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Surface-emitting mid-infrared quantum cascade lasers with high-contrast photonic crystal resonators
Gangyi Xu, Raffaele Colombelli, Remy Braive, Gregoire Beaudoin, Luc Le Gratiet, Anne Talneau, Laurence Ferlazzo, and Isabelle Sagnes »View Author Affiliations
Gangyi Xu,1,3
Raffaele Colombelli,1,4
Remy Braive,2
Gregoire Beaudoin,2
Luc Le Gratiet,2
Anne Talneau,2
Laurence Ferlazzo,2
and Isabelle Sagnes2
1Institut d’Electronique Fondamentale, Université Paris-Sud and CNRS, UMR8622, 91405 Orsay, France
2Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
3gangyi.xu@u-psud.fr
4raffaele.colombelli@u-psud.fr
Optics Express, Vol. 18, Issue 11, pp. 11979-11989 (2010)
http://dx.doi.org/10.1364/OE.18.011979
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Abstract
We have developed surface-emitting single-mode quantum cascade lasers which employ high-contrast photonic-crystal resonators. The devices operate on band-edge states of the photonic band-structure. The mode profile and polarization characteristics of the band-edge modes are calculated by three-dimensional finite-difference time-domain simulation. Experimentally, the spectral properties, the far-field patterns, and the polarization characteristics of the lasers are determined and compared with simulations. The good agreement between the simulations and the experiments confirms that the hexapolar mode at the Γ-point band-edge gives rise to lasing. By using a novel and advanced fabrication method, deep and vertical PhC holes are fabricated with no metal redeposition on the sidewalls, which improves the laser performance with respect to the current status. The angular of the output beam is ≈ 15°, and the side mode suppression ratio of the single mode emission is about 25 dB. The threshold current density at 78K and the maximum operation temperature are 7.6 kA/cm2 and 220 K, respectively. The performance is mainly limited by the loss induced by surface plasmon waveguide, which can be overcome by using an optimized dielectric waveguide structure.
© 2010 Optical Society of America
OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.5750) Optical devices : Resonators
(240.6680) Optics at surfaces : Surface plasmons
ToC Category:
Lasers and Laser Optics
History
Original Manuscript: March 29, 2010
Revised Manuscript: May 3, 2010
Manuscript Accepted: May 3, 2010
Published: May 21, 2010
Citation
Gangyi Xu, Raffaele Colombelli, Remy Braive, Gregoire Beaudoin, Luc Le Gratiet, Anne Talneau, Laurence Ferlazzo, and Isabelle Sagnes, "Surface-emitting mid-infrared quantum cascade lasers with high-contrast photonic crystal resonators," Opt. Express 18, 11979-11989 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11979
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References
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Andrews, A.
Austin, D.
Babuty, A.
Bahriz, M.
Barbieri, S.
Beaudoin, G.
Beere, H. E.
Benz, A.
Bermel, P.
Bouchoule, S.
Bousseksou, A.
Braive, R.
Burr, G.
Capasso, F.
Chassagneux, Y.
Cho, A. Y.
Chutinan, A.
Ciuti, C.
Cockburn, J.
Colombelli, R.
D’Urso, B.
Dapkus, P.
Davies, A.
Davies, G. A.
De Wilde, Y.
Deutsch, C.
F., C.
Fan, S.
Farjadpour, A.
Fasching, G.
Genner, U.
Gmachl, C.
Gratiet, L. L.
Guilet, S.
Hu, Q.
Hua Zhang, L.
Hwang, H. Y.
Ibanescu, M.
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Raj, R.
Ritchie, D. A.
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Ryu, H. Y.
Sagnes, I.
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Scherer, A.
Schrenk, W.
Sergent, A. M.
Sirtori, C.
Sivco, D. L.
Srinivasan, K.
Strasser, G.
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Tennant, D. M.
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Williams, B.
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- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Graded photonic crystal THz quantum cascade lasers,” Appl. Phys. Lett. 96, 031104 (2010). [CrossRef]
- G. Xu, V. Moreau, Y. Chassagneux, A. Bousseksou, R. Colombelli, G. Patriarche, G. Beaudoin, and I. Sagnes, “Surface emitting quantum cascade lasers with metallic photonic-crystal resonators,” Appl. Phys. Lett. 94, 221101 (2009). [CrossRef]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17, 9491 (2009). [CrossRef] [PubMed]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and G. A. Davies, “Electrically pumped photonic crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174 (2009). [CrossRef] [PubMed]
- A. Bousseksou, R. Colombelli, A. Babuty, Y. De Wilde, Y. Chassagneux, C. Sirtori, G. Patriarche, G. Beaudoin, and I. Sagnes, “A semiconductor laser device for the generation of surface-plasmons upon electrical injection,” Opt. Express 17, 9391 (2009). [CrossRef] [PubMed]
- L. Sapienza, A. Vasanelli, R. Colombelli, C. Ciuti, Y. Chassagneux, C. Manquest, U. Genner, and C. Sirtori, “Electrically Injected Cavity Polaritons,” Phys. Rev. Lett. 100, 136806 (2008). [CrossRef] [PubMed]
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- L. Sapienza, A. Vasanelli, R. Colombelli, C. Ciuti, Y. Chassagneux, C. Manquest, U. Genner, and C. Sirtori, “Electrically Injected Cavity Polaritons,” Phys. Rev. Lett. 100, 136806 (2008). [CrossRef] [PubMed]
- M. Bahriz, V. Moreau, J. Palomo, R. Colombelli, D. Austin, J. Cockburn, L. Wilson, A. Krysa, and J. Roberts, “Room-temperature operation of λ = 7.5 μm surface-plasmon quantum cascade lasers,” Appl. Phys. Lett. 88, 181103 (2006). [CrossRef]
- G. Xu, Y. Chassagneux, R. Colombelli, G. Beaudoin, and I. Sagnes, “Polarized single-lobed surface emission in mid-infrared, photonic-crystal, quantum-cascade lasers,” Opt. Lett. 35, 859 (2010). [CrossRef] [PubMed]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Graded photonic crystal THz quantum cascade lasers,” Appl. Phys. Lett. 96, 031104 (2010). [CrossRef]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17, 9491 (2009). [CrossRef] [PubMed]
- G. Xu, V. Moreau, Y. Chassagneux, A. Bousseksou, R. Colombelli, G. Patriarche, G. Beaudoin, and I. Sagnes, “Surface emitting quantum cascade lasers with metallic photonic-crystal resonators,” Appl. Phys. Lett. 94, 221101 (2009). [CrossRef]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and G. A. Davies, “Electrically pumped photonic crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174 (2009). [CrossRef] [PubMed]
- A. Bousseksou, R. Colombelli, A. Babuty, Y. De Wilde, Y. Chassagneux, C. Sirtori, G. Patriarche, G. Beaudoin, and I. Sagnes, “A semiconductor laser device for the generation of surface-plasmons upon electrical injection,” Opt. Express 17, 9391 (2009). [CrossRef] [PubMed]
- L. Sapienza, A. Vasanelli, R. Colombelli, C. Ciuti, Y. Chassagneux, C. Manquest, U. Genner, and C. Sirtori, “Electrically Injected Cavity Polaritons,” Phys. Rev. Lett. 100, 136806 (2008). [CrossRef] [PubMed]
- A. Bousseksou, V. Moreau, R. Colombelli, C. Sirtori, G. Patriarche, O. Mauguin, L. Largeau, G. Beaudoin, and I. Sagnes, “Surface-plasmon distributed-feedback mid-infrared quantum cascade lasers based on hybrid plasmon/air-guided modes,” Electron. Lett. 44, 807 (2008). [CrossRef]
- M. Bahriz, V. Moreau, J. Palomo, R. Colombelli, D. Austin, J. Cockburn, L. Wilson, A. Krysa, and J. Roberts, “Room-temperature operation of λ = 7.5 μm surface-plasmon quantum cascade lasers,” Appl. Phys. Lett. 88, 181103 (2006). [CrossRef]
- K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, M. Troccoli, and C. F., “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” Appl. Phys. Lett. 84, 4164–4166 (2004). [CrossRef]
- R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, F. Capasso, D. M. Tennant, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum Cascade Photonic-Crystal Surface-Emitting Laser,” Science 302, 1374 (2003). [CrossRef] [PubMed]
- K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002). [CrossRef]
- O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Graded photonic crystal THz quantum cascade lasers,” Appl. Phys. Lett. 96, 031104 (2010). [CrossRef]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17, 9491 (2009). [CrossRef] [PubMed]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and G. A. Davies, “Electrically pumped photonic crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174 (2009). [CrossRef] [PubMed]
- K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, M. Troccoli, and C. F., “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” Appl. Phys. Lett. 84, 4164–4166 (2004). [CrossRef]
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- L. Sapienza, A. Vasanelli, R. Colombelli, C. Ciuti, Y. Chassagneux, C. Manquest, U. Genner, and C. Sirtori, “Electrically Injected Cavity Polaritons,” Phys. Rev. Lett. 100, 136806 (2008). [CrossRef] [PubMed]
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- K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002). [CrossRef]
- L. Sapienza, A. Vasanelli, R. Colombelli, C. Ciuti, Y. Chassagneux, C. Manquest, U. Genner, and C. Sirtori, “Electrically Injected Cavity Polaritons,” Phys. Rev. Lett. 100, 136806 (2008). [CrossRef] [PubMed]
- G. Vecchi, F. Raineri, I. Sagnes, A. Yacomotti, P. Monnier, T. Karle, K.-H. Lee, R. Braive, L. L. Gratiet, S. Guilet, G. Beaudoin, A. Talneau, S. Bouchoule, A. Levenson, and R. Raj, “Continuous-wave operation of photonic band edge laser near 1.55 m on silicon wafer,” Opt. Express 15, 7551–7556 (2008). [CrossRef]
- S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]
- J. Vučković, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal Microcavities,” IEEE J. Quantum Electron. 38, 850 (2002). [CrossRef]
- S. Kohen, B. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005). [CrossRef]
- M. Bahriz, V. Moreau, J. Palomo, R. Colombelli, D. Austin, J. Cockburn, L. Wilson, A. Krysa, and J. Roberts, “Room-temperature operation of λ = 7.5 μm surface-plasmon quantum cascade lasers,” Appl. Phys. Lett. 88, 181103 (2006). [CrossRef]
- G. Xu, Y. Chassagneux, R. Colombelli, G. Beaudoin, and I. Sagnes, “Polarized single-lobed surface emission in mid-infrared, photonic-crystal, quantum-cascade lasers,” Opt. Lett. 35, 859 (2010). [CrossRef] [PubMed]
- G. Xu, V. Moreau, Y. Chassagneux, A. Bousseksou, R. Colombelli, G. Patriarche, G. Beaudoin, and I. Sagnes, “Surface emitting quantum cascade lasers with metallic photonic-crystal resonators,” Appl. Phys. Lett. 94, 221101 (2009). [CrossRef]
- G. Vecchi, F. Raineri, I. Sagnes, A. Yacomotti, P. Monnier, T. Karle, K.-H. Lee, R. Braive, L. L. Gratiet, S. Guilet, G. Beaudoin, A. Talneau, S. Bouchoule, A. Levenson, and R. Raj, “Continuous-wave operation of photonic band edge laser near 1.55 m on silicon wafer,” Opt. Express 15, 7551–7556 (2008). [CrossRef]
- O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]
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Appl. Phys. Lett.
- K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, M. Troccoli, and C. F., “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” Appl. Phys. Lett. 84, 4164–4166 (2004). [CrossRef]
- G. Xu, V. Moreau, Y. Chassagneux, A. Bousseksou, R. Colombelli, G. Patriarche, G. Beaudoin, and I. Sagnes, “Surface emitting quantum cascade lasers with metallic photonic-crystal resonators,” Appl. Phys. Lett. 94, 221101 (2009). [CrossRef]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Graded photonic crystal THz quantum cascade lasers,” Appl. Phys. Lett. 96, 031104 (2010). [CrossRef]
- K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002). [CrossRef]
- M. Bahriz, V. Moreau, J. Palomo, R. Colombelli, D. Austin, J. Cockburn, L. Wilson, A. Krysa, and J. Roberts, “Room-temperature operation of λ = 7.5 μm surface-plasmon quantum cascade lasers,” Appl. Phys. Lett. 88, 181103 (2006). [CrossRef]
Electron. Lett.
- A. Bousseksou, V. Moreau, R. Colombelli, C. Sirtori, G. Patriarche, O. Mauguin, L. Largeau, G. Beaudoin, and I. Sagnes, “Surface-plasmon distributed-feedback mid-infrared quantum cascade lasers based on hybrid plasmon/air-guided modes,” Electron. Lett. 44, 807 (2008). [CrossRef]
IEEE J. Quantum Electron.
- J. Vučković, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal Microcavities,” IEEE J. Quantum Electron. 38, 850 (2002). [CrossRef]
J. Appl. Phys.
- S. Kohen, B. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005). [CrossRef]
J. Opt. Soc. Am. B
- B. D’Urso, O. Painter, J. O’Brien, T. Tombrello, A. Scherer, and A. Yariv, “Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavitites,” J. Opt. Soc. Am. B 15(3), 1155–1159 (1998). [CrossRef]
J. Vac. Sci. Technol. B
- K.-H. Lee, S. Guilet, G. Patriarche, I. Sagnes, and A. Talneau, “Smooth sidewall in InP-based photonic crystal membrane etched by N2-based inductive coupled plasma,” J. Vac. Sci. Technol. B 26, 1326–1333 (2008). [CrossRef]
Nature
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Opt. Express
- L. Hua Zhang, “Andrea Dunbar, Giacomo Scalari, Romuald Houdr, and Jrme Faist, ”Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15, 16818–16827 (2007). [CrossRef] [PubMed]
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- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17, 9491 (2009). [CrossRef] [PubMed]
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- A. Bousseksou, R. Colombelli, A. Babuty, Y. De Wilde, Y. Chassagneux, C. Sirtori, G. Patriarche, G. Beaudoin, and I. Sagnes, “A semiconductor laser device for the generation of surface-plasmons upon electrical injection,” Opt. Express 17, 9391 (2009). [CrossRef] [PubMed]
Opt. Lett.
- A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006). [CrossRef] [PubMed]
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Phys. Rev. B
- S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]
- S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of a wavelength-scale photonic crystal resonator,” Phys. Rev. B 73, 235117 (2006). [CrossRef]
- M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002). [CrossRef]
- H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B 68, 045209 (2003). [CrossRef]
Phys. Rev. Lett.
- L. Sapienza, A. Vasanelli, R. Colombelli, C. Ciuti, Y. Chassagneux, C. Manquest, U. Genner, and C. Sirtori, “Electrically Injected Cavity Polaritons,” Phys. Rev. Lett. 100, 136806 (2008). [CrossRef] [PubMed]
Science
- O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]
- R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, F. Capasso, D. M. Tennant, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum Cascade Photonic-Crystal Surface-Emitting Laser,” Science 302, 1374 (2003). [CrossRef] [PubMed]
Other
- The finite elements solver Comsol Multiphysics has been employed for the simulations. Bloch-periodic boundary conditions where implemented.
2010, Chassagneux, Appl. Phys. Lett.
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. Khanna, E. Linfield, and A. Davies, “Graded photonic crystal THz quantum cascade lasers,” Appl. Phys. Lett. 96, 031104 (2010). [CrossRef]
- Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and G. A. Davies, “Electrically pumped photonic crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174 (2009). [CrossRef] [PubMed]
- G. Xu, V. Moreau, Y. Chassagneux, A. Bousseksou, R. Colombelli, G. Patriarche, G. Beaudoin, and I. Sagnes, “Surface emitting quantum cascade lasers with metallic photonic-crystal resonators,” Appl. Phys. Lett. 94, 221101 (2009). [CrossRef]
- L. Sapienza, A. Vasanelli, R. Colombelli, C. Ciuti, Y. Chassagneux, C. Manquest, U. Genner, and C. Sirtori, “Electrically Injected Cavity Polaritons,” Phys. Rev. Lett. 100, 136806 (2008). [CrossRef] [PubMed]
- A. Bousseksou, V. Moreau, R. Colombelli, C. Sirtori, G. Patriarche, O. Mauguin, L. Largeau, G. Beaudoin, and I. Sagnes, “Surface-plasmon distributed-feedback mid-infrared quantum cascade lasers based on hybrid plasmon/air-guided modes,” Electron. Lett. 44, 807 (2008). [CrossRef]
- K.-H. Lee, S. Guilet, G. Patriarche, I. Sagnes, and A. Talneau, “Smooth sidewall in InP-based photonic crystal membrane etched by N2-based inductive coupled plasma,” J. Vac. Sci. Technol. B 26, 1326–1333 (2008). [CrossRef]
- G. Vecchi, F. Raineri, I. Sagnes, A. Yacomotti, P. Monnier, T. Karle, K.-H. Lee, R. Braive, L. L. Gratiet, S. Guilet, G. Beaudoin, A. Talneau, S. Bouchoule, A. Levenson, and R. Raj, “Continuous-wave operation of photonic band edge laser near 1.55 m on silicon wafer,” Opt. Express 15, 7551–7556 (2008). [CrossRef]
- S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of a wavelength-scale photonic crystal resonator,” Phys. Rev. B 73, 235117 (2006). [CrossRef]
- M. Bahriz, V. Moreau, J. Palomo, R. Colombelli, D. Austin, J. Cockburn, L. Wilson, A. Krysa, and J. Roberts, “Room-temperature operation of λ = 7.5 μm surface-plasmon quantum cascade lasers,” Appl. Phys. Lett. 88, 181103 (2006). [CrossRef]
- S. Kohen, B. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005). [CrossRef]
- K. Srinivasan, O. Painter, R. Colombelli, C. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, M. Troccoli, and C. F., “Lasing mode pattern of a quantum cascade photonic crystal surface-emitting microcavity laser,” Appl. Phys. Lett. 84, 4164–4166 (2004). [CrossRef]
- R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. Gmachl, F. Capasso, D. M. Tennant, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum Cascade Photonic-Crystal Surface-Emitting Laser,” Science 302, 1374 (2003). [CrossRef] [PubMed]
- H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B 68, 045209 (2003). [CrossRef]
- J. Vučković, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal Microcavities,” IEEE J. Quantum Electron. 38, 850 (2002). [CrossRef]
- M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002). [CrossRef]
- K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, A. M. Sergent, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators,” Appl. Phys. Lett. 80(17), 3060–3062 (2002). [CrossRef]
- O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]
- S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]
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