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自旋反转模型是目前用于分析垂直腔面发射激光器(VCSELs)非线性动力学特性最常用的理论模型, 因此该模型中相关参量的取值至关重要. 本文基于对自由运行和平行光注入时1550 nm垂直腔面发射激光器(1550 nm-VCSELs)输出特性的实验测量结果, 对描述1550 nm-VCSELs 特性的SFM中光场衰减速率k、总载流子衰减速率N、线宽增强因子, 有源介质双折射速率p、自旋反转速率s、有源介质线性色散速率a 等关键参量进行了估值. 在此基础上, 利用所测得的这些关键参量的数值, 仿真了1550 nm-VCSELs的相关输出特性, 所得结果与实验结果符合.
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关键词:
- 1550 nm垂直腔面发射激光器 /
- 平行光注入 /
- 自旋反转模型
Spin-flip model (SFM) is a mostly used approach to analyzing the nonlinear dynamics of vertical-cavity surface-emitting laser (VCSEL), and therefore the value selections of some key parameters in this model are crucial. In this work, based on experimentally measured dynamical characteristics of a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL) under free running and parallel optical injection, some key parameters (field decay rate k, total carrier decay rate N, linewidth enhancement factor , active medium birefringence rate p, spin relaxation rate s, and active medium linear dispersion rate a) are estimated. Through experimentally measuring the noise spectrum of the laser, the relaxation oscillation frequency and the damping rate of the relaxation oscillations are calculated, and the photon lifetime can be preliminary estimated. After further amending the photon lifetime by considering the effect of the gain saturation on the damping rate of the relaxation oscillations, the value of k is determined. Based on the function relation between the laser relaxation oscillation frequency and the electrical pumping, the value of N is obtained. By experimentally acquiring the dynamical distribution mapping of the laser under parallel optical injection, the minimum Hopf bifurcation point of the Hopf bifurcation curve can be found, and then the value of is roughly estimated. According to the frequency difference between the two polarization components of the laser in the measured optical spectrum, the value of p can be calculated. The value of s is obtained by using the relationship between s and p. On the basis of the above determined parameter values, the value of a can be specified by numerically simulating the optical spectrum of the laser and comparing with experimentally obtained results. Moreover, by comparing the experimentally measured dynamical mapping of optical injection VCSEL with corresponding dynamical mapping simulated on the basis of the above mentioned parameters, the value of is rectified. Finally, further simulated results agree with relevant experimental observations.-
Keywords:
- 1550 nm vertical-cavity surface-emitting lasers (1550 nm-VCSEL) /
- parallel optical injection /
- spin-flip model
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[16] Al-Seyab R, Schires K, Hurtado A, Henning I D, Adams M J 2013 IEEE J. Sel. Top. Quantum Electron. 19 1700512
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[19] Adams M J, Alexandropoulos D 2009 IEEE J. Quantum Electron. 45 744
[20] Prez P, Valle A, Noriega I, Pesquera L 2014 J. Lightwave Technol. 32 1601
[21] Wang X F, Xia G Q, Wu Z M 2009 J. Opt. Soc. Am. B: Opt. Phys. 26 160
[22] Agrawal G P, Dutta N K 1993 Semiconductor Lasers (2nd Ed.) (Boston: Kluwer Academic Publishers) pp261-262
[23] Tatham M C, Lealman I F, Seltzer C P, Westbrook L D, Cooper D M 1992 IEEE J. Quantum Electron. 28 408
[24] Barland S, Spinicelli P, Giacomelli G, Marin F 2005 IEEE J. Quantum Electron. 41 1235
[25] Press W H, Teukolsky S A, Vetterling W T, Flannery B P 1992 Numerical Recipes in Fortran 77: the Art of Scientific Computing (2nd Ed.) (Cambridge: Cambridge University Press) pp678-683
[26] Prez P, Valle A, Pesquera L 2014 J. Opt. Soc. Am. B: Opt. Phys. 31 2574
[27] Homayounfar A, Adams M J 2007 Opt. Express 15 10504
[28] Chlouverakis K E, Al-Aswad K M, Henning I D, Adams M J 2003 Electron. Lett. 39 1185
[29] Gavrielides A, Kovanis V, Erneux T 1997 Opt. Commun. 136 253
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[31] Homayounfar A, Adams M J 2007 Opt. Commun. 269 119
[32] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p76 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学(北京: 高等教育出版社) 第76页]
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[1] Miguel M S, Feng Q, Moloney J V 1995 Phys. Rev. A 52 1728
[2] Regalado J M, Prati F, Miguel M S, Abraham N B 1997 IEEE J. Quantum Electron. 33 765
[3] Panajotov K, Berghmans F, Peeters M, Verschaffelt G, Danckaert J, Veretennicoff I, Thienpont H 1999 IEEE Photonic. Tech. L. 11 985
[4] Koyama F 2006 J. Lightwave Technol. 24 4502
[5] Wang W J, Li C, Zhou H Y, Wu H, Luan X X, Shi L, Guo X 2015 Chin. Phys. B 24 024209
[6] Lee M W, Hong Y H, Shore K A 2004 IEEE Photonic. Tech. L. 16 2392
[7] Kasukawa A 2012 IEEE Photonics J. 4 642
[8] Kawaguchi H, Mori T, Sato Y, Yamayoshi Y 2006 Jpn. J. Appl. Phys. 45 L894
[9] Sciamanna M, Panajotov K 2006 Phys. Rev. A 73 023811
[10] Wang X F, Xia G Q, Wu Z M 2009 Acta Phys. Sin. 58 4669 (in Chinese) [王小发, 夏光琼, 吴正茂 2009 58 4669]
[11] Xiang S Y, Pan W, Luo B, Yan L S, Zou X H, Li N Q, Zhu H N 2012 IEEE J. Quantum Electron. 48 1069
[12] Zhong Z Q, Wu Z M, Wu J G, Xia G Q 2013 IEEE Photonics J. 5 1500409
[13] Liu Q X, Pan W, Zhang L Y, Li N Q, Yan J 2015 Acta Phys. Sin. 64 024209 (in Chinese) [刘庆喜, 潘炜, 张力月, 李念强, 阎娟 2015 64 024209]
[14] Chen J J, Xia G Q, Wu Z M 2015 Chin. Phys. B 24 024210
[15] Al-Seyab R, Schires K, Khan N A, Hurtado A, Henning I D, Adams M J 2011 IEEE J. Sel. Top. Quantum Electron. 17 1242
[16] Al-Seyab R, Schires K, Hurtado A, Henning I D, Adams M J 2013 IEEE J. Sel. Top. Quantum Electron. 19 1700512
[17] Prez P, Valle A, Pesquera L, Quirce A 2013 IEEE J. Sel. Top. Quantum Electron. 19 1700408
[18] Salvide M F, Torre M S, Henning I D, Adams M J, Hurtado A 2015 IEEE J. Sel. Top. Quantum Electron. 21 1800309
[19] Adams M J, Alexandropoulos D 2009 IEEE J. Quantum Electron. 45 744
[20] Prez P, Valle A, Noriega I, Pesquera L 2014 J. Lightwave Technol. 32 1601
[21] Wang X F, Xia G Q, Wu Z M 2009 J. Opt. Soc. Am. B: Opt. Phys. 26 160
[22] Agrawal G P, Dutta N K 1993 Semiconductor Lasers (2nd Ed.) (Boston: Kluwer Academic Publishers) pp261-262
[23] Tatham M C, Lealman I F, Seltzer C P, Westbrook L D, Cooper D M 1992 IEEE J. Quantum Electron. 28 408
[24] Barland S, Spinicelli P, Giacomelli G, Marin F 2005 IEEE J. Quantum Electron. 41 1235
[25] Press W H, Teukolsky S A, Vetterling W T, Flannery B P 1992 Numerical Recipes in Fortran 77: the Art of Scientific Computing (2nd Ed.) (Cambridge: Cambridge University Press) pp678-683
[26] Prez P, Valle A, Pesquera L 2014 J. Opt. Soc. Am. B: Opt. Phys. 31 2574
[27] Homayounfar A, Adams M J 2007 Opt. Express 15 10504
[28] Chlouverakis K E, Al-Aswad K M, Henning I D, Adams M J 2003 Electron. Lett. 39 1185
[29] Gavrielides A, Kovanis V, Erneux T 1997 Opt. Commun. 136 253
[30] Chuang C F, Liao Y H, Lin C H, Chen S Y, Grillot F, Lin F Y 2014 Opt. Express 22 5651
[31] Homayounfar A, Adams M J 2007 Opt. Commun. 269 119
[32] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p76 (in Chinese) [刘秉正, 彭建华 2004 非线性动力学(北京: 高等教育出版社) 第76页]
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