Abstract

We present an extended ensemble Monte Carlo approach, allowing for the self-consistent modeling of terahertz difference frequency generation in quantum cascade lasers. Our simulations are validated against available experimental data for a current room temperature design. Tera-hertz output powers in the mW range are predicted for ideal light extraction.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
    [CrossRef]
  2. M. 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]
  3. C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
    [CrossRef]
  4. Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
    [CrossRef]
  5. K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
    [CrossRef]
  6. S. Fathololoumi, E. Dupont, C. Chan, Z. Wasilewski, S. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express20, 3866–3876 (2012).
    [CrossRef] [PubMed]
  7. B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42, 89–90 (2006).
    [CrossRef]
  8. R. C. Iotti and F. Rossi, “Carrier thermalization versus phonon-assisted relaxation in quantum-cascade lasers: A Monte Carlo approach,” Appl. Phys. Lett.78, 2902–2904 (2001).
    [CrossRef]
  9. X. Gao, D. Botez, and I. Knezevic, “X-valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study,” J. Appl. Phys.101, 063101 (2007).
    [CrossRef]
  10. A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys.110, 013108 (2011).
    [CrossRef]
  11. R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett.79, 3920–3922 (2001).
    [CrossRef]
  12. H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
    [CrossRef]
  13. O. Bonno, J.-L. Thobel, and F. Dessenne, “Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers,” J. Appl. Phys.97, 043702 (2005).
    [CrossRef]
  14. J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett.89, 211115 (2006).
    [CrossRef]
  15. C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
    [CrossRef]
  16. A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010).
  17. C. Jirauschek, “Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers,” Appl. Phys. Lett.96, 011103 (2010).
    [CrossRef]
  18. C. Jirauschek, “Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers,” Opt. Express18, 25922–25927 (2010).
    [CrossRef] [PubMed]
  19. Y. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, 1984).
  20. C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys.105, 123102 (2009).
    [CrossRef]
  21. C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron.45, 1059–1067 (2009).
    [CrossRef]
  22. G. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  23. N. Bloembergen, Nonlinear Optics (World Scientific, 1996).
  24. C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys.107, 013104 (2010).
    [CrossRef]
  25. K. Chiang, “Performance of the effective-index method for the analysis of dielectric waveguides,” Opt. Lett.16, 714–716 (1991).
    [CrossRef] [PubMed]
  26. J. Butler and J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron.10, 809–815 (1974).
    [CrossRef]
  27. S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys.97, 053106 (2005).
    [CrossRef]

2012 (2)

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

S. Fathololoumi, E. Dupont, C. Chan, Z. Wasilewski, S. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express20, 3866–3876 (2012).
[CrossRef] [PubMed]

2011 (3)

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys.110, 013108 (2011).
[CrossRef]

A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010).

2010 (3)

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

C. Jirauschek, “Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers,” Opt. Express18, 25922–25927 (2010).
[CrossRef] [PubMed]

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys.107, 013104 (2010).
[CrossRef]

2009 (2)

C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys.105, 123102 (2009).
[CrossRef]

C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron.45, 1059–1067 (2009).
[CrossRef]

2008 (2)

M. 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]

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

2007 (3)

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

X. Gao, D. Botez, and I. Knezevic, “X-valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study,” J. Appl. Phys.101, 063101 (2007).
[CrossRef]

C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
[CrossRef]

2006 (2)

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett.89, 211115 (2006).
[CrossRef]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42, 89–90 (2006).
[CrossRef]

2005 (2)

O. Bonno, J.-L. Thobel, and F. Dessenne, “Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers,” J. Appl. Phys.97, 043702 (2005).
[CrossRef]

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

2003 (1)

H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
[CrossRef]

2001 (2)

R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett.79, 3920–3922 (2001).
[CrossRef]

R. C. Iotti and F. Rossi, “Carrier thermalization versus phonon-assisted relaxation in quantum-cascade lasers: A Monte Carlo approach,” Appl. Phys. Lett.78, 2902–2904 (2001).
[CrossRef]

1991 (1)

1974 (1)

J. Butler and J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron.10, 809–815 (1974).
[CrossRef]

Adams, R. W.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Amann, M. C.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Bai, Y.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Ban, D.

Bandyopadhyay, N.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Belkin, M.

A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010).

M. 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]

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Belkin, M. A.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Belyanin, A.

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

M. 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. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (World Scientific, 1996).

Boehm, G.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Bonno, O.

O. Bonno, J.-L. Thobel, and F. Dessenne, “Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers,” J. Appl. Phys.97, 043702 (2005).
[CrossRef]

Botez, D.

X. Gao, D. Botez, and I. Knezevic, “X-valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study,” J. Appl. Phys.101, 063101 (2007).
[CrossRef]

Butler, J.

J. Butler and J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron.10, 809–815 (1974).
[CrossRef]

Callebaut, H.

H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
[CrossRef]

Cao, J. C.

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett.89, 211115 (2006).
[CrossRef]

Capasso, F.

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

M. 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. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Chan, C.

Chiang, K.

Cho, A.

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Dessenne, F.

O. Bonno, J.-L. Thobel, and F. Dessenne, “Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers,” J. Appl. Phys.97, 043702 (2005).
[CrossRef]

Dupont, E.

Faist, J.

M. 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]

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

Fathololoumi, S.

Fischer, M.

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

M. 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]

Gao, X.

X. Gao, D. Botez, and I. Knezevic, “X-valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study,” J. Appl. Phys.101, 063101 (2007).
[CrossRef]

Geiser, M.

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

Grasse, C.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Hu, Q.

S. Fathololoumi, E. Dupont, C. Chan, Z. Wasilewski, S. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express20, 3866–3876 (2012).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42, 89–90 (2006).
[CrossRef]

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

H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
[CrossRef]

Iotti, R. C.

R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett.79, 3920–3922 (2001).
[CrossRef]

R. C. Iotti and F. Rossi, “Carrier thermalization versus phonon-assisted relaxation in quantum-cascade lasers: A Monte Carlo approach,” Appl. Phys. Lett.78, 2902–2904 (2001).
[CrossRef]

Jang, M.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Jirauschek, C.

S. Fathololoumi, E. Dupont, C. Chan, Z. Wasilewski, S. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express20, 3866–3876 (2012).
[CrossRef] [PubMed]

A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys.110, 013108 (2011).
[CrossRef]

A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010).

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

C. Jirauschek, “Monte Carlo study of intrinsic linewidths in terahertz quantum cascade lasers,” Opt. Express18, 25922–25927 (2010).
[CrossRef] [PubMed]

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys.107, 013104 (2010).
[CrossRef]

C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys.105, 123102 (2009).
[CrossRef]

C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron.45, 1059–1067 (2009).
[CrossRef]

C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
[CrossRef]

Knezevic, I.

X. Gao, D. Botez, and I. Knezevic, “X-valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study,” J. Appl. Phys.101, 063101 (2007).
[CrossRef]

Kohen, S.

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

Köhler, R.

R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett.79, 3920–3922 (2001).
[CrossRef]

Kumar, S.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42, 89–90 (2006).
[CrossRef]

H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
[CrossRef]

Laframboise, S.

Liu, H.

Lu, Q. Y.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Lü, J. T.

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett.89, 211115 (2006).
[CrossRef]

Lugli, P.

A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys.110, 013108 (2011).
[CrossRef]

A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010).

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys.107, 013104 (2010).
[CrossRef]

C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys.105, 123102 (2009).
[CrossRef]

C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
[CrossRef]

Matyas, A.

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys.107, 013104 (2010).
[CrossRef]

Mátyás, A.

S. Fathololoumi, E. Dupont, C. Chan, Z. Wasilewski, S. Laframboise, D. Ban, A. Mátyás, C. Jirauschek, Q. Hu, and H. Liu, “Terahertz quantum cascade lasers operating up to ∼200 K with optimized oscillator strength and improved injection tunneling,” Opt. Express20, 3866–3876 (2012).
[CrossRef] [PubMed]

A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys.110, 013108 (2011).
[CrossRef]

A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010).

Oakley, D.

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Pflügl, C.

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

Razeghi, M.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Reno, J. L.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42, 89–90 (2006).
[CrossRef]

H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
[CrossRef]

Rossi, F.

R. C. Iotti and F. Rossi, “Carrier thermalization versus phonon-assisted relaxation in quantum-cascade lasers: A Monte Carlo approach,” Appl. Phys. Lett.78, 2902–2904 (2001).
[CrossRef]

R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett.79, 3920–3922 (2001).
[CrossRef]

Scamarcio, G.

C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
[CrossRef]

Scarpa, G.

C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
[CrossRef]

Shen, Y.

Y. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, 1984).

Sivco, D.

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Slivken, S.

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

Thobel, J.-L.

O. Bonno, J.-L. Thobel, and F. Dessenne, “Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers,” J. Appl. Phys.97, 043702 (2005).
[CrossRef]

Tredicucci, A.

R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett.79, 3920–3922 (2001).
[CrossRef]

Turner, G.

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Vijayraghavan, K.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Vineis, C.

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Vitiello, M. S.

C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
[CrossRef]

Vizbaras, A.

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

Wang, Q.

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

Wasilewski, Z.

Williams, B. S.

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42, 89–90 (2006).
[CrossRef]

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

H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
[CrossRef]

Wittmann, A.

M. 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]

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

Xie, F.

M. 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]

Zoroofchi, J.

J. Butler and J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron.10, 809–815 (1974).
[CrossRef]

Appl. Phys. Lett. (10)

M. 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]

C. Pflügl, M. Belkin, Q. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, and F. Capasso, “Surface-emitting terahertz quantum cascade laser source based on intracavity difference-frequency generation,” Appl. Phys. Lett.93, 161110 (2008).
[CrossRef]

Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Room temperature single-mode terahertz sources based on intracavity difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.99, 131106 (2011).
[CrossRef]

K. Vijayraghavan, R. W. Adams, A. Vizbaras, M. Jang, C. Grasse, G. Boehm, M. C. Amann, and M. A. Belkin, “Terahertz sources based on Čerenkov difference-frequency generation in quantum cascade lasers,” Appl. Phys. Lett.100, 251104 (2012).
[CrossRef]

R. C. Iotti and F. Rossi, “Carrier thermalization versus phonon-assisted relaxation in quantum-cascade lasers: A Monte Carlo approach,” Appl. Phys. Lett.78, 2902–2904 (2001).
[CrossRef]

R. Köhler, R. C. Iotti, A. Tredicucci, and F. Rossi, “Design and simulation of terahertz quantum cascade lasers,” Appl. Phys. Lett.79, 3920–3922 (2001).
[CrossRef]

H. Callebaut, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Analysis of transport properties of terahertz quantum cascade lasers,” Appl. Phys. Lett.83, 207–209 (2003).
[CrossRef]

J. T. Lü and J. C. Cao, “Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers,” Appl. Phys. Lett.89, 211115 (2006).
[CrossRef]

A. Mátyás, M. Belkin, P. Lugli, and C. Jirauschek, “Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs,” Appl. Phys. Lett.96, 201110 (2010).

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

Electron. Lett. (1)

B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “High-power terahertz quantum-cascade lasers,” Electron. Lett.42, 89–90 (2006).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. Jirauschek, “Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation,” IEEE J. Quantum Electron.45, 1059–1067 (2009).
[CrossRef]

J. Butler and J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron.10, 809–815 (1974).
[CrossRef]

J. Appl. Phys. (7)

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

C. Jirauschek and P. Lugli, “Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers,” J. Appl. Phys.105, 123102 (2009).
[CrossRef]

C. Jirauschek, A. Matyas, and P. Lugli, “Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions,” J. Appl. Phys.107, 013104 (2010).
[CrossRef]

X. Gao, D. Botez, and I. Knezevic, “X-valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study,” J. Appl. Phys.101, 063101 (2007).
[CrossRef]

A. Mátyás, P. Lugli, and C. Jirauschek, “Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers,” J. Appl. Phys.110, 013108 (2011).
[CrossRef]

C. Jirauschek, G. Scarpa, P. Lugli, M. S. Vitiello, and G. Scamarcio, “Comparative analysis of resonant phonon THz quantum cascade lasers,” J. Appl. Phys.101, 086109 (2007).
[CrossRef]

O. Bonno, J.-L. Thobel, and F. Dessenne, “Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers,” J. Appl. Phys.97, 043702 (2005).
[CrossRef]

Nat. Photonics (1)

M. Belkin, F. Capasso, A. Belyanin, D. Sivco, A. Cho, D. Oakley, C. Vineis, and G. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics1, 288–292 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (3)

G. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

N. Bloembergen, Nonlinear Optics (World Scientific, 1996).

Y. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

(a) Conduction band diagram of one period of the BTC structure at 300K for a bias of 38kV/cm. The three energy levels marked in red indicate the level subset contributing most to χ(2) in Eq. (1). (b) Tapered ridge waveguide structure, viewed from top.

Fig. 2
Fig. 2

Temperature dependent simulation results: (a) MIR powers; (b) and (c) THz powers and conversion efficiencies for (b) facet emission and (c) surface outcoupling.

Equations (6)

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

χ ( 2 ) = 1 2 ε 0 L P , m , n d m d m n d n n E 2 D 0 f ( K m n K m n ) d ε , K m n = ( 1 ω n i γ n ω + 1 ω n m + i γ n m + ω ) ( 1 ω m i γ m + ω 2 + 1 ω m i γ m ω 1 ) .
z A 3 = i ω 2 c n 3 f 321 χ ( 2 ) A 1 A 2 * exp ( i Δ k z ) a 2 A 3 ,
P f = ω 2 8 ε 0 c 3 n 1 n 2 n 3 | χ ( 2 ) | 2 P 1 P 2 S eff L coh 2 .
P g = P a = 2 L a P f .
P ˜ g = 2 L ( a + κ ) P f .
P s = 2 L κ P f .

Metrics