waveguide-coupled AlGaAs/ GaAs microcavity ring and disk resonator with high finesse and 21.6-nm free spectral range. Optics Lett, 1997, 22 (16): 1244~1246
[3] F. C. Blom, D.R.van Dijk, H. J. W. M. Hoekstra et al. Experimental study of integrated-optics microcavity resonators: Toward an all-optical switching device. Applied Physics Lett, 1997, 71(6): 747~749
[4] Yamamoto, R. Slusher. Optical process in microcavities. Phys Today, 1993, 46(10): 66~77
[5] H. Cao. Lasing in random media. Wave in Random Media, 2003, 13:1~39
[6] V. M. Alpalkov, M. E. Raikh, B. Shapiro. Random resonator and prelocalizated mode in disorder dielectric films, Phys. Rev. Lett., 2002, l89: 016802
[7]刘劲松,王春,吕健滔等.随机激光器的准态模理论.中国激光(增刊), 2004 31(4): 26~28
[8] X. Y. Jiang, C. M. Soukoulis. Time dependent theory for random lasers. Phys. Rev. Lett., 2000, 85(1): 70~73
[9] C. Vanneste, P. Sebbah. Selective of localized modes in active random media. Phys. Rev. Lett., 2001, 87: 183903
[10] H. Cao, Y. G. Zhao, H. C. Ong et al. Far-field characteristics of random lasers. Phys.Rev. B, 1999, 59: 15107~15111
[11] V. S. Letokhov. Generation of light a scattering medium with negative resonance absorption. Sov. Phys., 1968, 26(8): 835~840
[12] N. M. Lawandy, R. M. Sslschandran, A.S.Lgomes et al. Laser action in strongly scattering media. Nature, 1994, 368: 436~43
[13] N. M. Lawandy, D. S. Wiersma, A. Lagendijk. Random laser. Nature, 1995, 373: 203~204
[14] H. Cao, Y. G. Zhao, S. T. Ho et al. Random Laser Action in Semiconductor Powder. Phys. Rev. Lett.,1999, 82(11): 2278~2281
[15] H. Cao, J. Y. Xu, D. Z. Zhang et al. Spatial Confinement of Laser Light in Active Random Media. Phys. Rev. Lett., 2000, 84 (24): 5584~5587
[16] H. Cao, J. Y. Xu, E. W. Seelig et al. Microlaser made of disorder media. Appl. Phys. Lett., 2000, 76(21): 2997~2999
[17] H. Cao, Y. Ling, J. Y. Xu et al. Photon statistics of lasers with resonant feedback. Phys. Rev. Lett., 2001, 86: 4524~4527
[18] G. A. Berg, M. Kempe, A. Z. Genack. Dynamics of stimulate emission from random media. Phys. Rev.E , 1997, 56: 6118~6124
[19] C. M. Soukoulis, X. Y. Jiang, J. Y. Xu et al. Dynamic response and relaxation oscillations in random lasers. Phys. Rev. B, 2002, 65: 041103~041107
[20] P. W. Anderson. Absence of diffusion in certain random lattices. Phys. Rev., 1958, 109: 1492~1505
[21] Yu. Zyuzin. Transmission fluctuations and spectral rigidity of lasing states in a random amplifying medium. Phys. Rev .E, 1995, 51: 5274~5278
[22] Deng, D. S. Wiersma. Coherent backscattering of light from random media with inhomogeneous gain coefficient. Phys. Rev. B, 1997, 56: 178~181
[23] V. Tutov, A. A. Maradudin, T. A. Leskova. Scattering of light from an amplifying medium bounded by a randomly rough surface. Phys. Rev. B, 1999, 60: 12692~12704
[24] D. S. Wiersma, M. P. van Albada, Ad Lagendijk. Coherent Backscattering of Light fromAmplifying Random Media. Phys. Rev. Lett,. 1995, 75: 1739~1742
[25] P. C. de Oliveira, A. E. Perkins, N. M. Lawandy. Coherent backscattering from high-gain scattering media. Opt. Lett, 1996, 21: 1685~1687
[26] G. Zacharakis, N. A. Papadogiannis, T. G. Papzoglou. Random lasing following two-photon excitation of highly scattering gain media. Appl. Phys. Lett., 2002, 81: 2511~2513
[27] B. Liu, A. Yamilov, Y. Ling et al. Dynamic nonlinear effect on lasing in a random medium. Phys. Rev. Lett., 2003, 91: 063903
[28] D. S. Wiersma, S. Cavalieri. A temperature-tunable random laser. Nature, 2001, 414: 708~709
[29] D. S. Wiersma, M. Colocci, R. Righini. Temperature-control light diffusion in random media. Phys. Rev. A, 2001, 64: 144208
[30]葛德彪,闫玉波.电磁波有限使用差分法. (第一版).西安:西安电子科技大学出版社, 2002. 8~89
[31]王长清,祝西里.电磁场计算中的有限使用差分方法. (第一版).北京:北京大学出版社, 1994. 1~90
[32]高本庆.时域有限差分法. (第一版).北京:国防工业出版社, 1995. 1~106
[33] J. P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves. J. Computational Physics, 1994, 114(1): 185~200
[34] J. P. Berenger. Perfectly matched layer for FDTD solution of wave-structure interaction problems. IEEE Trans. Antennas and Propagation, 1996, 51(1): 110~117
[35] J. P. Berenger. A perfectly matched layer for free-space simulations in finite-difference comuter codes. Annales des telecommunications, 1996, 51(1): 36~46
[36] M. Qiu, S. He. Numerical method for computing defect modes in two-dimensional photonic crystals with dielectric or metallic inclusions. Phys. Rev. B., 2000, 61(19): 2871~2876
[37] S. C. Hagness, R. M. Joseph, A. Taflove. Subpicosecond electrodynamics of distributed Bragg reflector microlasers: results from finite difference time domain simulations. Radio Science, 1996, 31(4): 931~941
[38] P. Sebbah, C. Vanneste. Random laser in the localized regime. Phys. Rev. B, 2002, 66(14): 4202
[39]王可嘉,王宏,刘劲松.随机激光器的最新进展.激光与光电子学进展, 2003, 40(2): 51~54
[40] A. L. Burin, M. A. Ratner, H. Cao et al. Model for a random laser. Phys. Rev. Lett, 2001, 87(21): 5503
[41] H. Cao, J. Y. Xu, Y. Ling et al. Mode repulsion and mode coupling in random lasers. Phys. Rev. B., 2003, 67(16): 1101
[42]刘劲松,刘海,王春等.二维随机介质中准态模的频谱时间演化特性.物理学报, 2005, 53: 3117~3121
[43]刘海,刘劲松,王春.不同分布区域的散射颗粒对二维随机激光器腔内各模式的影响.光学与光电子技术, 2006, 4(1): 34~37
[44]刘劲松,王宏.随机激光器中准态模式的阈值与其局域化程度的关系.物理学报,2004, 53(12): 4224~4227
[45] Ito. T, Tomita. M. Polarization-dependent laser action in a two-dimensional random medium. Phys. Rev. E, 2002, 66: 027601
[46]郁道银,谈恒英.工程光学. (第一版).北京:机械工业出版社, 2003. 179~287