Abstract

We report the design, fabrication and experimental characterization of surface-emitting terahertz (THz) frequency quantum cascade lasers (QCLs) with distributed feedback concentric-circular-gratings. Single-mode operation is achieved at 3.73 THz with a side-mode suppression ratio as high as ~30 dB. The device emits ~5 times the power of a ridge laser of similar dimensions, with little degradation in the maximum operation temperature. Two lobes are observed in the far-field emission pattern, each of which has a divergence angle as narrow as ~13.5° × 7°. We demonstrate that deformation of the device boundary, caused by anisotropic wet chemical etching is the cause of this double-lobed profile, rather than the expected ring-shaped pattern.

© 2013 Optical Society of America

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    [CrossRef]
  24. W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
    [CrossRef]

2013

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

2012

2011

A. K. Wójcik, N. Yu, F. Capasso, A. Belyanin, “Nonlinear optical interactions of laser modes in quantum cascade lasers,” J. Mod. Opt. 58(9), 727–742 (2011).
[CrossRef]

2010

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

2009

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

S. Kumar, Q. Hu, J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineults, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17(12), 9491–9502 (2009).
[CrossRef] [PubMed]

L. Mahler, M. I. Amanti, C. Walther, A. Tredicucci, F. Beltram, J. Faist, H. E. Beere, D. A. Ritchie, “Distributed feedback ring resonators for vertically emitting terahertz quantum cascade lasers,” Opt. Express 17(15), 13031–13039 (2009).
[CrossRef] [PubMed]

2008

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

2007

2006

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

B. Williams, S. Kumar, Q. Hu, J. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 18–19 (2006).
[CrossRef]

S.-H. Kim, S.-K. Kim, Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73(23), 235117 (2006).
[CrossRef]

2005

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

2003

2002

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Akalin, T.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Amanti, M.

M. Amanti, M. Fischer, C. Walther, G. Scalari, J. Faist, “Horn antennas for terahertz quantum cascade lasers,” Electron. Lett. 43(10), 125–126 (2007).
[CrossRef]

Amanti, M. I.

Andrews, A. M.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Andronico, A.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Ban, D.

Barbieri, S.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineults, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17(12), 9491–9502 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Beck, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

Beere, H. E.

L. Mahler, M. I. Amanti, C. Walther, A. Tredicucci, F. Beltram, J. Faist, H. E. Beere, D. A. Ritchie, “Distributed feedback ring resonators for vertically emitting terahertz quantum cascade lasers,” Opt. Express 17(15), 13031–13039 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Belkin, M. A.

Beltram, F.

L. Mahler, M. I. Amanti, C. Walther, A. Tredicucci, F. Beltram, J. Faist, H. E. Beere, D. A. Ritchie, “Distributed feedback ring resonators for vertically emitting terahertz quantum cascade lasers,” Opt. Express 17(15), 13031–13039 (2009).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Belyanin, A.

A. K. Wójcik, N. Yu, F. Capasso, A. Belyanin, “Nonlinear optical interactions of laser modes in quantum cascade lasers,” J. Mod. Opt. 58(9), 727–742 (2011).
[CrossRef]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Bewley, W.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Bour, D.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Capasso, F.

N. Yu, Q. Wang, F. Capasso, “Beam engineering of quantum cascade lasers,” Laser Photonics Rev. 6(1), 24–46 (2012).
[CrossRef]

A. K. Wójcik, N. Yu, F. Capasso, A. Belyanin, “Nonlinear optical interactions of laser modes in quantum cascade lasers,” J. Mod. Opt. 58(9), 727–742 (2011).
[CrossRef]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

Chan, C. W. I.

Chassagneux, Y.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineults, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17(12), 9491–9502 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

Colombelli, R.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineults, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17(12), 9491–9502 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

Corzine, S.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Crozier, K. B.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Cubukcu, E.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Davies, A. G.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineults, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17(12), 9491–9502 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Detz, H.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Deutsch, C.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Diehl, L.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Dupont, E.

Evans, A. J.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Faist, J.

L. Mahler, M. I. Amanti, C. Walther, A. Tredicucci, F. Beltram, J. Faist, H. E. Beere, D. A. Ritchie, “Distributed feedback ring resonators for vertically emitting terahertz quantum cascade lasers,” Opt. Express 17(15), 13031–13039 (2009).
[CrossRef] [PubMed]

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. Amanti, M. Fischer, C. Walther, G. Scalari, J. Faist, “Horn antennas for terahertz quantum cascade lasers,” Electron. Lett. 43(10), 125–126 (2007).
[CrossRef]

Fan, J. A.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

Fathololoumi, S.

Fatt Lim, D.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Filloux, P.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Fischer, M.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. Amanti, M. Fischer, C. Walther, G. Scalari, J. Faist, “Horn antennas for terahertz quantum cascade lasers,” Electron. Lett. 43(10), 125–126 (2007).
[CrossRef]

Fung Yu, S.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Gellie, P.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Giles Davies, A.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Höfler, G.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Hu, Q.

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Jirauschek, C.

Kats, M. A.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Khanna, S.

Khanna, S. P.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineults, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17(12), 9491–9502 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

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W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Kim, S.-H.

S.-H. Kim, S.-K. Kim, Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73(23), 235117 (2006).
[CrossRef]

Kim, S.-K.

S.-H. Kim, S.-K. Kim, Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73(23), 235117 (2006).
[CrossRef]

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E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Köhler, R.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Kumar, S.

Lachab, M.

Laframboise, S. R.

Lampin, J.-F.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Lee, A. W.

Lee, Y.-H.

S.-H. Kim, S.-K. Kim, Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73(23), 235117 (2006).
[CrossRef]

Leo, G.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Li, L.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Liang, G.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Liang, H.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Lindle, J.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Linfield, E.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Linfield, E. H.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineults, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Predictable surface emission patterns in terahertz photonic-crystal quantum cascade lasers,” Opt. Express 17(12), 9491–9502 (2009).
[CrossRef] [PubMed]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

J. A. Fan, M. A. Belkin, F. Capasso, S. Khanna, M. Lachab, A. G. Davies, E. H. Linfield, “Surface emitting terahertz quantum cascade laser with a double-metal waveguide,” Opt. Express 14(24), 11672–11680 (2006).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Liu, H. C.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

S. Fathololoumi, E. Dupont, C. W. I. Chan, Z. R. Wasilewski, S. R. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, H. C. Liu, “Terahertz quantum cascade lasers operating up to ~200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express 20(4), 3866–3876 (2012).
[CrossRef] [PubMed]

Mahler, L.

Maineult, W.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Maineults, W.

Mátyás, A.

Meyer, J. R.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Mujagic, E.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Nobile, M.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Peytavit, E.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Qin, Q.

Razeghi, M.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Reno, J.

B. Williams, S. Kumar, Q. Hu, J. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 18–19 (2006).
[CrossRef]

Reno, J. L.

Ritchie, D. A.

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457(7226), 174–178 (2009).
[CrossRef] [PubMed]

L. Mahler, M. I. Amanti, C. Walther, A. Tredicucci, F. Beltram, J. Faist, H. E. Beere, D. A. Ritchie, “Distributed feedback ring resonators for vertically emitting terahertz quantum cascade lasers,” Opt. Express 17(15), 13031–13039 (2009).
[CrossRef] [PubMed]

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Rossi, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Scalari, G.

M. I. Amanti, M. Fischer, G. Scalari, M. Beck, J. Faist, “Low-divergence single-mode terahertz quantum cascade laser,” Nat. Photonics 3(10), 586–590 (2009).
[CrossRef]

M. Amanti, M. Fischer, C. Walther, G. Scalari, J. Faist, “Horn antennas for terahertz quantum cascade lasers,” Electron. Lett. 43(10), 125–126 (2007).
[CrossRef]

Scheuer, J.

Schrenk, W.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Seng Tan, C.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Sirtori, C.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

Slivken, S.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Strasser, G.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[CrossRef]

Tredicucci, A.

L. Mahler, M. I. Amanti, C. Walther, A. Tredicucci, F. Beltram, J. Faist, H. E. Beere, D. A. Ritchie, “Distributed feedback ring resonators for vertically emitting terahertz quantum cascade lasers,” Opt. Express 17(15), 13031–13039 (2009).
[CrossRef] [PubMed]

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417(6885), 156–159 (2002).
[CrossRef] [PubMed]

Unterrainer, K.

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

Vurgaftman, I.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Walther, C.

Wang, Q.

N. Yu, Q. Wang, F. Capasso, “Beam engineering of quantum cascade lasers,” Laser Photonics Rev. 6(1), 24–46 (2012).
[CrossRef]

Wang, Q. J.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Wasilewski, Z. R.

Wei Min Lee, A.

Williams, B.

B. Williams, S. Kumar, Q. Hu, J. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett. 42(2), 18–19 (2006).
[CrossRef]

Williams, B. S.

Wojcik, A. K.

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Wójcik, A. K.

A. K. Wójcik, N. Yu, F. Capasso, A. Belyanin, “Nonlinear optical interactions of laser modes in quantum cascade lasers,” J. Mod. Opt. 58(9), 727–742 (2011).
[CrossRef]

Yariv, A.

Yu, J. S.

W. Bewley, J. Lindle, I. Vurgaftman, J. R. Meyer, A. J. Evans, S. Slivken, M. Razeghi, C. S. Kim, J. S. Yu, “Beam steering in high-power CW quantum-cascade lasers,” IEEE J. Quantum Electron. 41(6), 833–841 (2005).
[CrossRef]

Yu, N.

N. Yu, Q. Wang, F. Capasso, “Beam engineering of quantum cascade lasers,” Laser Photonics Rev. 6(1), 24–46 (2012).
[CrossRef]

A. K. Wójcik, N. Yu, F. Capasso, A. Belyanin, “Nonlinear optical interactions of laser modes in quantum cascade lasers,” J. Mod. Opt. 58(9), 727–742 (2011).
[CrossRef]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

N. Yu, L. Diehl, E. Cubukcu, D. Bour, S. Corzine, G. Höfler, A. K. Wojcik, K. B. Crozier, A. Belyanin, F. Capasso, “Coherent coupling of multiple transverse modes in quantum cascade lasers,” Phys. Rev. Lett. 102(1), 013901 (2009).
[CrossRef] [PubMed]

Zhang, Y.

G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. Giles Davies, E. Linfield, D. Fatt Lim, C. Seng Tan, S. Fung Yu, H. C. Liu, Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102(3), 031119 (2013).
[CrossRef]

Appl. Phys. Lett.

W. Maineult, P. Gellie, A. Andronico, P. Filloux, G. Leo, C. Sirtori, S. Barbieri, E. Peytavit, T. Akalin, J.-F. Lampin, H. E. Beere, D. A. Ritchie, “Metal-metal terahertz quantum cascade laser with micro-transverse-electromagnetic-horn antenna,” Appl. Phys. Lett. 93(18), 183508 (2008).
[CrossRef]

E. Mujagić, C. Deutsch, H. Detz, P. Klang, M. Nobile, A. M. Andrews, W. Schrenk, K. Unterrainer, G. Strasser, “Vertically emitting terahertz quantum cascade ring lasers,” Appl. Phys. Lett. 95(1), 011120 (2009).
[CrossRef]

S. Kumar, Q. Hu, J. L. Reno, “186 K operation of terahertz quantum-cascade lasers based on a diagonal design,” Appl. Phys. Lett. 94(13), 131105 (2009).
[CrossRef]

Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, S. P. Khanna, E. H. Linfield, A. G. Davies, “Graded photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 96(3), 031104 (2010).
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Figures (9)

Fig. 1
Fig. 1

(a) Three-dimensional schematic representation of the THz concentric-circular-grating quantum cascade laser design. The semitransparent rectangle represents the two-dimensional (2D) simulation plane. (b) 2D simulated magnetic field distribution making use of the 360°rotational symmetry of the designed structure. The magnified views show the widths of the metal in each period and the boundary region without metal coverage, indicated as R1, R2, … R15 and δ, respectively. The black lines represent metal.

Fig. 2
Fig. 2

(a) Electric field distribution of the standard second-order DFB CCG THz QCL in the central region. (b) – (d) Mode spectra of the structures for different R15 with other parameters unchanged. (e) – (g) the corresponding electric-field (Ez) profiles of the expected modes, highlighted by the red arrows in (b) – (d), respectively, obtained at the middle height of the active region.

Fig. 3
Fig. 3

(a), (b), (c) Simulation results after each adjustment of the slit locations. (i) Electric field (|E|) distribution of the expected mode at the central part of the grating. The first five slits are numbered 1, 2, …,5, and their locations are indicated by the white arrows. White dashed lines near the arrows indicate the original locations of the slits. The displacement distance of each slit is given above the arrow. (ii) Mode spectrum of the adjusted structure, a red arrow indicates the expected mode. (iii) The electric-field (Ez) profile.

Fig. 4
Fig. 4

(a) Optical microscope image of a fabricated CCG DFB THz QCL. A three-spoke bridge structure connects the concentric rings together to allow electrical pumping of the whole grating. (b) Mode spectrum of the device using 3D full-wave simulation to take the higher azimuthal modes into account. Only the first four lowest order azimuthal modes are plotted. The electric field distributions of the modes with lowest losses (the fundamental and second azimuthal modes, highlighted by a red circle) are shown in the inset. (c), (d) Comparison of the Bessel function J0(r) and –J2(r), and Y0(r) and –Y2(r), respectively. The fundamental and second-order Bessel functions coincide except in the first few peaks.

Fig. 5
Fig. 5

(a) Light-current-voltage characterization of the CCG device at different heatsink temperatures under pulsed mode operation. (b) Emission spectra of the device at 9 K heatsink temperation as a function of injected current, from threshold to the rollover. The inset shows a logarithmic scale plot of the spectrum, demonstrating a side-mode suppression ratio of around 30 dB.

Fig. 6
Fig. 6

(a) Measured far-field pattern of a typical THz CCG QCL. (b), (c), and (d) Electric field distributions and the corresponding far-field patterns for the fundamental, the first-order and second-order azimuthal modes, respectively.

Fig. 7
Fig. 7

(a) Scanning electron-beam microscope images of the anisotropic sidewall profiles caused by wet chemical etching. The sidewalls of the upper and lower boundaries are more vertical than those of the left and right boundaries. (b) The change of electric field distribution and far-field pattern caused by a slight (2 um) deformation of the circular active region disk.

Fig. 8
Fig. 8

Coherent superimposition of the far fields of the fundamental and second-order azimuthal modes. (a) – (e) Resulting far-field patterns with the phase difference of the two modes Δϕ varies from 0° to 120°. (f) Resulting far-field pattern with Δϕ = 0° but 1.5 times amplitude for the second-order azimuthal mode.

Fig. 9
Fig. 9

Splitting of the fundamental azimuthal mode under deformation. (a) Electric field distribution of the original fundamental azimuthal mode. (b), (c) Electric field distributions of the splitted deformed fundamental azimuthal modes, and their corresponding far-field patterns (d), (e), respectively.

Equations (3)

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E z ( r ) = [ A ( r ) J m ( k r ) + B ( r ) Y m ( k r ) ] e i m φ
× ( ϵ 1 × H ) ω 2 c 2 H = 0
H ( r , z , φ ) = H ( r , z ) e i m φ

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