Abstract

We designed a quantum cascade semiconductor optical amplifier (QCSOA) structure for enhanced four-wave mixing (FWM) of short optical pulses in midinfrared. To analyze FWM characteristics in a QCSOA, the evolution in the time and spectral domains of two input optical pulses with different frequencies during propagation is calculated using the finite-difference beam propagation method. Calculated third-order susceptibility responsible for FWM resonance nonlinearity of the modified structure is enhanced by two orders of magnitude. Simulation results reveal that quantum cascade structure parameters and injected pump and probe powers are extremely important in determining the amplified FWM optical pulse characteristics in both the time and frequency domains.

© 2013 Optical Society of America

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  1. M. Gurnick and T. DeTemple, “Synthetic nonlinear semiconductors,” IEEE J. Quantum Electron. 19, 791–794 (1983).
    [CrossRef]
  2. F. Capasso, C. Sirtori, and A. Y. Cho, “Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared,” IEEE J. Quantum Electron. 30, 1313–1326 (1994).
    [CrossRef]
  3. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
    [CrossRef]
  4. R. W. Boyd, Nonlinear Optics (Academic, 2007).
  5. S. Banerjee and K. A. Shore, “MIR and NIR nonlinear optical processing using intersubband χ(3) in triple quantum well structures,” Semicond. Sci. Technol. 18, 655–660 (2003).
    [CrossRef]
  6. S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
    [CrossRef]
  7. D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order nonlinearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59, 2932–2934 (1991).
    [CrossRef]
  8. D. Indjin, Z. Ikonic, V. Milanovic, and J. Radovanovic, “Optimization of resonant second and third order nonlinearities in step and continuously graded semiconductor quantum wells,” IEEE J. Quantum Electron. 34, 795–802 (1998).
    [CrossRef]
  9. M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
    [CrossRef]
  10. C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
    [CrossRef]
  11. S. Tomic, V. Milanovic, and Z. Ikonic, “Optimization of intersubband resonant second-order susceptibility in asymmetric graded AlxGa1−xAs quantum wells using supersymmetric quantum mechanics,” Phys. Rev. B 56, 1033–1036 (1997).
    [CrossRef]
  12. S. Banerjee, P. S. Spencer, and K. A. Shore, “Tunable quantum cascade lasers with phase-matched third harmonic generation,” Appl. Phys. Lett. 89, 051113 (2006).
    [CrossRef]
  13. M. Giovannini, M. Beck, N. Hoyler, and J. Faist, “Second harmonic generation in (111)-oriented InP-based quantum cascade laser,” J. Appl. Phys. 101, 103107 (2007).
    [CrossRef]
  14. J. Bai and D. S. Citrin, “Intracavity nonlinearities in quantum-cascade lasers,” J. Appl. Phys. 106, 031101 (2009).
    [CrossRef]
  15. M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
    [CrossRef]
  16. S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
    [CrossRef]
  17. C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
    [CrossRef]
  18. G. Chen, T. Yang, C. Peng, and R. Martini, “Self-consistent approach for quantum cascade laser characteristic simulation,” IEEE J. Quantum Electron. 47, 1086–1093 (2011).
    [CrossRef]
  19. N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000).
    [CrossRef]
  20. J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagation in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263–1269 (1998).
    [CrossRef]
  21. J. M. Tang, P. S. Spencer, and K. A. Shore, “Amplification of picosecond optical pulses in midinfrared intersubband semiconductor optical amplifiers,” Appl. Phys. Lett. 77, 2449–2451 (2000).
    [CrossRef]
  22. Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
    [CrossRef]
  23. H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, “Time-domain up conversion measurements of group-velocity dispersion in quantum cascade lasers,” Opt. Express 15, 15898–15907 (2007).
    [CrossRef]
  24. N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
    [CrossRef]

2012 (1)

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

2011 (2)

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

G. Chen, T. Yang, C. Peng, and R. Martini, “Self-consistent approach for quantum cascade laser characteristic simulation,” IEEE J. Quantum Electron. 47, 1086–1093 (2011).
[CrossRef]

2010 (1)

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

2009 (1)

J. Bai and D. S. Citrin, “Intracavity nonlinearities in quantum-cascade lasers,” J. Appl. Phys. 106, 031101 (2009).
[CrossRef]

2008 (1)

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

2007 (3)

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, “Time-domain up conversion measurements of group-velocity dispersion in quantum cascade lasers,” Opt. Express 15, 15898–15907 (2007).
[CrossRef]

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

M. Giovannini, M. Beck, N. Hoyler, and J. Faist, “Second harmonic generation in (111)-oriented InP-based quantum cascade laser,” J. Appl. Phys. 101, 103107 (2007).
[CrossRef]

2006 (1)

S. Banerjee, P. S. Spencer, and K. A. Shore, “Tunable quantum cascade lasers with phase-matched third harmonic generation,” Appl. Phys. Lett. 89, 051113 (2006).
[CrossRef]

2003 (1)

S. Banerjee and K. A. Shore, “MIR and NIR nonlinear optical processing using intersubband χ(3) in triple quantum well structures,” Semicond. Sci. Technol. 18, 655–660 (2003).
[CrossRef]

2002 (1)

M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
[CrossRef]

2000 (2)

N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000).
[CrossRef]

J. M. Tang, P. S. Spencer, and K. A. Shore, “Amplification of picosecond optical pulses in midinfrared intersubband semiconductor optical amplifiers,” Appl. Phys. Lett. 77, 2449–2451 (2000).
[CrossRef]

1999 (1)

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

1998 (2)

D. Indjin, Z. Ikonic, V. Milanovic, and J. Radovanovic, “Optimization of resonant second and third order nonlinearities in step and continuously graded semiconductor quantum wells,” IEEE J. Quantum Electron. 34, 795–802 (1998).
[CrossRef]

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagation in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263–1269 (1998).
[CrossRef]

1997 (1)

S. Tomic, V. Milanovic, and Z. Ikonic, “Optimization of intersubband resonant second-order susceptibility in asymmetric graded AlxGa1−xAs quantum wells using supersymmetric quantum mechanics,” Phys. Rev. B 56, 1033–1036 (1997).
[CrossRef]

1996 (1)

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

1994 (1)

F. Capasso, C. Sirtori, and A. Y. Cho, “Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared,” IEEE J. Quantum Electron. 30, 1313–1326 (1994).
[CrossRef]

1991 (1)

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order nonlinearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59, 2932–2934 (1991).
[CrossRef]

1990 (1)

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[CrossRef]

1983 (1)

M. Gurnick and T. DeTemple, “Synthetic nonlinear semiconductors,” IEEE J. Quantum Electron. 19, 791–794 (1983).
[CrossRef]

Adams, R. W.

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

Akikusa, N.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Auyang, S. Y.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order nonlinearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59, 2932–2934 (1991).
[CrossRef]

Bai, J.

J. Bai and D. S. Citrin, “Intracavity nonlinearities in quantum-cascade lasers,” J. Appl. Phys. 106, 031101 (2009).
[CrossRef]

Banerjee, S.

S. Banerjee, P. S. Spencer, and K. A. Shore, “Tunable quantum cascade lasers with phase-matched third harmonic generation,” Appl. Phys. Lett. 89, 051113 (2006).
[CrossRef]

S. Banerjee and K. A. Shore, “MIR and NIR nonlinear optical processing using intersubband χ(3) in triple quantum well structures,” Semicond. Sci. Technol. 18, 655–660 (2003).
[CrossRef]

Beck, M.

M. Giovannini, M. Beck, N. Hoyler, and J. Faist, “Second harmonic generation in (111)-oriented InP-based quantum cascade laser,” J. Appl. Phys. 101, 103107 (2007).
[CrossRef]

Beere, H. E.

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

Belkin, M. A.

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

Beltram, F.

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

Berger, V.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

Bois, P.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

Bour, D.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2007).

Cai, H.

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

Capasso, F.

H. Choi, L. Diehl, F. Capasso, D. Bour, S. Corzine, J. Zhu, G. Hofler, and T. B. Norris, “Time-domain up conversion measurements of group-velocity dispersion in quantum cascade lasers,” Opt. Express 15, 15898–15907 (2007).
[CrossRef]

M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

F. Capasso, C. Sirtori, and A. Y. Cho, “Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared,” IEEE J. Quantum Electron. 30, 1313–1326 (1994).
[CrossRef]

Charles, W. O.

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

Chen, G.

G. Chen, T. Yang, C. Peng, and R. Martini, “Self-consistent approach for quantum cascade laser characteristic simulation,” IEEE J. Quantum Electron. 47, 1086–1093 (2011).
[CrossRef]

Chen, J. X.

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

Cheng, L. W.

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

Cho, A.

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

Cho, A. Y.

M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
[CrossRef]

F. Capasso, C. Sirtori, and A. Y. Cho, “Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared,” IEEE J. Quantum Electron. 30, 1313–1326 (1994).
[CrossRef]

Choa, F. S.

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

Choi, H.

Chung, Y.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[CrossRef]

Citrin, D. S.

J. Bai and D. S. Citrin, “Intracavity nonlinearities in quantum-cascade lasers,” J. Appl. Phys. 106, 031101 (2009).
[CrossRef]

Corzine, S.

Dagli, N.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[CrossRef]

Das, N. K.

N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000).
[CrossRef]

DeTemple, T.

M. Gurnick and T. DeTemple, “Synthetic nonlinear semiconductors,” IEEE J. Quantum Electron. 19, 791–794 (1983).
[CrossRef]

Diehl, L.

Edamura, T.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Faist, J.

M. Giovannini, M. Beck, N. Hoyler, and J. Faist, “Second harmonic generation in (111)-oriented InP-based quantum cascade laser,” J. Appl. Phys. 101, 103107 (2007).
[CrossRef]

Fiore, A.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

Giovannini, M.

M. Giovannini, M. Beck, N. Hoyler, and J. Faist, “Second harmonic generation in (111)-oriented InP-based quantum cascade laser,” J. Appl. Phys. 101, 103107 (2007).
[CrossRef]

Gmachl, C.

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

Gmachl, C. F.

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

Green, R. P.

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

Gurnick, M.

M. Gurnick and T. DeTemple, “Synthetic nonlinear semiconductors,” IEEE J. Quantum Electron. 19, 791–794 (1983).
[CrossRef]

Hofler, G.

Hoyler, N.

M. Giovannini, M. Beck, N. Hoyler, and J. Faist, “Second harmonic generation in (111)-oriented InP-based quantum cascade laser,” J. Appl. Phys. 101, 103107 (2007).
[CrossRef]

Hutchinson, A.

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

Ikonic, Z.

D. Indjin, Z. Ikonic, V. Milanovic, and J. Radovanovic, “Optimization of resonant second and third order nonlinearities in step and continuously graded semiconductor quantum wells,” IEEE J. Quantum Electron. 34, 795–802 (1998).
[CrossRef]

S. Tomic, V. Milanovic, and Z. Ikonic, “Optimization of intersubband resonant second-order susceptibility in asymmetric graded AlxGa1−xAs quantum wells using supersymmetric quantum mechanics,” Phys. Rev. B 56, 1033–1036 (1997).
[CrossRef]

Indjin, D.

D. Indjin, Z. Ikonic, V. Milanovic, and J. Radovanovic, “Optimization of resonant second and third order nonlinearities in step and continuously graded semiconductor quantum wells,” IEEE J. Quantum Electron. 34, 795–802 (1998).
[CrossRef]

Ishihara, M.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Jang, M.

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

Johnson, A. M.

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

Kasahara, K.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Kawaguchi, H.

N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000).
[CrossRef]

Kohler, R.

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

Kumazaki, N.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Lalanne, E.

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

Liu, P. Q.

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

Liu, S.

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

Martini, R.

G. Chen, T. Yang, C. Peng, and R. Martini, “Self-consistent approach for quantum cascade laser characteristic simulation,” IEEE J. Quantum Electron. 47, 1086–1093 (2011).
[CrossRef]

Mauro, C.

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

Milanovic, V.

D. Indjin, Z. Ikonic, V. Milanovic, and J. Radovanovic, “Optimization of resonant second and third order nonlinearities in step and continuously graded semiconductor quantum wells,” IEEE J. Quantum Electron. 34, 795–802 (1998).
[CrossRef]

S. Tomic, V. Milanovic, and Z. Ikonic, “Optimization of intersubband resonant second-order susceptibility in asymmetric graded AlxGa1−xAs quantum wells using supersymmetric quantum mechanics,” Phys. Rev. B 56, 1033–1036 (1997).
[CrossRef]

Nagle, J.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

Norris, T. B.

Peng, C.

G. Chen, T. Yang, C. Peng, and R. Martini, “Self-consistent approach for quantum cascade laser characteristic simulation,” IEEE J. Quantum Electron. 47, 1086–1093 (2011).
[CrossRef]

Radovanovic, J.

D. Indjin, Z. Ikonic, V. Milanovic, and J. Radovanovic, “Optimization of resonant second and third order nonlinearities in step and continuously graded semiconductor quantum wells,” IEEE J. Quantum Electron. 34, 795–802 (1998).
[CrossRef]

Ritchie, D. A.

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

Rosencher, E.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

Shore, K. A.

S. Banerjee, P. S. Spencer, and K. A. Shore, “Tunable quantum cascade lasers with phase-matched third harmonic generation,” Appl. Phys. Lett. 89, 051113 (2006).
[CrossRef]

S. Banerjee and K. A. Shore, “MIR and NIR nonlinear optical processing using intersubband χ(3) in triple quantum well structures,” Semicond. Sci. Technol. 18, 655–660 (2003).
[CrossRef]

J. M. Tang, P. S. Spencer, and K. A. Shore, “Amplification of picosecond optical pulses in midinfrared intersubband semiconductor optical amplifiers,” Appl. Phys. Lett. 77, 2449–2451 (2000).
[CrossRef]

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagation in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263–1269 (1998).
[CrossRef]

Sirtori, C.

F. Capasso, C. Sirtori, and A. Y. Cho, “Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared,” IEEE J. Quantum Electron. 30, 1313–1326 (1994).
[CrossRef]

Sivco, D. L.

M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

Spencer, P. S.

S. Banerjee, P. S. Spencer, and K. A. Shore, “Tunable quantum cascade lasers with phase-matched third harmonic generation,” Appl. Phys. Lett. 89, 051113 (2006).
[CrossRef]

J. M. Tang, P. S. Spencer, and K. A. Shore, “Amplification of picosecond optical pulses in midinfrared intersubband semiconductor optical amplifiers,” Appl. Phys. Lett. 77, 2449–2451 (2000).
[CrossRef]

Sugimoto, M.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order nonlinearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59, 2932–2934 (1991).
[CrossRef]

Sugiyama, A.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Takagi, Y.

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Tang, J. M.

J. M. Tang, P. S. Spencer, and K. A. Shore, “Amplification of picosecond optical pulses in midinfrared intersubband semiconductor optical amplifiers,” Appl. Phys. Lett. 77, 2449–2451 (2000).
[CrossRef]

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagation in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263–1269 (1998).
[CrossRef]

Tomic, S.

S. Tomic, V. Milanovic, and Z. Ikonic, “Optimization of intersubband resonant second-order susceptibility in asymmetric graded AlxGa1−xAs quantum wells using supersymmetric quantum mechanics,” Phys. Rev. B 56, 1033–1036 (1997).
[CrossRef]

Tredicucci, A.

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

Troccoli, M.

M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
[CrossRef]

Vinter, B.

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

Walrod, D.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order nonlinearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59, 2932–2934 (1991).
[CrossRef]

Wang, X.

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

Wolff, P. A.

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order nonlinearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59, 2932–2934 (1991).
[CrossRef]

Yamayoshi, Y.

N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000).
[CrossRef]

Yang, T.

G. Chen, T. Yang, C. Peng, and R. Martini, “Self-consistent approach for quantum cascade laser characteristic simulation,” IEEE J. Quantum Electron. 47, 1086–1093 (2011).
[CrossRef]

Zhu, J.

Appl. Phys. Lett. (7)

D. Walrod, S. Y. Auyang, P. A. Wolff, and M. Sugimoto, “Observation of third order nonlinearity due to intersubband transitions in AlGaAs/GaAs superlattices,” Appl. Phys. Lett. 59, 2932–2934 (1991).
[CrossRef]

M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Mid-infrared λ∼7.4  μm. quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett. 80, 4103–4105 (2002).
[CrossRef]

C. Mauro, R. P. Green, A. Tredicucci, F. Beltram, H. E. Beere, and D. A. Ritchie, “Amplification of terahertz radiation in quantum cascade structures,” Appl. Phys. Lett. 102, 61101 (2007).
[CrossRef]

S. Banerjee, P. S. Spencer, and K. A. Shore, “Tunable quantum cascade lasers with phase-matched third harmonic generation,” Appl. Phys. Lett. 89, 051113 (2006).
[CrossRef]

M. Jang, R. W. Adams, J. X. Chen, W. O. Charles, C. Gmachl, L. W. Cheng, F. S. Choa, and M. A. Belkin, “Room-temperature operation of 3.6 μm In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser sources based on intracavity second harmonic generation,” Appl. Phys. Lett. 97, 141103 (2010).
[CrossRef]

S. Liu, H. Cai, E. Lalanne, P. Q. Liu, X. Wang, C. Gmachl, and A. M. Johnson, “Second harmonic generation in quantum cascade lasers pumped by femtosecond mid-infrared pulses,” Appl. Phys. Lett. 99, 122104 (2011).
[CrossRef]

J. M. Tang, P. S. Spencer, and K. A. Shore, “Amplification of picosecond optical pulses in midinfrared intersubband semiconductor optical amplifiers,” Appl. Phys. Lett. 77, 2449–2451 (2000).
[CrossRef]

IEEE J. Quantum Electron. (7)

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[CrossRef]

G. Chen, T. Yang, C. Peng, and R. Martini, “Self-consistent approach for quantum cascade laser characteristic simulation,” IEEE J. Quantum Electron. 47, 1086–1093 (2011).
[CrossRef]

N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000).
[CrossRef]

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagation in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263–1269 (1998).
[CrossRef]

D. Indjin, Z. Ikonic, V. Milanovic, and J. Radovanovic, “Optimization of resonant second and third order nonlinearities in step and continuously graded semiconductor quantum wells,” IEEE J. Quantum Electron. 34, 795–802 (1998).
[CrossRef]

M. Gurnick and T. DeTemple, “Synthetic nonlinear semiconductors,” IEEE J. Quantum Electron. 19, 791–794 (1983).
[CrossRef]

F. Capasso, C. Sirtori, and A. Y. Cho, “Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared,” IEEE J. Quantum Electron. 30, 1313–1326 (1994).
[CrossRef]

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

S. Liu, E. Lalanne, P. Q. Liu, X. Wang, C. F. Gmachl, and A. M. Johnson, “Femtosecond carrier dynamics and nonlinear effects in quantum cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 92–104 (2012).
[CrossRef]

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Kohler, A. Hutchinson, and A. Cho, “Dependence of the device performance on number of stages in quantum-cascade lasers,” IEEE J. Sel. Top. Quantum Electron. 5, 808–816 (1999).
[CrossRef]

J. Appl. Phys. (2)

M. Giovannini, M. Beck, N. Hoyler, and J. Faist, “Second harmonic generation in (111)-oriented InP-based quantum cascade laser,” J. Appl. Phys. 101, 103107 (2007).
[CrossRef]

J. Bai and D. S. Citrin, “Intracavity nonlinearities in quantum-cascade lasers,” J. Appl. Phys. 106, 031101 (2009).
[CrossRef]

Jpn. J. Appl. Phys. (1)

N. Kumazaki, Y. Takagi, M. Ishihara, K. Kasahara, A. Sugiyama, N. Akikusa, and T. Edamura, “Spectral behavior of linewidth enhancement factor of a mid-infrared quantum cascade laser,” Jpn. J. Appl. Phys. 47, 6320–6326 (2008).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

S. Tomic, V. Milanovic, and Z. Ikonic, “Optimization of intersubband resonant second-order susceptibility in asymmetric graded AlxGa1−xAs quantum wells using supersymmetric quantum mechanics,” Phys. Rev. B 56, 1033–1036 (1997).
[CrossRef]

Science (1)

E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum engineering of optical nonlinearities,” Science 271, 168–173 (1996).
[CrossRef]

Semicond. Sci. Technol. (1)

S. Banerjee and K. A. Shore, “MIR and NIR nonlinear optical processing using intersubband χ(3) in triple quantum well structures,” Semicond. Sci. Technol. 18, 655–660 (2003).
[CrossRef]

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, 2007).

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Figures (4)

Fig. 1.
Fig. 1.

Conduction band diagram with squared modulus of wave functions of one active region and two injector regions under the electric field. The nonlinear transitions involve E3, E4, E5, and E6 levels. The layer thicknesses (in nanometers) of one period of active/injector material in QCSOA from left to right starting from the injection barrier are 3.8/1.5/1.2/6.7/1.2/5.3/2.3/4.0/1.1/3.6/1.2/3.2/1.2/3.0/1.6/3.0, where the bold numbers refer to barriers and the underlined layers have Si doping of 2×1017cm3.

Fig. 2.
Fig. 2.

Schematic diagram of the energy levels arrangement for the quantum wells in the proposed structure.

Fig. 3.
Fig. 3.

(a) Frequency spectra of input (dashed line) and output pulses (solid line) for Ep=10fJ and Eq=1fJ. Temporal output pulse shapes obtained from the output spectrum: (b) pump pulse, (c) probe pulse, and (d) FWM signal pulse.

Fig. 4.
Fig. 4.

(a) Frequency spectra of the input (dashed line) and output pulses (solid line). For Ep=1pJ and Eq=0.1pJ. Output pulse shapes obtained from the output spectrum: (b) pump pulse, (c) probe pulse, and (d) FWM pulse.

Tables (1)

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Table 1. List of Quantities

Equations (6)

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

χ3(ω4)=Ne43ε0z35z45z64z63(ωpωqω34iγ34)(ω4ω63iγ63)[1(ωpω53iγ53)+1(ωqω53iγ53)],
[z+i2β22t2+γ2+ib2|V(t,z)|2]V(t,z)=12(1iαN)gN[V(t,z)+T222V(t,ω)t2],
gp(z,τ)t=2[g0gN(z,τ)]τs2gN(z,τ)Ws|V(z,τ)|2,
V(t)=Vp(t)+Vq(t)exp(iΔωt),
αn(ω,N)=[Reχ(1)(ω,N)]N/[Imχ(1)(ω,N)]N,
V(0,τ)=Einτ0πexp(τ22τ0),

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