Abstract

We demonstrate terahertz (THz) frequency laser emission around 3.2 THz from localized modes in one-dimensional disordered grating systems. The disordered structures are patterned on top of the double-metal waveguide of a THz quantum cascade laser. Multiple emission peaks are observed within a frequency range corresponding to the bandgap of a periodic counterpart with no disorder, indicating the presence of mode localization aided by Bragg scattering. Simulations and experimental measurements provide strong evidence for the spatial localization of the THz laser modes.

© 2018 Chinese Laser Press

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References

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  1. H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
    [Crossref]
  2. P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
    [Crossref]
  3. J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
    [Crossref]
  4. A. Consoli, D. Mariano, N. U. Wetter, and C. López, “Large area resonant feedback random lasers based on dye-doped biopolymer films,” Opt. Express 23, 29954–29963 (2015).
    [Crossref]
  5. A. Consoli and C. Lopez, “Emission regimes of random lasers with spatially localized feedback,” Opt. Express 24, 10912–10920 (2016).
    [Crossref]
  6. D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2013).
    [Crossref]
  7. L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
    [Crossref]
  8. R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
    [Crossref]
  9. B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
    [Crossref]
  10. G. Liang, T. Liu, Q. J. Wang, and S. Member, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
    [Crossref]
  11. H. C. Liu, C. Y. Song, and A. J. SpringThorpe, “Terahertz quantum-well photodetector,” Appl. Phys. Lett. 84, 4068–4070 (2004).
    [Crossref]
  12. M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
    [Crossref]
  13. B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
    [Crossref]
  14. G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
    [Crossref]
  15. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature 457, 174–178 (2009).
    [Crossref]
  16. G. Liang, H. Liang, Y. Zhang, S. P. Khanna, L. Li, A. G. Davies, E. Linfield, D. F. Lim, C. S. Tan, S. F. Yu, H. C. Liu, and Q. J. Wang, “Single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Appl. Phys. Lett. 102, 031119 (2013).
    [Crossref]
  17. G. Liang, H. Liang, Y. Zhang, L. Li, and A. G. Davies, “Low divergence single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Opt. Express 21, 31872–31882 (2013).
    [Crossref]
  18. L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
    [Crossref]
  19. M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
    [Crossref]
  20. S. Schönhuber, M. Brandstetter, T. Hisch, C. Deutsch, M. Krall, H. Detz, A. M. Andrews, G. Strasser, S. Rotter, and K. Unterrainer, “Random lasers for broadband directional emission,” Optica 3, 1035–1038 (2016).
    [Crossref]
  21. Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
    [Crossref]
  22. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–676 (1979).
    [Crossref]
  23. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
    [Crossref]
  24. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
    [Crossref]
  25. S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
    [Crossref]
  26. V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
    [Crossref]
  27. L. I. Deych, D. Zaslavsky, and A. A. Lisyansky, “Statistics of the Lyapunov exponent in 1D random periodic-on-average systems,” Phys. Rev. Lett. 81, 5390–5393 (1998).
    [Crossref]
  28. S. H. Chang, H. Cao, and S. T. Ho, “Cavity formation and light propagation in partially ordered and completely random one-dimensional systems,” IEEE J. Quantum Electron. 39, 364–374 (2003).
    [Crossref]
  29. K. Y. Bliokh, Y. P. Bliokh, and V. D. Freilikher, “Resonances in one-dimensional disordered systems: localization of energy and resonant transmission,” J. Opt. Soc. Am. B 21, 113–120 (2004).
    [Crossref]
  30. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
    [Crossref]
  31. M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
    [Crossref]
  32. I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
    [Crossref]

2017 (1)

G. Liang, T. Liu, Q. J. Wang, and S. Member, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
[Crossref]

2016 (3)

A. Consoli and C. Lopez, “Emission regimes of random lasers with spatially localized feedback,” Opt. Express 24, 10912–10920 (2016).
[Crossref]

S. Schönhuber, M. Brandstetter, T. Hisch, C. Deutsch, M. Krall, H. Detz, A. M. Andrews, G. Strasser, S. Rotter, and K. Unterrainer, “Random lasers for broadband directional emission,” Optica 3, 1035–1038 (2016).
[Crossref]

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

2015 (2)

A. Consoli, D. Mariano, N. U. Wetter, and C. López, “Large area resonant feedback random lasers based on dye-doped biopolymer films,” Opt. Express 23, 29954–29963 (2015).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

2014 (1)

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

2013 (3)

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

G. Liang, H. Liang, Y. Zhang, L. Li, and A. G. Davies, “Low divergence single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Opt. Express 21, 31872–31882 (2013).
[Crossref]

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2013).
[Crossref]

2012 (1)

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

2011 (1)

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

2010 (2)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

2009 (3)

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

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

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

2007 (3)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
[Crossref]

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
[Crossref]

2004 (3)

H. C. Liu, C. Y. Song, and A. J. SpringThorpe, “Terahertz quantum-well photodetector,” Appl. Phys. Lett. 84, 4068–4070 (2004).
[Crossref]

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

K. Y. Bliokh, Y. P. Bliokh, and V. D. Freilikher, “Resonances in one-dimensional disordered systems: localization of energy and resonant transmission,” J. Opt. Soc. Am. B 21, 113–120 (2004).
[Crossref]

2003 (2)

S. H. Chang, H. Cao, and S. T. Ho, “Cavity formation and light propagation in partially ordered and completely random one-dimensional systems,” IEEE J. Quantum Electron. 39, 364–374 (2003).
[Crossref]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

2002 (2)

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
[Crossref]

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

2000 (1)

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

1998 (1)

L. I. Deych, D. Zaslavsky, and A. A. Lisyansky, “Statistics of the Lyapunov exponent in 1D random periodic-on-average systems,” Phys. Rev. Lett. 81, 5390–5393 (1998).
[Crossref]

1995 (1)

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
[Crossref]

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

1979 (1)

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–676 (1979).
[Crossref]

Abrahams, E.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–676 (1979).
[Crossref]

Anderson, P. W.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–676 (1979).
[Crossref]

Andrews, A. M.

Barbieri, S.

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

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Beaudoin, G.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Beere, H.

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

Beere, H. E.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

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

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

Belkin, M.

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

Beltram, F.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

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

Belyanin, A.

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

Bliokh, K. Y.

Bliokh, Y. P.

Brandstetter, M.

Callebaut, H.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

Cao, H.

S. H. Chang, H. Cao, and S. T. Ho, “Cavity formation and light propagation in partially ordered and completely random one-dimensional systems,” IEEE J. Quantum Electron. 39, 364–374 (2003).
[Crossref]

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Capasso, F.

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Castellano, F.

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

Chang, R. P. H.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Chang, S. H.

S. H. Chang, H. Cao, and S. T. Ho, “Cavity formation and light propagation in partially ordered and completely random one-dimensional systems,” IEEE J. Quantum Electron. 39, 364–374 (2003).
[Crossref]

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Chassagneux, Y.

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

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Chong, Y.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

Colombelli, R.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

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

Consoli, A.

Davies, A. G.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

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

G. Liang, H. Liang, Y. Zhang, L. Li, and A. G. Davies, “Low divergence single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Opt. Express 21, 31872–31882 (2013).
[Crossref]

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

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

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

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

Davies, G.

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

De Wilde, Y.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Detz, H.

Deutsch, C.

Deych, L. I.

L. I. Deych, D. Zaslavsky, and A. A. Lisyansky, “Statistics of the Lyapunov exponent in 1D random periodic-on-average systems,” Phys. Rev. Lett. 81, 5390–5393 (1998).
[Crossref]

Dietz, R. J. B.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

Faist, J.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Fallert, J.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

Fang, T.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Freilikher, V. D.

K. Y. Bliokh, Y. P. Bliokh, and V. D. Freilikher, “Resonances in one-dimensional disordered systems: localization of energy and resonant transmission,” J. Opt. Soc. Am. B 21, 113–120 (2004).
[Crossref]

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
[Crossref]

Garcia, P. D.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

Graf, M.

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

Greusard, L.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Hisch, T.

Ho, S. T.

S. H. Chang, H. Cao, and S. T. Ho, “Cavity formation and light propagation in partially ordered and completely random one-dimensional systems,” IEEE J. Quantum Electron. 39, 364–374 (2003).
[Crossref]

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Hofstetter, D.

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

Hu, Q.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

Hu, X.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Hwang, W. S.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Iotti, R. C.

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

Jena, D.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Kalt, H.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

Kelly, M. M.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Khanna, S. P.

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

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

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

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

Klingshirn, C.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

Kohler, R.

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

Krall, M.

Kumar, S.

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
[Crossref]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

Lee, A. W. M.

Li, L.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

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

G. Liang, H. Liang, Y. Zhang, L. Li, and A. G. Davies, “Low divergence single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Opt. Express 21, 31872–31882 (2013).
[Crossref]

Li, L. H.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

Liang, G.

G. Liang, T. Liu, Q. J. Wang, and S. Member, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
[Crossref]

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

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

G. Liang, H. Liang, Y. Zhang, L. Li, and A. G. Davies, “Low divergence single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Opt. Express 21, 31872–31882 (2013).
[Crossref]

Liang, H.

G. Liang, H. Liang, Y. Zhang, L. Li, and A. G. Davies, “Low divergence single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Opt. Express 21, 31872–31882 (2013).
[Crossref]

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

Liang, H. K.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

Liansky, B. A.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
[Crossref]

Licciardello, D. C.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–676 (1979).
[Crossref]

Lim, D. F.

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

Linfiel, E. H.

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

Linfield, E.

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

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

Linfield, E. H.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

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

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

Lisyansky, A. A.

L. I. Deych, D. Zaslavsky, and A. A. Lisyansky, “Statistics of the Lyapunov exponent in 1D random periodic-on-average systems,” Phys. Rev. Lett. 81, 5390–5393 (1998).
[Crossref]

Liu, H. C.

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

H. C. Liu, C. Y. Song, and A. J. SpringThorpe, “Terahertz quantum-well photodetector,” Appl. Phys. Lett. 84, 4068–4070 (2004).
[Crossref]

Liu, L.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Liu, T.

G. Liang, T. Liu, Q. J. Wang, and S. Member, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
[Crossref]

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

Liu, X.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Lodahl, P.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

Lopez, C.

López, C.

Mahler, L.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

Maineult, W.

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

Mansha, S.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

Maradudin, A. A.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
[Crossref]

Mariano, D.

Mcgurn, A. R.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
[Crossref]

Member, S.

G. Liang, T. Liu, Q. J. Wang, and S. Member, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
[Crossref]

Meng, B.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

Moldovan-Doyen, I. C.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Nobile, M.

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

Pflügl, C.

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

Qin, Q.

Ramakrishnan, T. V.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–676 (1979).
[Crossref]

Reno, J. L.

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
[Crossref]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

Ritchie, D.

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

Ritchie, D. A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

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

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

Ronzani, A.

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

Rossi, F.

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

Rotter, S.

Sagnes, I.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Sapienza, L.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

Sartor, J.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

Scalari, G.

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

Schneider, D.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

Schönhuber, S.

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Sebbah, P.

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
[Crossref]

Seelig, E. W.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Segev, M.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Sensale-Rodriguez, B.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Sevin, G.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Shen, Y.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Sivco, D. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

Smolka, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

Song, C. Y.

H. C. Liu, C. Y. Song, and A. J. SpringThorpe, “Terahertz quantum-well photodetector,” Appl. Phys. Lett. 84, 4068–4070 (2004).
[Crossref]

SpringThorpe, A. J.

H. C. Liu, C. Y. Song, and A. J. SpringThorpe, “Terahertz quantum-well photodetector,” Appl. Phys. Lett. 84, 4068–4070 (2004).
[Crossref]

Stobbe, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

Strasser, G.

Strupiechonski, E.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Tahy, K.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Talora, V.

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

Tan, C. S.

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

Tao, J.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

Thyrrestrup, H.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

Tredicucci, A.

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

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

Unterrainer, K.

Vanneste, C.

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
[Crossref]

Vitiello, M. S.

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

Walther, C.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

Wang, Q.

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

Wang, Q. J.

G. Liang, T. Liu, Q. J. Wang, and S. Member, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
[Crossref]

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

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

Wetter, N. U.

Wiersma, D. S.

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2013).
[Crossref]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

Williams, B. S.

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
[Crossref]

S. Kumar, B. S. Williams, Q. Qin, A. W. M. Lee, and J. L. Reno, “Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal-metal waveguides,” Opt. Express 15, 113–128 (2007).
[Crossref]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

Xing, H. G.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Xu, G.

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

Xu, J. Y.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Yan, R. S.

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Yu, S. F.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

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

Yu, X.

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

Yurkevich, I. V.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
[Crossref]

Zaslavsky, D.

L. I. Deych, D. Zaslavsky, and A. A. Lisyansky, “Statistics of the Lyapunov exponent in 1D random periodic-on-average systems,” Phys. Rev. Lett. 81, 5390–5393 (1998).
[Crossref]

Zeng, Y.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

Zhang, D. Z.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Zhang, Y.

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

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

G. Liang, H. Liang, Y. Zhang, L. Li, and A. G. Davies, “Low divergence single-mode surface-emitting concentric-circular-grating terahertz quantum cascade lasers,” Opt. Express 21, 31872–31882 (2013).
[Crossref]

ACS Photon. (2)

G. Liang, X. Hu, X. Yu, Y. Shen, L. H. Li, A. G. Davies, E. H. Linfield, H. K. Liang, Y. Zhang, and S. F. Yu, “Integrated terahertz graphene modulator with 100% modulation depth,” ACS Photon. 2, 1559–1566 (2015).
[Crossref]

Y. Zeng, G. Liang, H. K. Liang, S. Mansha, B. Meng, T. Liu, X. Hu, J. Tao, L. Li, A. G. Davies, E. H. Linfield, Y. Zhang, Y. Chong, and Q. J. Wang, “Designer multimode localized random lasing in amorphous lattices at terahertz frequencies,” ACS Photon. 3, 2453–2460 (2016).
[Crossref]

Appl. Phys. Lett. (5)

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, “Terahertz quantum-cascade laser at lambda approximate to 100 μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124–2126 (2003).
[Crossref]

I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98, 231112 (2011).
[Crossref]

H. C. Liu, C. Y. Song, and A. J. SpringThorpe, “Terahertz quantum-well photodetector,” Appl. Phys. Lett. 84, 4068–4070 (2004).
[Crossref]

M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, “Terahertz range quantum well infrared photodetector,” Appl. Phys. Lett. 84, 475–477 (2004).
[Crossref]

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

IEEE J. Quantum Electron. (1)

S. H. Chang, H. Cao, and S. T. Ho, “Cavity formation and light propagation in partially ordered and completely random one-dimensional systems,” IEEE J. Quantum Electron. 39, 364–374 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

M. Belkin, Q. Wang, C. Pflügl, A. Belyanin, S. P. Khanna, A. G. Davies, E. H. Linfiel, and F. Capasso, “High-temperature operation of terahertz quantum cascade laser sources,” IEEE J. Sel. Top. Quantum Electron. 15, 952–967 (2009).
[Crossref]

G. Liang, T. Liu, Q. J. Wang, and S. Member, “Recent developments of terahertz quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 23, 1200118 (2017).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Commun. (2)

M. S. Vitiello, M. Nobile, A. Ronzani, A. Tredicucci, F. Castellano, V. Talora, L. Li, E. H. Linfield, and A. G. Davies, “Photonic quasi-crystal terahertz lasers,” Nat. Commun. 5, 5884 (2014).
[Crossref]

B. Sensale-Rodriguez, R. S. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

Nat. Photonics (4)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).
[Crossref]

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009).
[Crossref]

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2013).
[Crossref]

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
[Crossref]

Nature (3)

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

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

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Opt. Express (4)

Optica (1)

Phys. Rev. B (1)

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
[Crossref]

Phys. Rev. E (1)

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. Mcgurn, “Enhanced transmission due to disorder,” Phys. Rev. E 51, 6301–6304 (1995).
[Crossref]

Phys. Rev. Lett. (3)

L. I. Deych, D. Zaslavsky, and A. A. Lisyansky, “Statistics of the Lyapunov exponent in 1D random periodic-on-average systems,” Phys. Rev. Lett. 81, 5390–5393 (1998).
[Crossref]

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–676 (1979).
[Crossref]

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[Crossref]

Science (2)

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327, 1352–1355 (2010).
[Crossref]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1.

Diagram of the THz QCL structure with a 1D disordered grating. Insets: top view of the device (top left), and scanning electron microscope (SEM) image of the fabricated QCL with disordered grating (bottom right); here, the aperture width is 3.5 μm and the disorder degree is 0.2.

Fig. 2.
Fig. 2.

(a) Ensemble-averaged transmission spectrum over 100 different configurations of the 1D disordered gratings for each degree of disorder. In the simulation, the 3D disordered waveguide structure was simplified to a 1D grating using an estimated refractive index contrast and without considering waveguide or material loss. (b) Ensemble-averaged gain threshold, calculated from 20 different configurations for each degree of disorder and taking the mean gain threshold at each frequency bin. The simulation was simplified to a 2D calculation of the structural cross sections where the xz plane was considered, while the grating was assumed to be infinite in the y direction. For Δd=0, the peak at Δω/ω0=0.15 is induced by resonance with the wire bonding areas. This resonance is disrupted and therefore disappears when disorder is introduced. The free carrier absorption losses of the active material were not considered.

Fig. 3.
Fig. 3.

(a) LIV curves and (b) emission spectrum at 4.26 A for the fabricated 1D periodic QCL. (c) LIV curves and (d) emission spectra for the fabricated 1D disordered QCL with Δd=0.2. Emission spectra were measured at a heat-sink temperature of 10 K with a resolution of 0.2  cm1. Aperture width of the devices is 3.5 μm.

Fig. 4.
Fig. 4.

(a) Diagram showing two different sets of disordered gratings with disorder degree of Δd=0.2 fabricated on the same ridge, with the two lasers being pumped separately. (b) Emission spectra under different pumping conditions. Peaks are labelled by the frequency value in THz. (c) Calculated mode distributions (red curves) corresponding to four emission peaks when the “cold” laser was not pumped. The simulation was simplified to a 2D calculation of the structural cross sections where the xz plane was considered, while the grating was assumed to be infinite in the y direction. For the cold laser, imag(nGaAs/AlGaAs)=0.01i; while for the hot laser, imag(nGaAs/AlGaAs)=0.01i. Inset: field distribution snapshots of the top-view structure calculation (xy plane within the active region, as shown in Fig. 1). The calculation results for cross section (red curves) and top view (field distribution snapshots) of the same structure agree well.

Fig. 5.
Fig. 5.

Emission spectra of a 1D disordered QCL without (red curve) and with (violet dashed curve) partial covering by a copper sheet. The pumping current is 4.09 A. All the peaks are labelled by their frequency values in THz. The arrows are referred to in the text.

Tables (1)

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Table 1. Peak Frequencies (THz) and the Corresponding Lasing Threshold Currents (A) Corresponding to the Spectra in Fig. 3(d)

Equations (1)

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Lϵ=[abs(Ez)dx]2/(Ez)2dx