Abstract

We demonstrate a framework to understand and predict the far-field emission in terahertz frequency photonic-crystal quantum cascade lasers. The devices, which employ a high-performance three-well active region, are lithographically tunable and emit in the 104-120 µm wavelength range. A peak output power of 7 mW in pulsed mode is obtained at 10 K, and the typical device maximum operating temperature is 136 K. We identify the photonic-crystal band-edge states involved in the lasing process as originating from the hexapole and monopole modes at the G point of the photonic band structure, as designed. The theoretical far-field patterns, obtained via finite-difference time-domain simulations, are in excellent agreement with experiment. Polarization measurements further support the theory, and the role of the bonding wires in the emission process is elucidated.

© 2009 Optical Society of America

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    [CrossRef]
  13. Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (1)

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 (London) 457, 174 (2009).
[CrossRef]

2008 (2)

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, "Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K," Opt. Express 16, 3242 (2008).
[CrossRef] [PubMed]

2007 (6)

B. S. Williams, "Terahertz quantum cascade lasers," Nat. Photon. 1, 517-525 (2007).
[CrossRef]

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[CrossRef]

M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, "Horn antennas for terahertz quantum cascade lasers," Electron. Lett. 43, 573 (2007).
[CrossRef]

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, "Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap," Opt. Express 15, 5948 (2007).
[CrossRef] [PubMed]

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

2006 (3)

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]

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]

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

2005 (2)

S. Kohen, B. Williams, and Q. Hu, "Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators," J. Appl. Phys. 97, 053106 (2005).
[CrossRef]

B. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Distributed-feedback terahertz quantum cascade lasers with laterally corrugated metal waveguides," Opt. Lett. 30, 2909-2911 (2005).
[CrossRef] [PubMed]

2002 (4)

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 (2002).
[CrossRef]

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (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, 3060-3062 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities," IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

1983 (1)

G. A. Samara, "Temperature and pressure dependences of the dielectric constants of semiconductors," Phys. Rev. B 27, 3494-3505 (1983).
[CrossRef]

Adam, A. J. L.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Aers, G. C.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Alton, J.

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

Amanti, M. I.

M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, "Horn antennas for terahertz quantum cascade lasers," Electron. Lett. 43, 573 (2007).
[CrossRef]

Andronico, A.

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Bahriz, M.

Barbieri, S.

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 (London) 457, 174 (2009).
[CrossRef]

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Beere, H. E.

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 (London) 457, 174 (2009).
[CrossRef]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Belkin, M. A.

Beltram, F.

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Bermel, P.

Burr, G.

Cao, J. C.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Capasso, F.

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, "Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K," Opt. Express 16, 3242 (2008).
[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, 3060-3062 (2002).
[CrossRef]

Chassagneux, Y.

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 (London) 457, 174 (2009).
[CrossRef]

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

Cho, A. Y.

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, 3060-3062 (2002).
[CrossRef]

Chutinan, A.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 (2002).
[CrossRef]

Colombelli, R.

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 (London) 457, 174 (2009).
[CrossRef]

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

M. Bahriz, V. Moreau, R. Colombelli, O. Crisafulli, and O. Painter, "Design of mid-IR and THz quantum cascade laser cavities with complete TM photonic bandgap," Opt. Express 15, 5948 (2007).
[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, 3060-3062 (2002).
[CrossRef]

Coudevylle, J. R.

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Crisafulli, O.

Davies, A. G.

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, "Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K," Opt. Express 16, 3242 (2008).
[CrossRef] [PubMed]

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Davies, G. A.

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 (London) 457, 174 (2009).
[CrossRef]

Dhillon, S.

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

Faist, J.

M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, "Horn antennas for terahertz quantum cascade lasers," Electron. Lett. 43, 573 (2007).
[CrossRef]

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[CrossRef]

Fan, J. A.

Farjadpour, A.

Fischer, M.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[CrossRef]

M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, "Horn antennas for terahertz quantum cascade lasers," Electron. Lett. 43, 573 (2007).
[CrossRef]

Gao, J. R.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Gellie, P.

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Gmachl, C.

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, 3060-3062 (2002).
[CrossRef]

Hormoz, S.

Hovenier, J. N.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Hoyler, N.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[CrossRef]

Hu, Q.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (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]

B. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Distributed-feedback terahertz quantum cascade lasers with laterally corrugated metal waveguides," Opt. Lett. 30, 2909-2911 (2005).
[CrossRef] [PubMed]

Hwang, H. Y.

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, 3060-3062 (2002).
[CrossRef]

Ibanescu, M.

Imada, M.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 (2002).
[CrossRef]

Iotti, R. C.

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

K¨ohler, R.

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Ka?salynas, I.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Khanna, S.

Khanna, S. P.

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 (London) 457, 174 (2009).
[CrossRef]

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Kim, S. H.

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]

Kim, S. K.

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]

Klaassen, T. O.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Kohen, S.

S. Kohen, B. Williams, and Q. Hu, "Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators," J. Appl. Phys. 97, 053106 (2005).
[CrossRef]

Kumar, S.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

B. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Distributed-feedback terahertz quantum cascade lasers with laterally corrugated metal waveguides," Opt. Lett. 30, 2909-2911 (2005).
[CrossRef] [PubMed]

Lachab, M.

Laframboise, S. R.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Lee, Y. H.

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]

Leo, G.

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Linfield, E. H.

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 (London) 457, 174 (2009).
[CrossRef]

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, and E. H. Linfield, "Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K," Opt. Express 16, 3242 (2008).
[CrossRef] [PubMed]

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Liu, H. C.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Luo, H.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Maineult, W.

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 (London) 457, 174 (2009).
[CrossRef]

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Mochizuki, M.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 (2002).
[CrossRef]

Moreau, V.

Noda, S.

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 (2002).
[CrossRef]

Orlova, E. E.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Painter, O.

Palomo, J.

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

Reno, J. L.

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

B. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Distributed-feedback terahertz quantum cascade lasers with laterally corrugated metal waveguides," Opt. Lett. 30, 2909-2911 (2005).
[CrossRef] [PubMed]

Ritchie, D. A.

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 (London) 457, 174 (2009).
[CrossRef]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Rodriguez, A.

Rossi, F.

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Roundy, D.

Samara, G. A.

G. A. Samara, "Temperature and pressure dependences of the dielectric constants of semiconductors," Phys. Rev. B 27, 3494-3505 (1983).
[CrossRef]

Scalari, G.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[CrossRef]

M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, "Horn antennas for terahertz quantum cascade lasers," Electron. Lett. 43, 573 (2007).
[CrossRef]

Sergent, A. M.

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, 3060-3062 (2002).
[CrossRef]

Sirtori, C.

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[CrossRef]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

Sivco, D. L.

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, 3060-3062 (2002).
[CrossRef]

Terazzi, R.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[CrossRef]

Tredicucci, A.

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[CrossRef]

Unterrainer, K.

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, 3060-3062 (2002).
[CrossRef]

Walther, C.

M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, "Horn antennas for terahertz quantum cascade lasers," Electron. Lett. 43, 573 (2007).
[CrossRef]

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[CrossRef]

Wasilewski, Z. R.

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Williams, B.

S. Kohen, B. Williams, and Q. Hu, "Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators," J. Appl. Phys. 97, 053106 (2005).
[CrossRef]

B. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Distributed-feedback terahertz quantum cascade lasers with laterally corrugated metal waveguides," Opt. Lett. 30, 2909-2911 (2005).
[CrossRef] [PubMed]

Williams, B. S.

B. S. Williams, "Terahertz quantum cascade lasers," Nat. Photon. 1, 517-525 (2007).
[CrossRef]

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Appl. Phys. Lett. (5)

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 131122 (2007).
[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, 3060-3062 (2002).
[CrossRef]

H. Luo, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, H. C. Liu, and J. C. Cao, "Terahertz quantum-cascade lasers based on a three-well active module," Appl. Phys. Lett. 90, 041112 (2007).
[CrossRef]

Y. Chassagneux, J. Palomo, R. Colombelli, S. Dhillon, C. Sirtori, H. E. Beere, J. Alton, and D. A. Ritchie, "Terahertz microcavity lasers with subwavelength mode volumes and thresholds in the milliampere range," Appl. Phys. Lett. 90, 091113 (2007).
[CrossRef]

A. J. L. Adam, I. Ka˘salynas, J. N. Hovenier, T. O. Klaassen, J. R. Gao, E. E. Orlova, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Beam patterns of terahertz quantum cascade lasers with subwavelength cavity dimensions," Appl. Phys. Lett. 88, 151105 (2006).
[CrossRef]

Electron. Lett. (1)

M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, "Horn antennas for terahertz quantum cascade lasers," Electron. Lett. 43, 573 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Vuckovic, M. Loncar, H. Mabchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities," IEEE J. Quantum Electron. 38, 850 (2002).
[CrossRef]

J. Appl. Phys. (2)

P. Gellie, W. Maineult, A. Andronico, G. Leo, C. Sirtori, S. Barbieri, Y. Chassagneux, J. R. Coudevylle, R. Colombelli, S. P. Khanna, E. H. Linfield, and A. G. Davies, "Effect of transverse mode structure on the far field pattern of metal-metal terahertz quantum cascade lasers," J. Appl. Phys. 104, 124513 (2008).
[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]

Nat. Photon. (1)

B. S. Williams, "Terahertz quantum cascade lasers," Nat. Photon. 1, 517-525 (2007).
[CrossRef]

Nature (London) (2)

R. K¨ohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, "THz semiconductor-heterostructure laser," Nature (London) 417, 156 (2002).
[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 (London) 457, 174 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (3)

M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, "Multidirectionally distributed feedback photonic crystal lasers," Phys. Rev. B 65, 195306 (2002).
[CrossRef]

G. A. Samara, "Temperature and pressure dependences of the dielectric constants of semiconductors," Phys. Rev. B 27, 3494-3505 (1983).
[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]

Other (3)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Norwood, MA: Artech, 2000).

K. Sakay, Terahertz optoelectronics (New York: Springer, 2005).
[CrossRef]

D. Mittleman, Sensing with Terahertz radiation (New York: Springer Books, 2004).

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Figures (9)

Fig. 1.
Fig. 1.

Conduction band profile of two periods of the GaAs/Al0.15Ga0.85As QC heterostructure. The moduli squared and energies of the wavefunctions are shown. The wavefunctions which are relevant to the laser operation are in color. The applied electric field is 12.5 kV/cm, i.e. 54.6 meV per period. The layer thicknesses - from left to right starting from the injection barrier - are 4.8/9.4/2.4/7.2/4.2/15.7 nm (The AlGaAs barriers are in bold). The central 5.5 nm of the 15.7 nm-thick quantum well is n-doped with silicon to a level of 5.0×1016 cm-3. The energy of the laser transition (E43), its dipole matrix element (z43) and the corresponding oscillator strength (f43) are reported in the upper right corner of the figure.

Fig. 2.
Fig. 2.

(a) Light-current and voltage-current characteristics at different temperatures for sample L207. The devices were processed as laser ridges, 2 mm long and 200 µm wide. The threshold current density is 910 A/cm2 at 78K (860 A/cm2 at 10 K). The devices were operated with 300 ns pulses at a 20 kHz repetition rate; detection was achieved with a liquid-helium cooled silicon bolometer, and using f/1 collection optics. The peak output power of these metal-metal Fabry-Perot THz lasers is typically in the sub-mW range. (b) Laser threshold current density as a function of heat-sink temperature for a typical device. T max is 165 K. Inset: Typical laser spectrum at T=10 K

Fig. 3.
Fig. 3.

(a) Optical microscopy image of a typical device. The PC pattern is written into the top metallic surface only. No semiconductor etch is used. (b) Photonic band structure for TM polarized light in the trigonal structure used for the experiments (see (a)), with an r/a ratio of 2/9 (0.222). The calculation has been performed in three dimensions, using Bloch-periodic conditions applied at the unit cell boundaries. The metal is approximated to be perfect, and the active region is modeled with a purely real effective index neff =3.6.

Fig. 4.
Fig. 4.

Central Panel: Magnified view of the photonic band structure around the Γ point, with the reduced energy corresponding to the fabricated devices indicated. The electric field distributions (E z ) of the band-edge states located at the Γ point of the photonic band structure (labeled A, B, C and D) are also shown. The calculation has been performed for an infinite, periodic lattice with E z , i.e. the electric field normal to the plane, shown as a color-scale. The area surrounded by the dotted black lines corresponds to the unit cell used in the calculation, and the values of the field at the center of the active region are shown. The circles correspond to the holes in the top metallization. The band-edge A (bipole) and B (quadrupole) are doubly degenerate. The band-edge C (hexapole) and D (monopole) are non-degenerate.

Fig. 5.
Fig. 5.

(a) Laser spectra at T=78 K for different values of the PC period, a. In each case, injection currents were used that gave the highest laser output power. The spectra - which are offset for clarity - were acquired using an FTIR spectrometer, operating in rapid scan mode with a resolution of 0.125 cm-1 and a DTGS far-infared detector. The PC principally supports two modes. (b) L-I and V-I characteristics at a heat-sink temperature of 78 K of a PC device. The lattice period is 36.1 µm, and the T max was 136 K. Other lasers with different PC periods all exhibit a T max higher than 127 K, except for the device with period 38.9 µm, which lased up to 110 K. (c) Temperature dependence of the emission frequency of a PC laser with a period equal to 38.2 µm (red curve). A temperature tuning of 8 GHz was obtained between 10 K and 130 K. At low temperature, the non-linear temperature tuning can be explained using the static variation of the refractive index of the GaAs. The black line represents the numerically calculated emission frequency using the temperature dependence of the static refractive index of GaAs.

Fig. 6.
Fig. 6.

Laser spectra at T=78 K for different values of the PC period (as in Fig. 5(a)), plotted in reduced frequency units (a/λ). The dotted lines correspond to the predicted spectral positions of the band-edge C (hexapole) and the band-edge D (monopole) modes. The spectra are offset for clarity.

Fig. 7.
Fig. 7.

(a) Electric field distribution (Ez component) - obtained with a 2D FDTD simulation - for the band-edge hexapole mode labeled C. The size of the simulation field is 800×800 µm2, and it encompasses the whole device surface. PML layers are placed at the boundaries of the simulation field. (b) Calculated far-field profile for the hexapole mode represented in (a). The far-field has been obtained using the transverse magnetic near-field in the metal holes only. The field outside the holes, i.e above the metal surface, was assumed to be zero. (c) Experimental far-field pattern of the mode at a/λ=0.315. The measurement has been performed at 78 K by scanning a Golay cell detector at a constant distance from the laser.

Fig. 8.
Fig. 8.

(a) Electric field distribution (E z component) - obtained with a 2D FDTD simulation - for the band-edge monopole mode labeled D. The highest Q factor mode is shown. (b) Calculated far-field pattern obtained from the near-field profile in (a). (c) Experimental far-field pattern of the mode at a/λ=0.36. (d) Optical microscopy image of the measured device. The red circles mark the position of the holes masked by bonding. (e) E z - obtained with a 2D FDTD simulation - for the band-edge monopole mode labeled D when the presence of the bonding wire - as shown in (d) - is taken into account. Unlike (a), the envelope function now exhibits a nodal line. (f) Calculated far-field pattern obtained from the near-field in (e). The experimental far-field profile (c) is in excellent agreement with theory when the effect of the bonding wires are taken into account.

Fig. 9.
Fig. 9.

Polarization in the far-field: a comparison between theory and experiment. The arrows represent the electric field direction. (a) and (c) show experimental data for devices operating on the hexapole (C) and monopole (D) modes, respectively. One point in two has been measured, the other points are obtained through interpolation. The directions of the arrow correspond to the maxima of the electric field polarizations. The length of the arrows represent the ratio p=(Imax -Imin )/(Imax +Imin ). The greater the length of the arrow, the closer the polarization is to linear. The dotted lines are guides to the eye. (b) and (d) show simulations of the far-field polarization for the hexapole and monopole modes, respectively, taking into account the bonding. The length of the arrows represents in this plot the calculated farfield intensity (r values on the right scale) normalized to one.

Equations (1)

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ArrowLength=p=Imax(θ)Imin(θ)Imax(θ)+Imin(θ)

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