Abstract

A systematic optimization study of quantum cascade lasers with integrated nonlinearity for third-harmonic generation is performed. To model current transport the Pauli master equation is solved using a Monte Carlo approach. A multi-objective particle swarm optimization algorithm is applied to obtain the Pareto front. Our theoretical analysis indicates an optimized structure with five orders of magnitude increase in the generated third-harmonic power with respect to the reference design. This striking performance comes with a low threshold current density of about 1.6 kA/cm2 and is attributed to double resonant phonon scattering assisted extraction and injection scheme of the laser.

© 2014 Optical Society of America

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References

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  1. N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
    [Crossref] [PubMed]
  2. M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
    [Crossref]
  3. M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
    [Crossref]
  4. A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
    [Crossref]
  5. H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
    [Crossref]
  6. P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
    [Crossref]
  7. M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
    [Crossref]
  8. R. W. Boyd, Nonlinear Optics (Academic, 2008), 3rd ed.
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  14. C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 011103 (2010).
    [Crossref]
  15. J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
    [Crossref]
  16. D. Hofstetter, M. Beck, T. Aellen, and J. Faist, “High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 μm,” Appl. Phys. Lett. 78, 396–398 (2001).
    [Crossref]
  17. Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
    [Crossref]
  18. M. Yamanishi, K. Fujita, T. Edamura, and H. Kan, “Indirect pump scheme for quantum cascade lasers: dynamics of electron-transport and very high T0-values,” Opt. Express 16, 20748–20758 (2008).
    [Crossref] [PubMed]
  19. S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-thz quantum cascade laser operating significantly above the temperature of ħω/kB,” Nature Physics 7, 166–171 (2011).
    [Crossref]
  20. D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
    [Crossref]
  21. A. Wacker, “Extraction-controlled quantum cascade lasers,” Appl. Phys. Lett. 97, 081105 (2010).
    [Crossref]
  22. J. Faist, “Wallplug efficiency of quantum cascade lasers: Critical parameters and fundamental limits,” Appl. Phys. Lett. 90, 253512 (2007).
    [Crossref]

2012 (1)

A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
[Crossref]

2011 (1)

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-thz quantum cascade laser operating significantly above the temperature of ħω/kB,” Nature Physics 7, 166–171 (2011).
[Crossref]

2010 (6)

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

A. Wacker, “Extraction-controlled quantum cascade lasers,” Appl. Phys. Lett. 97, 081105 (2010).
[Crossref]

C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 011103 (2010).
[Crossref]

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

G. Milovanovic and H. Kosina, “A semiclassical transport model for quantum cascade lasers based on the pauli master equation,” J. Comput. Electron. 9, 211–217 (2010).
[Crossref]

2009 (1)

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

2008 (2)

M. Yamanishi, K. Fujita, T. Edamura, and H. Kan, “Indirect pump scheme for quantum cascade lasers: dynamics of electron-transport and very high T0-values,” Opt. Express 16, 20748–20758 (2008).
[Crossref] [PubMed]

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

2007 (2)

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

J. Faist, “Wallplug efficiency of quantum cascade lasers: Critical parameters and fundamental limits,” Appl. Phys. Lett. 90, 253512 (2007).
[Crossref]

2005 (1)

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

2004 (1)

2003 (1)

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

2002 (1)

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

2001 (1)

D. Hofstetter, M. Beck, T. Aellen, and J. Faist, “High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 μm,” Appl. Phys. Lett. 78, 396–398 (2001).
[Crossref]

1999 (1)

M. V. Fischetti, “Master-equation approach to the study of electronic transport in small semiconductor devices,” Phys. Rev. B 59, 4901 (1999).
[Crossref]

1994 (1)

C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663 (1994).
[Crossref]

Adams, R.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

Aellen, T.

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

D. Hofstetter, M. Beck, T. Aellen, and J. Faist, “High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 μm,” Appl. Phys. Lett. 78, 396–398 (2001).
[Crossref]

Beck, M.

A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
[Crossref]

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

D. Hofstetter, M. Beck, T. Aellen, and J. Faist, “High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 μm,” Appl. Phys. Lett. 78, 396–398 (2001).
[Crossref]

Belkin, M.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

Belkin, M. A.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

Belyanin, A.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

T. Mosely, A. Belyanin, C. Gmachl, D. Sivco, M. Peabody, and A. Cho, “Third harmonic generation in a quantum cascade laser with monolithically integrated resonant optical nonlinearity,” Opt. Express 12, 2972–2976 (2004).
[Crossref] [PubMed]

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Bismuto, A.

A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
[Crossref]

Blaser, S.

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

Botez, D.

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008), 3rd ed.

Callebaut, H.

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

Capasso, F.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663 (1994).
[Crossref]

Chan, C. W. I.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-thz quantum cascade laser operating significantly above the temperature of ħω/kB,” Nature Physics 7, 166–171 (2011).
[Crossref]

Charles, W.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

Chen, J.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

Cheng, L.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

Cho, A.

Cho, A. Y.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Choa, F.-S.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

Colombelli, R.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Diehl, L.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

Dikmelik, Y.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Edamura, T.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

M. Yamanishi, K. Fujita, T. Edamura, and H. Kan, “Indirect pump scheme for quantum cascade lasers: dynamics of electron-transport and very high T0-values,” Opt. Express 16, 20748–20758 (2008).
[Crossref] [PubMed]

Escarra, M. D.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Faist, J.

A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
[Crossref]

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

J. Faist, “Wallplug efficiency of quantum cascade lasers: Critical parameters and fundamental limits,” Appl. Phys. Lett. 90, 253512 (2007).
[Crossref]

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

D. Hofstetter, M. Beck, T. Aellen, and J. Faist, “High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 μm,” Appl. Phys. Lett. 78, 396–398 (2001).
[Crossref]

C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663 (1994).
[Crossref]

Fan, J.-Y.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Fischer, M.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

Fischetti, M. V.

M. V. Fischetti, “Master-equation approach to the study of electronic transport in small semiconductor devices,” Phys. Rev. B 59, 4901 (1999).
[Crossref]

Franz, K. J.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Fujita, K.

Furuta, S.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

Gmachl, C.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

T. Mosely, A. Belyanin, C. Gmachl, D. Sivco, M. Peabody, and A. Cho, “Third harmonic generation in a quantum cascade laser with monolithically integrated resonant optical nonlinearity,” Opt. Express 12, 2972–2976 (2004).
[Crossref] [PubMed]

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Gmachl, C. F.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Hinkov, B.

A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
[Crossref]

Hoffman, A. J.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Hofstetter, D.

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

D. Hofstetter, M. Beck, T. Aellen, and J. Faist, “High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 μm,” Appl. Phys. Lett. 78, 396–398 (2001).
[Crossref]

Hu, Q.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-thz quantum cascade laser operating significantly above the temperature of ħω/kB,” Nature Physics 7, 166–171 (2011).
[Crossref]

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

Jang, M.

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

Jirauschek, C.

C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 011103 (2010).
[Crossref]

Kan, H.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

M. Yamanishi, K. Fujita, T. Edamura, and H. Kan, “Indirect pump scheme for quantum cascade lasers: dynamics of electron-transport and very high T0-values,” Opt. Express 16, 20748–20758 (2008).
[Crossref] [PubMed]

Khurgin, J. B.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Kocharovsky, V.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Kosina, H.

G. Milovanovic and H. Kosina, “A semiclassical transport model for quantum cascade lasers based on the pauli master equation,” J. Comput. Electron. 9, 211–217 (2010).
[Crossref]

Kumar, S.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-thz quantum cascade laser operating significantly above the temperature of ħω/kB,” Nature Physics 7, 166–171 (2011).
[Crossref]

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

Liu, P. Q.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Mawst, L.

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

Meyer, J.

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

Milovanovic, G.

G. Milovanovic and H. Kosina, “A semiclassical transport model for quantum cascade lasers based on the pauli master equation,” J. Comput. Electron. 9, 211–217 (2010).
[Crossref]

Mosely, T.

Oakley, D. C.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

Owschimikow, N.

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Peabody, M.

Pflugl, C.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

Reno, J. L.

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-thz quantum cascade laser operating significantly above the temperature of ħω/kB,” Nature Physics 7, 166–171 (2011).
[Crossref]

Rochat, M.

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

Scandolo, S.

C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663 (1994).
[Crossref]

Shin, J.

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

Sirtori, C.

C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663 (1994).
[Crossref]

Sivco, D.

Sivco, D. L.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Terazzi, R.

A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
[Crossref]

Turner, G. W.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

Vineis, C. J.

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

Vurgaftman, I.

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

Wacker, A.

A. Wacker, “Extraction-controlled quantum cascade lasers,” Appl. Phys. Lett. 97, 081105 (2010).
[Crossref]

Wang, Q. J.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

Wang, X.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

Wittmann, A.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

Xie, F.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

Yamanishi, M.

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

M. Yamanishi, K. Fujita, T. Edamura, and H. Kan, “Indirect pump scheme for quantum cascade lasers: dynamics of electron-transport and very high T0-values,” Opt. Express 16, 20748–20758 (2008).
[Crossref] [PubMed]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1988), 3rd ed.

Appl. Phys. Lett. (9)

M. Jang, R. Adams, J. Chen, W. Charles, C. Gmachl, L. Cheng, F.-S. Choa, and M. Belkin, “Room-temperature operation of 3.6 μm ingaas/alinas quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[Crossref]

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, and J. Faist, “Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett. 92, 201101 (2008).
[Crossref]

A. Bismuto, R. Terazzi, B. Hinkov, M. Beck, and J. Faist, “Fully automatized quantum cascade laser design by genetic optimization,” Appl. Phys. Lett. 101, 021103 (2012).
[Crossref]

C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett. 96, 011103 (2010).
[Crossref]

D. Hofstetter, M. Beck, T. Aellen, and J. Faist, “High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 μm,” Appl. Phys. Lett. 78, 396–398 (2001).
[Crossref]

Q. J. Wang, C. Pflugl, L. Diehl, F. Capasso, T. Edamura, S. Furuta, M. Yamanishi, and H. Kan, “High performance quantum cascade lasers based on three-phonon-resonance design,” Appl. Phys. Lett. 94, 011103 (2009).
[Crossref]

D. Botez, S. Kumar, J. Shin, L. Mawst, I. Vurgaftman, and J. Meyer, “Temperature dependence of the key electro-optical characteristics for midinfrared emitting quantum cascade lasers,” Appl. Phys. Lett. 97, 071101 (2010).
[Crossref]

A. Wacker, “Extraction-controlled quantum cascade lasers,” Appl. Phys. Lett. 97, 081105 (2010).
[Crossref]

J. Faist, “Wallplug efficiency of quantum cascade lasers: Critical parameters and fundamental limits,” Appl. Phys. Lett. 90, 253512 (2007).
[Crossref]

IEEE J. Quantum Elect. (1)

J. Faist, D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser, “Bound-to-continuum and two-phonon resonance, quantum-cascade lasers for high duty cycle, high-temperature operation,” IEEE J. Quantum Elect. 38, 533–546 (2002).
[Crossref]

J. Appl. Phys. (1)

H. Callebaut and Q. Hu, “Importance of coherence for electron transport in terahertz quantum cascade lasers,” J. Appl. Phys. 98, 104505 (2005).
[Crossref]

J. Comput. Electron. (1)

G. Milovanovic and H. Kosina, “A semiclassical transport model for quantum cascade lasers based on the pauli master equation,” J. Comput. Electron. 9, 211–217 (2010).
[Crossref]

Nat. Photonics (2)

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[Crossref]

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

Nature Physics (1)

S. Kumar, C. W. I. Chan, Q. Hu, and J. L. Reno, “A 1.8-thz quantum cascade laser operating significantly above the temperature of ħω/kB,” Nature Physics 7, 166–171 (2011).
[Crossref]

Opt. Express (2)

Phys. Rev. B (2)

C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663 (1994).
[Crossref]

M. V. Fischetti, “Master-equation approach to the study of electronic transport in small semiconductor devices,” Phys. Rev. B 59, 4901 (1999).
[Crossref]

Phys. Rev. Lett. (1)

N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, “Resonant second-order nonlinear optical processes in quantum cascade lasers,” Phys. Rev. Lett. 90, 043902 (2003).
[Crossref] [PubMed]

Other (2)

A. Yariv, Quantum Electronics (Wiley, 1988), 3rd ed.

R. W. Boyd, Nonlinear Optics (Academic, 2008), 3rd ed.

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Figures (4)

Fig. 1
Fig. 1 (a) Pareto front for THG. Triangles represent the results of various particles in the search space and circles indicate the obtained Pareto front. The dash-dot line corresponds to the merit function of the best design if it had different values of χ(3). (b) Temporal evolution of the intra-cavity power in the optimized device. The prediction of Eq. (2) is indicated by the dashed line. A typical mode cross-section of 90μm2 is used in the calculations. Single-mode optical cavity is assumed. (c) The merit function and wavelength of the optimized design as functions of the applied electric field. Strong linear Stark tuning of the pump laser transition around the peak of the merit function allows a broad tunability of the generated TH frequency.
Fig. 2
Fig. 2 Conduction band diagrams and squared wavefunctions of (a) the reference design at an electric field of 46.5kV/cm. (b) The optimized design at an electric field of 60.1kV/cm, where the merit function peaks. The optimized structure can be viewed as double phonon-photon-double phonon (5P) structure. (c) The schematic of the transition between levels of the optimized design. ‘e’ and ‘i’ represent the extractor and injector levels, respectively.
Fig. 3
Fig. 3 Energy-position-resolved electron density of the (a) reference and (b) optimized design at T = 300K and at the electric field of maximum merit function.
Fig. 4
Fig. 4 (a) The spectrum of electrons distribution. (b) Current density-field characteristics of the optimized structure. At small electric fields, the transition 2 → i1 lases with a wavelength similar to the transition 2 → 1 at higher electric fields. The electron sheet density difference between these transitions multiplied by the corresponding dipole matrix element is shown. (c) The merit function and the threshold current density at room temperature as functions of the doping density. An effective optical loss (α = (αm + αw)/Γ) of 35 cm−1 is assumed for a doping density of 3 × 1017cm−3. With the assumption of Γ = 0.65, αm = 2cm−1, and αw = αscat + γndop [22], the optical loss at other doping concentrations can be extrapolated as shown in the figure. γ is a constant [22] and a value of αscatt = 2.5cm−1 is assumed for the passive waveguide loss.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

W 3 ω = 9 ω 2 16 c 4 ε 0 2 n eff ( 3 ω ) n eff 3 ( ω ) | χ ( 3 ) ( 3 ω ) | 2 S eff W ω 3 l coh 2 ,
W ω = 8 π n eff ( ω ) h c A m L t spon 3 g ( ν 0 ) λ 3 τ ( g 0 α w + α m Γ ) ,

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