Abstract

The design of the active region of a current-pumped quantum-cascade laser to achieve maximal gain is proposed. Starting with an arbitrary smooth potential, a family of isospectral Hamiltonians with a predefined energy spectrum is generated by use of the inverse spectral theory. By varying the relevant control parameter, one varies the potential shape, inducing changes in transition dipole moments and electron–phonon scattering times, and thus finds the potential that gives the largest gain. As an example, a simple step quantum-well structure with just a few layers is then designed such that, in postgrowth heating-induced layer interdiffusion, it will acquire a shape that is as close as possible to that of the optimal smooth potential.

© 2002 Optical Society of America

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  1. R. F. Kazarinov and R. A. Suris, “Possibility of the amplification electromagnetic waves in a semiconductor with superlattice,” Sov. Phys. Semicond. 5, 707–711 (1971).
  2. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264, 553–556 (1994).
    [CrossRef] [PubMed]
  3. J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
    [CrossRef]
  4. C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
    [CrossRef]
  5. C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
    [CrossRef]
  6. C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
    [CrossRef]
  7. C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
    [CrossRef]
  8. C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
    [CrossRef]
  9. F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
    [CrossRef]
  10. J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
    [CrossRef] [PubMed]
  11. V. Berger, “Three-level laser based on intersubband transitions in asymmetric quantum wells: a theoretical study,” Semicond. Sci. Technol. 9, 1493–1499 (1994).
    [CrossRef]
  12. S. Tomić, V. Milanović, and Z. Ikonić, “Gain optimization in optically pumped AlGaAs unipolar quantum-cascade lasers,” IEEE J. Quantum Electron. 37, 1337–1344 (2001).
    [CrossRef]
  13. C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
    [CrossRef]
  14. B. N. Zakhariev and V. M. Chabanov, “New situation in quantum mechanics (wonderful potentials from the inverse problems),” Inverse Probl. 13, R47–R79 (1997).
    [CrossRef]
  15. P. Blood, “On the dimensionality of optical absorption, gain and recombination in quantum-confined structures,” IEEE J. Quantum Electron. 36, 354–362 (2000).
    [CrossRef]
  16. G. Sun and J. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111 (1993).
    [CrossRef]
  17. S. Tomić, “Optimization of nonlinear optical properties in AlGaAs quantum wells: inverse spectral theory,” Ph.D. dissertation (University of Belgrade, Belgrade, Yugoslavia, 1998).
  18. V. Milanović and Z. Ikonić, “Equispaced-level Hamiltonians with the variable effective mass following the potential,” Phys. Rev. B 54, 1998–2003 (1996).
    [CrossRef]
  19. C. Sirtori, F. Capasso, and J. Faist, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663–8674 (1994).
    [CrossRef]
  20. X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
    [CrossRef]
  21. W. C. H. Choy, “Tailoring light and heavy holes of GaAsP–AlGaAs quantum wells by using interdiffusion for polarization-independent amplifier applications,” IEEE J. Quantum Electron. 36, 164–171 (2000).
    [CrossRef]
  22. T. E. Schlesinger and T. Kuech, “Determination of the interdiffusion of Al and Ga in undoped (Al, Ga)As/GaAs quantum wells,” Appl. Phys. Lett. 49, 519–521 (1986).
    [CrossRef]
  23. J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
    [CrossRef]
  24. J. Wang, J.-P. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photon. Technol. Lett. 8, 1001–1003 (1996).
    [CrossRef]
  25. S. Vlaev, F. Garcia-Moliner, and V. R. Velasco, “Electronic states of digital versus analog graded quantum wells,” Phys. Rev. B 52, 13784 (1995).
    [CrossRef]

2001 (2)

S. Tomić, V. Milanović, and Z. Ikonić, “Gain optimization in optically pumped AlGaAs unipolar quantum-cascade lasers,” IEEE J. Quantum Electron. 37, 1337–1344 (2001).
[CrossRef]

J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
[CrossRef]

2000 (3)

W. C. H. Choy, “Tailoring light and heavy holes of GaAsP–AlGaAs quantum wells by using interdiffusion for polarization-independent amplifier applications,” IEEE J. Quantum Electron. 36, 164–171 (2000).
[CrossRef]

P. Blood, “On the dimensionality of optical absorption, gain and recombination in quantum-confined structures,” IEEE J. Quantum Electron. 36, 354–362 (2000).
[CrossRef]

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

1999 (1)

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

1998 (3)

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

1997 (2)

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

B. N. Zakhariev and V. M. Chabanov, “New situation in quantum mechanics (wonderful potentials from the inverse problems),” Inverse Probl. 13, R47–R79 (1997).
[CrossRef]

1996 (6)

V. Milanović and Z. Ikonić, “Equispaced-level Hamiltonians with the variable effective mass following the potential,” Phys. Rev. B 54, 1998–2003 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

J. Wang, J.-P. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photon. Technol. Lett. 8, 1001–1003 (1996).
[CrossRef]

1995 (1)

S. Vlaev, F. Garcia-Moliner, and V. R. Velasco, “Electronic states of digital versus analog graded quantum wells,” Phys. Rev. B 52, 13784 (1995).
[CrossRef]

1994 (3)

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

V. Berger, “Three-level laser based on intersubband transitions in asymmetric quantum wells: a theoretical study,” Semicond. Sci. Technol. 9, 1493–1499 (1994).
[CrossRef]

C. Sirtori, F. Capasso, and J. Faist, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663–8674 (1994).
[CrossRef]

1993 (1)

G. Sun and J. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111 (1993).
[CrossRef]

1986 (1)

T. E. Schlesinger and T. Kuech, “Determination of the interdiffusion of Al and Ga in undoped (Al, Ga)As/GaAs quantum wells,” Appl. Phys. Lett. 49, 519–521 (1986).
[CrossRef]

1971 (1)

R. F. Kazarinov and R. A. Suris, “Possibility of the amplification electromagnetic waves in a semiconductor with superlattice,” Sov. Phys. Semicond. 5, 707–711 (1971).

Baillargeon, J. N.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

Barbieri, S.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

Beck, M.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

Berger, V.

V. Berger, “Three-level laser based on intersubband transitions in asymmetric quantum wells: a theoretical study,” Semicond. Sci. Technol. 9, 1493–1499 (1994).
[CrossRef]

Blood, P.

P. Blood, “On the dimensionality of optical absorption, gain and recombination in quantum-confined structures,” IEEE J. Quantum Electron. 36, 354–362 (2000).
[CrossRef]

Capasso, F.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

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

C. Sirtori, F. Capasso, and J. Faist, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663–8674 (1994).
[CrossRef]

Chabanov, V. M.

B. N. Zakhariev and V. M. Chabanov, “New situation in quantum mechanics (wonderful potentials from the inverse problems),” Inverse Probl. 13, R47–R79 (1997).
[CrossRef]

Chen, X.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Cho, A. Y.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

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

Choy, W. C. H.

W. C. H. Choy, “Tailoring light and heavy holes of GaAsP–AlGaAs quantum wells by using interdiffusion for polarization-independent amplifier applications,” IEEE J. Quantum Electron. 36, 164–171 (2000).
[CrossRef]

Chu, S. N. G.

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

Collot, P.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

Faist, J.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

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

C. Sirtori, F. Capasso, and J. Faist, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663–8674 (1994).
[CrossRef]

Garcia-Moliner, F.

S. Vlaev, F. Garcia-Moliner, and V. R. Velasco, “Electronic states of digital versus analog graded quantum wells,” Phys. Rev. B 52, 13784 (1995).
[CrossRef]

Gmachi, C.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

Gmachl, C.

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

Hutchinson, A. L.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

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

Hybertsen, M. S.

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

Ikonic, Z.

J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
[CrossRef]

S. Tomić, V. Milanović, and Z. Ikonić, “Gain optimization in optically pumped AlGaAs unipolar quantum-cascade lasers,” IEEE J. Quantum Electron. 37, 1337–1344 (2001).
[CrossRef]

V. Milanović and Z. Ikonić, “Equispaced-level Hamiltonians with the variable effective mass following the potential,” Phys. Rev. B 54, 1998–2003 (1996).
[CrossRef]

Indjin, D.

J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
[CrossRef]

Jagadish, C.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Julien, F. H.

J. Wang, J.-P. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photon. Technol. Lett. 8, 1001–1003 (1996).
[CrossRef]

Kazarinov, R. F.

R. F. Kazarinov and R. A. Suris, “Possibility of the amplification electromagnetic waves in a semiconductor with superlattice,” Sov. Phys. Semicond. 5, 707–711 (1971).

Khurgin, J.

G. Sun and J. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111 (1993).
[CrossRef]

Kruck, P.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

Kuech, T.

T. E. Schlesinger and T. Kuech, “Determination of the interdiffusion of Al and Ga in undoped (Al, Ga)As/GaAs quantum wells,” Appl. Phys. Lett. 49, 519–521 (1986).
[CrossRef]

Leburton, J.-P.

J. Wang, J.-P. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photon. Technol. Lett. 8, 1001–1003 (1996).
[CrossRef]

Li, N.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Liu, H. C.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

Liu, X.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Lu, W.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Milanovic, V.

S. Tomić, V. Milanović, and Z. Ikonić, “Gain optimization in optically pumped AlGaAs unipolar quantum-cascade lasers,” IEEE J. Quantum Electron. 37, 1337–1344 (2001).
[CrossRef]

J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
[CrossRef]

V. Milanović and Z. Ikonić, “Equispaced-level Hamiltonians with the variable effective mass following the potential,” Phys. Rev. B 54, 1998–2003 (1996).
[CrossRef]

Nagle, J.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

Oesterle, U.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

Paiella, R.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

Radovanovic, J.

J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
[CrossRef]

Saar, A.

J. Wang, J.-P. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photon. Technol. Lett. 8, 1001–1003 (1996).
[CrossRef]

Schlesinger, T. E.

T. E. Schlesinger and T. Kuech, “Determination of the interdiffusion of Al and Ga in undoped (Al, Ga)As/GaAs quantum wells,” Appl. Phys. Lett. 49, 519–521 (1986).
[CrossRef]

Shen, S. C.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Sirtori, C.

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

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

C. Sirtori, F. Capasso, and J. Faist, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663–8674 (1994).
[CrossRef]

Sivco, D. L.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

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

Sun, G.

G. Sun and J. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111 (1993).
[CrossRef]

Suris, R. A.

R. F. Kazarinov and R. A. Suris, “Possibility of the amplification electromagnetic waves in a semiconductor with superlattice,” Sov. Phys. Semicond. 5, 707–711 (1971).

Tan, H. H.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Todorovic, G.

J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
[CrossRef]

Tomic, S.

S. Tomić, V. Milanović, and Z. Ikonić, “Gain optimization in optically pumped AlGaAs unipolar quantum-cascade lasers,” IEEE J. Quantum Electron. 37, 1337–1344 (2001).
[CrossRef]

Tredicucci, A.

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

Velasco, V. R.

S. Vlaev, F. Garcia-Moliner, and V. R. Velasco, “Electronic states of digital versus analog graded quantum wells,” Phys. Rev. B 52, 13784 (1995).
[CrossRef]

Vlaev, S.

S. Vlaev, F. Garcia-Moliner, and V. R. Velasco, “Electronic states of digital versus analog graded quantum wells,” Phys. Rev. B 52, 13784 (1995).
[CrossRef]

Wang, J.

J. Wang, J.-P. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photon. Technol. Lett. 8, 1001–1003 (1996).
[CrossRef]

Xu, W.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Yuan, S.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Yuan, X. Z.

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Zakhariev, B. N.

B. N. Zakhariev and V. M. Chabanov, “New situation in quantum mechanics (wonderful potentials from the inverse problems),” Inverse Probl. 13, R47–R79 (1997).
[CrossRef]

Appl. Phys. Lett. (5)

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, “Continuous wave operation of midinfrared (7.4–8.6-μm) quantum cascade laser up to 110 K temperature,” Appl. Phys. Lett. 68, 1745–1747 (1996).
[CrossRef]

C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, and A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at λ=8.5 μm,” Appl. Phys. Lett. 72, 1430–1432 (1998).
[CrossRef]

C. Gmachi, A. Tredicucci, F. Capasso, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, and A. Y. Cho, “High power λ≈8 μm quantum cascade lasers with near optimum performance,” Appl. Phys. Lett. 72, 3130–3132 (1998).
[CrossRef]

C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlGaAs quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998).
[CrossRef]

T. E. Schlesinger and T. Kuech, “Determination of the interdiffusion of Al and Ga in undoped (Al, Ga)As/GaAs quantum wells,” Appl. Phys. Lett. 49, 519–521 (1986).
[CrossRef]

IEEE J. Quantum Electron. (5)

W. C. H. Choy, “Tailoring light and heavy holes of GaAsP–AlGaAs quantum wells by using interdiffusion for polarization-independent amplifier applications,” IEEE J. Quantum Electron. 36, 164–171 (2000).
[CrossRef]

S. Tomić, V. Milanović, and Z. Ikonić, “Gain optimization in optically pumped AlGaAs unipolar quantum-cascade lasers,” IEEE J. Quantum Electron. 37, 1337–1344 (2001).
[CrossRef]

P. Blood, “On the dimensionality of optical absorption, gain and recombination in quantum-confined structures,” IEEE J. Quantum Electron. 36, 354–362 (2000).
[CrossRef]

G. Sun and J. Khurgin, “Optically pumped four-level infrared laser based on intersubband transitions in multiple quantum wells: feasibility study,” IEEE J. Quantum Electron. 29, 1104–1111 (1993).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Pulsed and continuous-wave operation of long wavelength infrared (λ=9.3 μm) quantum cascade,” IEEE J. Quantum Electron. 33, 89–93 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

F. Capasso, C. Gmachi, R. Paiella, A. Tredicucci, A. L. Hutchinson, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, and H. C. Liu, “New frontiers in quantum cascade lasers and applications,” IEEE J. Sel. Top. Quantum Electron. 6, 931–947 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Wang, J.-P. Leburton, F. H. Julien, and A. Saar, “Design and performance optimization of optically-pumped mid-infrared intersubband semiconductor lasers,” IEEE Photon. Technol. Lett. 8, 1001–1003 (1996).
[CrossRef]

Inverse Probl. (1)

B. N. Zakhariev and V. M. Chabanov, “New situation in quantum mechanics (wonderful potentials from the inverse problems),” Inverse Probl. 13, R47–R79 (1997).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (1)

X. Liu, N. Li, X. Chen, W. Lu, W. Xu, X. Z. Yuan, N. Li, S. C. Shen, S. Yuan, H. H. Tan, and C. Jagadish, “Wavelength tuning of GaAs/AlGaAs quantum well infrared photodetectors by thermal interdiffusion,” Jpn. J. Appl. Phys., Part 1 38, 5044–5046 (1999).
[CrossRef]

Phys. Rev. B (4)

J. Radovanović, G. Todorović, V. Milanović, Z. Ikonić, and D. Indjin, “Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities,” Phys. Rev. B 63, 115327 (2001).
[CrossRef]

S. Vlaev, F. Garcia-Moliner, and V. R. Velasco, “Electronic states of digital versus analog graded quantum wells,” Phys. Rev. B 52, 13784 (1995).
[CrossRef]

V. Milanović and Z. Ikonić, “Equispaced-level Hamiltonians with the variable effective mass following the potential,” Phys. Rev. B 54, 1998–2003 (1996).
[CrossRef]

C. Sirtori, F. Capasso, and J. Faist, “Nonparabolicity and a sum rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells,” Phys. Rev. B 50, 8663–8674 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, M. S. Hybertsen, and A. Y. Cho, “Quantum cascade lasers without intersubband population inversion,” Phys. Rev. Lett. 76, 411–414 (1996).
[CrossRef] [PubMed]

Science (1)

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

Semicond. Sci. Technol. (1)

V. Berger, “Three-level laser based on intersubband transitions in asymmetric quantum wells: a theoretical study,” Semicond. Sci. Technol. 9, 1493–1499 (1994).
[CrossRef]

Sov. Phys. Semicond. (1)

R. F. Kazarinov and R. A. Suris, “Possibility of the amplification electromagnetic waves in a semiconductor with superlattice,” Sov. Phys. Semicond. 5, 707–711 (1971).

Superlattices Microstruct. (2)

J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Continuous wave operation of quantum cascade laser based on vertical transitions at λ=4.6 μm,” Superlattices Microstruct. 19, 341–345 (1996).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long wavelength vertical transition quantum cascade lasers operating cw at 110 K,” Superlattices Microstruct. 19, 357–363 (1996).
[CrossRef]

Other (1)

S. Tomić, “Optimization of nonlinear optical properties in AlGaAs quantum wells: inverse spectral theory,” Ph.D. dissertation (University of Belgrade, Belgrade, Yugoslavia, 1998).

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Figures (7)

Fig. 1
Fig. 1

Schematic view of the potential variation caused by shifting the energy of the kth state of initial potential U(z) by δ, for the IST method.

Fig. 2
Fig. 2

Examples of initial PT potentials (lowest traces) with the E31 spacing set to 152 meV by appropriate choice of parameter a. The top and middle traces show the results of applying the IST, with values of the transform parameter α as denoted, to render symmetric or asymmetric potentials in all cases such that E21 equals the specified value (the LO phonon energy).

Fig. 3
Fig. 3

Values of state spacings ΔE31 and ΔE21 as functions of the s parameter in the initial PT potential.

Fig. 4
Fig. 4

Dipole matrix element z32 and relaxation time τ21 relative to parameters in the PT potential and to parameter α in the IST-derived potential.

Fig. 5
Fig. 5

Profiles of the IST-optimized structure (dashed curve), the initial stepwise-constant three-layer structure used for interdiffusion (dashed–dotted curve), and the profile generated by interdiffusion (solid curve).

Fig. 6
Fig. 6

IST-optimized and interdiffusion-generated potential with K0=40 kV/cm bias included, and wave functions of the three relevant states in interdiffused QWs.

Fig. 7
Fig. 7

Calculated dependence of relaxation rates Wij on in-plane wave vector k for the interdiffused (solid curves) and the IST-optimized (dashed curves) QWs at T=77 K.

Tables (2)

Tables Icon

Table 1 Dipole Matrix Element z32, Transition Times τij, Figures of Merit Ξ, and Local Gain g Calculated for IST-Optimized and Three-Layer Interdiffused Structures

Tables Icon

Table 2 Scattering Ratesa of Acoustic Phonons Wija and Polar Optical Phonons Wijpo at k=0

Equations (26)

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

n3t=Je-n3τ32-n3τ31,
n2t=-n2τ21+n3τ32,
n1t=-Je+n3τ31+n2τ21,
Gm=4πen0λ(2Γ)z322τ31-τ21τ32J,
1τij=1τijpo+1τija,
Wija=Dc2kbTm*2πcL3 |Gij(qz)|2dqz,
Wijpo(k)=e2ωLO[n(ωLO)+1]8πp× |Gij(qz)|22kqzm*2+2qz22m*+Ei-Ej-ωLO21/2dqz,
Ξ=z322τ31-τ21τ32.
-22m* d2ψidz2+U(z)ψi=Eiψi,i=1, 2 ,, k ,, n.
UIST(z, Ek+δ, α)
=U(z)-2m* d2dz2 ln{W[ψδ(z, α), ψk(z)]},
W(ψδ, ψk, α)=ψδ(z, α) dψk(z)dz-ψk(z) dψδ(z, α)dz.
ψδ(z, α)=ξ1(z)+αξ2(z),
ψiIST(z, α)=1[1-δ/(Ei-Eδ)]1/2 ψi(z)-2m*δ2 ψδ(z, α)W[ψδ(z, α), ψk(z)] ×-z ψi(z)ψk(z)dz,ik,
ψδIST(z, α)=C ψk(z)W[ψδ(z, α), ψk(z)].
ddz 1m(z) dψ(z)dz+q[E-θm(z)]ψ(z)=0,
d2u(y)dy2+qm*[E-U(y)]u(y)=0,
m(t)=14qm*θ[s1(t)s2(t)]2,
d2s(t)dt2-qm*UIST(t)s(t)=0,
z(t)=0tm*m(t)1/2dt,
m(z, E)=m(z)1+E-U(z)Eg(z),
zij=1Ei-Ej 22m0 -ψi(z) ddz ψj(z)M(Ei, z)dz+- ψi(z)M(Ej, z) dψjdz dz,
- ψi1+Ei-U(z)Ei-U(z)+Eg(z)ψidz=1.
x(z, t)=j=1N xj2 erfz-zj-1Ld-erfz-zjLd+x02 1-erfz-z0Ld+xN+12×1+erfz-zNLd,
U(z)=-22m*a2 s(s+1)cosh2(z/a).
En=-22m*a2[s-(n-1)]2,n=1, 2 ,, [s]+1,

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