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We present a quasi-three-dimensional efficient model for simulating and designing the terahertz quantum cascade laser with nonlinear axial waveguide structure, based on the finite difference beam propagation method. The traditional beam propagation method is widely used to simulate the beam profile of the passive waveguide. In order to study the active device, however, the current induced variation in the active region should also be considered in the numerical simulation model. In the model presented in this paper, the phase and the amplitude of the propagating confined field in the active waveguide are determined by a few linear and non-linear effects. The parameters relating to the linear effects, such as the intrinsic refractive index profile and the intrinsic losses of the waveguide under zero current injection, are calculated by using COMSOL-Multiphysics. While the non-linear effects, such as the modal gain and the refractive index variation induced by current injection, are considered in a rigorous way by including the rate-equation set for calculating the carrier dynamics in the active region. The parameters used in the rate-equation set are obtained by referring to the literature and fitting the experimental results of the considered terahertz lasers. By adding the current induced gain and refractive index variation, the presented beam propagation model is able to simulate many current-dependant properties of a laser, such as the output power, the gain guiding effect, and the self-focusing effect. We show in this paper that the latter two effects have influence on inner-waveguide beam profile, and the competitive balance between them determines the output beam quality. By utilizing this numerical model, the terahertz quantum cascade laser with tapered waveguide structure is simulated, and the influences of the taper angle on output power and beam quality are investigated. According to the simulation results, we find that there is an obvious increase in the output power when the taper angle is increased from 0 to 3 degree, while the increment in the output power decreases rapidly when the taper angle is further increased. Besides, we observe that for the far field the full width at half maximum of the output beam decreases sharply with increasing the taper angle. However, when the taper angle equals 8 degree, multiple lateral modes are observed, which indicates poor output beam quality of this device and poor beam coupling efficiency between this device and the power meter.Therefore, although the simulation results show that the output power of this device is higher than that of the device with 5 degree taper angle, the experiment results show that the measured output power is lower. So the taper angle is not the larger the better, but there exists an optimum value, at which the terahertz quantum cascade laser can achieve the highest effective output power.
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Keywords:
- terahertz quantum cascade laser /
- tapered laser /
- beam propagation method /
- numerical simulation
[1] Faist J, Capasso F, Sivco D L, Sirtori C, Hutchinson A L, Cho A Y 1994 Science 264 553
[2] Kohler R, Tredicucci A, Beltram F, Beere H E, Linfield E H, Davies A G, Ritchie D A, Iotti R C, Rossi F 2002 Nature 417 156
[3] Kumar S 2011 IEEE J. Sel. Top. Quantum Electron. 17 38
[4] Li H, Han Y J, Tan Z Y, Zhang R, Cao J C 2010 Acta Phys. Sin. 59 2169 (in Chinese) [黎华, 韩英军, 谭智勇, 张戎, 曹俊诚 2010 物理学报 59 2169]
[5] Wan W J, Yin R, Tan Z Y, Wang F, Han Y J, Cao J C 2013 Acta Phys. Sin. 62 210701 (in Chinese) [万文坚, 尹嵘, 谭智勇, 王丰, 韩英军, 曹俊诚 2013 物理学报 62 210701]
[6] Williams B S, Kumar S, Hu Q, Reno J L 2006 Electron. Lett. 42 89
[7] Williams B, Kumar S, Hu Q, Reno J 2005 Opt. Express 13 3331
[8] Li L, Chen L, Zhu J, Freeman J, Dean P, Valavanis A, Davies A G, Linfield E H 2014 Electron. Lett. 50 309
[9] Kumar S, Hu Q, Reno J L 2009 Appl. Phys. Lett. 94 131105
[10] Kumar S, Williams B S, Qin Q, Lee A W, Hu Q, Reno J L 2007 Opt. Express 15 113
[11] Burghoff D, Kao T Y, Han N, Chan C W I, Cai X, Yang Y, Hayton D J, Gao J R, Reno J L, Hu Q 2014 Nat. Photon. 8 462
[12] Li Y, Wang J, Yang N, Liu J, Wang T, Liu F, Wang Z, Chu W, Duan S 2013 Opt. Express 21 15998
[13] Kohen S, Williams B S, Hu Q 2005 J. Appl. Phys. 97 053106
[14] Okamoto K 2006 Fundamentals of Optical Waveguides (San Diego: Elsevier Inc.) p365
[15] Marciante J R, Agrawal G P 1996 IEEE J. Quantum Electron. 32 590
[16] Liu J Q, Chen J Y, Liu F Q, Li L, Wang L J, Wang Z G 2010 Chin. Phys. Lett. 27 104205
[17] Li H, Manceau J M, Andronico A, Jagtap V, Sirtori C, Li L H, Linfield E H, Davies A G, Barbieri S 2014 Appl. Phys. Lett. 104 241102
[18] Wang J, Wu W D, Zhang X L, Duan S Q 2012 Chin. J. Comput. Phys. 29 127 (in Chinese) [王健, 吴卫东, 章小丽, 段素青 2012 计算物理 29 127]
[19] Coldren L A, Corzine S W 1995 Diode Lasers and Photonic Integrated Circuits (New York: John Wiley Sons, Inc.) p209
[20] Choi H, Diehl L, Wu Z K, Giovannini M, Faist J, Capasso F, Norris T B 2008 Phys. Rev. Lett. 100 167401
[21] Jirauschek C 2010 Appl. Phys. Lett. 96 011103
[22] Barbieri S, Sirtori C, Page H, Beck M, Faist J, Nagle J 2000 IEEE J. Quantum Electron. 36 736
[23] Thompson M G, Rae A R, Mo X, Penty R V, White I H 2009 IEEE J. Sel. Top. Quantum Electron. 15 661
[24] Xu T, Bardella P, Montrosset I 2013 IEEE Photon. Technol. Lett. 25 63
[25] Hadley G R 1992 IEEE J. Quantum Electron. 28 363
[26] Nikitichev D, Ding Y, Cataluna M, Rafailov E, Drzewietzki L, Breuer S, Elsaesser W, Rossetti M, Bardella P, Xu T, Montrosset I, Krestnikov I, Livshits D, Ruiz M, Tran M, Robert Y, Krakowski M 2012 Laser Phys. 22 715
[27] Li J C, Chen J B, Fan Z B, Ma K, Lou Y L 2002 J. Optoelectron. Laser 13 87 (in Chinese) [李俊昌, 陈劲波, 樊则宾, 马琨, 楼宇丽 2002 光电子激光 13 87]
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[1] Faist J, Capasso F, Sivco D L, Sirtori C, Hutchinson A L, Cho A Y 1994 Science 264 553
[2] Kohler R, Tredicucci A, Beltram F, Beere H E, Linfield E H, Davies A G, Ritchie D A, Iotti R C, Rossi F 2002 Nature 417 156
[3] Kumar S 2011 IEEE J. Sel. Top. Quantum Electron. 17 38
[4] Li H, Han Y J, Tan Z Y, Zhang R, Cao J C 2010 Acta Phys. Sin. 59 2169 (in Chinese) [黎华, 韩英军, 谭智勇, 张戎, 曹俊诚 2010 物理学报 59 2169]
[5] Wan W J, Yin R, Tan Z Y, Wang F, Han Y J, Cao J C 2013 Acta Phys. Sin. 62 210701 (in Chinese) [万文坚, 尹嵘, 谭智勇, 王丰, 韩英军, 曹俊诚 2013 物理学报 62 210701]
[6] Williams B S, Kumar S, Hu Q, Reno J L 2006 Electron. Lett. 42 89
[7] Williams B, Kumar S, Hu Q, Reno J 2005 Opt. Express 13 3331
[8] Li L, Chen L, Zhu J, Freeman J, Dean P, Valavanis A, Davies A G, Linfield E H 2014 Electron. Lett. 50 309
[9] Kumar S, Hu Q, Reno J L 2009 Appl. Phys. Lett. 94 131105
[10] Kumar S, Williams B S, Qin Q, Lee A W, Hu Q, Reno J L 2007 Opt. Express 15 113
[11] Burghoff D, Kao T Y, Han N, Chan C W I, Cai X, Yang Y, Hayton D J, Gao J R, Reno J L, Hu Q 2014 Nat. Photon. 8 462
[12] Li Y, Wang J, Yang N, Liu J, Wang T, Liu F, Wang Z, Chu W, Duan S 2013 Opt. Express 21 15998
[13] Kohen S, Williams B S, Hu Q 2005 J. Appl. Phys. 97 053106
[14] Okamoto K 2006 Fundamentals of Optical Waveguides (San Diego: Elsevier Inc.) p365
[15] Marciante J R, Agrawal G P 1996 IEEE J. Quantum Electron. 32 590
[16] Liu J Q, Chen J Y, Liu F Q, Li L, Wang L J, Wang Z G 2010 Chin. Phys. Lett. 27 104205
[17] Li H, Manceau J M, Andronico A, Jagtap V, Sirtori C, Li L H, Linfield E H, Davies A G, Barbieri S 2014 Appl. Phys. Lett. 104 241102
[18] Wang J, Wu W D, Zhang X L, Duan S Q 2012 Chin. J. Comput. Phys. 29 127 (in Chinese) [王健, 吴卫东, 章小丽, 段素青 2012 计算物理 29 127]
[19] Coldren L A, Corzine S W 1995 Diode Lasers and Photonic Integrated Circuits (New York: John Wiley Sons, Inc.) p209
[20] Choi H, Diehl L, Wu Z K, Giovannini M, Faist J, Capasso F, Norris T B 2008 Phys. Rev. Lett. 100 167401
[21] Jirauschek C 2010 Appl. Phys. Lett. 96 011103
[22] Barbieri S, Sirtori C, Page H, Beck M, Faist J, Nagle J 2000 IEEE J. Quantum Electron. 36 736
[23] Thompson M G, Rae A R, Mo X, Penty R V, White I H 2009 IEEE J. Sel. Top. Quantum Electron. 15 661
[24] Xu T, Bardella P, Montrosset I 2013 IEEE Photon. Technol. Lett. 25 63
[25] Hadley G R 1992 IEEE J. Quantum Electron. 28 363
[26] Nikitichev D, Ding Y, Cataluna M, Rafailov E, Drzewietzki L, Breuer S, Elsaesser W, Rossetti M, Bardella P, Xu T, Montrosset I, Krestnikov I, Livshits D, Ruiz M, Tran M, Robert Y, Krakowski M 2012 Laser Phys. 22 715
[27] Li J C, Chen J B, Fan Z B, Ma K, Lou Y L 2002 J. Optoelectron. Laser 13 87 (in Chinese) [李俊昌, 陈劲波, 樊则宾, 马琨, 楼宇丽 2002 光电子激光 13 87]
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