Abstract

We describe a procedure to optimize mid-infrared quantum cascade lasers with respect to the resonant second-order optical susceptibility, based on supersymmetric quantum mechanics. Realization of the optimized potential can be obtained by composition grading of ternary alloys, such as in InGaAs/AlInAs-based structures. The approach yields designs not only with strongly enhanced predicted nonlinear conversion efficiencies, but also with significantly improved modal gain compared with demonstrated devices.

© 2006 Optical Society of America

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  1. S. L. Chuang, "Introduction to the feature issue on mid-infrared quantum cascade lasers," IEEE J. Quantum Electron. 38, 510-510 (2002).
    [CrossRef]
  2. G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
    [CrossRef]
  3. F. Cooper, A. Khare, and U. Sukhatme, "Supersymmetry and quantum mechanics," Phys. Rep. 251, 267-385 (1995).
    [CrossRef]
  4. S. Tomić, V. Milanović, and Z. Ikonić, "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]
  5. V. Milanović and Z. Ikonić, "On the optimization of resonant intersubband nonlinear optical susceptibilities in semiconductor quantum wells," IEEE J. Quantum Electron. 32, 1316-1323 (1996).
    [CrossRef]
  6. O. Madelung, Semiconductors—Basic Data, (Springer, New York, 1996), Chap. 2.
    [CrossRef]
  7. G. D. Sanders and Y. C. Chang, "Effects of uniaxial stress on the electronic and optical properties of GaAs-AlxGa1-xAs quantum wells," Phys. Rev. B 32,4282-4285 (1985).
    [CrossRef]
  8. J. G. Cody, D. L. Mathine, R. Droopad, and G. N. Maracas, "Application of the digital alloy composition grading technique to strained InGaAs/GaAs/AlGaAs diode laser active regions," J. Vac. Sci. Technol. B 12, 1075-1077 (1994).
    [CrossRef]
  9. M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
    [CrossRef]
  10. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 2003), Chap. 12.
  11. O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
    [CrossRef]

2004

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

2003

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

2002

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

S. L. Chuang, "Introduction to the feature issue on mid-infrared quantum cascade lasers," IEEE J. Quantum Electron. 38, 510-510 (2002).
[CrossRef]

1997

S. Tomić, V. Milanović, and Z. Ikonić, "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

V. Milanović and Z. Ikonić, "On the optimization of resonant intersubband nonlinear optical susceptibilities in semiconductor quantum wells," IEEE J. Quantum Electron. 32, 1316-1323 (1996).
[CrossRef]

1995

F. Cooper, A. Khare, and U. Sukhatme, "Supersymmetry and quantum mechanics," Phys. Rep. 251, 267-385 (1995).
[CrossRef]

1994

J. G. Cody, D. L. Mathine, R. Droopad, and G. N. Maracas, "Application of the digital alloy composition grading technique to strained InGaAs/GaAs/AlGaAs diode laser active regions," J. Vac. Sci. Technol. B 12, 1075-1077 (1994).
[CrossRef]

1985

G. D. Sanders and Y. C. Chang, "Effects of uniaxial stress on the electronic and optical properties of GaAs-AlxGa1-xAs quantum wells," Phys. Rev. B 32,4282-4285 (1985).
[CrossRef]

Belyanin, A.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Buell, D.

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

Capasso, F.

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Chang, Y. C.

G. D. Sanders and Y. C. Chang, "Effects of uniaxial stress on the electronic and optical properties of GaAs-AlxGa1-xAs quantum wells," Phys. Rev. B 32,4282-4285 (1985).
[CrossRef]

Chen, J.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

Cho, A. Y.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Chuang, S. L.

S. L. Chuang, "Introduction to the feature issue on mid-infrared quantum cascade lasers," IEEE J. Quantum Electron. 38, 510-510 (2002).
[CrossRef]

Cody, J. G.

J. G. Cody, D. L. Mathine, R. Droopad, and G. N. Maracas, "Application of the digital alloy composition grading technique to strained InGaAs/GaAs/AlGaAs diode laser active regions," J. Vac. Sci. Technol. B 12, 1075-1077 (1994).
[CrossRef]

Coldren, L. A.

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

Cooper, F.

F. Cooper, A. Khare, and U. Sukhatme, "Supersymmetry and quantum mechanics," Phys. Rep. 251, 267-385 (1995).
[CrossRef]

Droopad, R.

J. G. Cody, D. L. Mathine, R. Droopad, and G. N. Maracas, "Application of the digital alloy composition grading technique to strained InGaAs/GaAs/AlGaAs diode laser active regions," J. Vac. Sci. Technol. B 12, 1075-1077 (1994).
[CrossRef]

Gmachl, G.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Hall, E.

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

Huntington, A.

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

Ikonic, Z.

S. Tomić, V. Milanović, and Z. Ikonić, "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]

V. Milanović and Z. Ikonić, "On the optimization of resonant intersubband nonlinear optical susceptibilities in semiconductor quantum wells," IEEE J. Quantum Electron. 32, 1316-1323 (1996).
[CrossRef]

Khare, A.

F. Cooper, A. Khare, and U. Sukhatme, "Supersymmetry and quantum mechanics," Phys. Rep. 251, 267-385 (1995).
[CrossRef]

Koda, R.

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

Malis, O.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

Maracas, G. N.

J. G. Cody, D. L. Mathine, R. Droopad, and G. N. Maracas, "Application of the digital alloy composition grading technique to strained InGaAs/GaAs/AlGaAs diode laser active regions," J. Vac. Sci. Technol. B 12, 1075-1077 (1994).
[CrossRef]

Mathine, D. L.

J. G. Cody, D. L. Mathine, R. Droopad, and G. N. Maracas, "Application of the digital alloy composition grading technique to strained InGaAs/GaAs/AlGaAs diode laser active regions," J. Vac. Sci. Technol. B 12, 1075-1077 (1994).
[CrossRef]

Milanovic, V.

S. Tomić, V. Milanović, and Z. Ikonić, "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]

V. Milanović and Z. Ikonić, "On the optimization of resonant intersubband nonlinear optical susceptibilities in semiconductor quantum wells," IEEE J. Quantum Electron. 32, 1316-1323 (1996).
[CrossRef]

Owschimikow, N.

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Peabody, M. L.

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Reddy, M. H. M.

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

Sanders, G. D.

G. D. Sanders and Y. C. Chang, "Effects of uniaxial stress on the electronic and optical properties of GaAs-AlxGa1-xAs quantum wells," Phys. Rev. B 32,4282-4285 (1985).
[CrossRef]

Sergent, A. M.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Sivco, D. L.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

Sukhatme, U.

F. Cooper, A. Khare, and U. Sukhatme, "Supersymmetry and quantum mechanics," Phys. Rep. 251, 267-385 (1995).
[CrossRef]

Tomic, S.

S. Tomić, V. Milanović, and Z. Ikonić, "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]

Appl. Phys. Lett.

M. H. M. Reddy, A. Huntington, D. Buell, R. Koda, E. Hall, and L. A. Coldren, "Molecular-beam expitaxy growth of high-quality active regions with strained InxGa1-xAs quantum wells and lattice-matched AlxGayIn(1-x-y)As barriers using submonolayer superlattices," Appl. Phys. Lett. 80, 3509-3511 (2002).
[CrossRef]

Electron. Lett.

O. Malis, A. Belyanin, D. L. Sivco, J. Chen, A. M. Sergent, G. Gmachl, and A. Y. Cho, "Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching," Electron. Lett. 40, 1586-1587 (2004).
[CrossRef]

IEEE J. Quantum Electron.

S. L. Chuang, "Introduction to the feature issue on mid-infrared quantum cascade lasers," IEEE J. Quantum Electron. 38, 510-510 (2002).
[CrossRef]

G. Gmachl, A. Belyanin, D. L. Sivco, M. L. Peabody, N. Owschimikow, A. M. Sergent, F. Capasso, and A. Y. Cho, "Optimized second-harmonic generation in quantum cascade lasers," IEEE J. Quantum Electron. 39, 1345-1355 (2003).
[CrossRef]

V. Milanović and Z. Ikonić, "On the optimization of resonant intersubband nonlinear optical susceptibilities in semiconductor quantum wells," IEEE J. Quantum Electron. 32, 1316-1323 (1996).
[CrossRef]

J. Vac. Sci. Technol. B

J. G. Cody, D. L. Mathine, R. Droopad, and G. N. Maracas, "Application of the digital alloy composition grading technique to strained InGaAs/GaAs/AlGaAs diode laser active regions," J. Vac. Sci. Technol. B 12, 1075-1077 (1994).
[CrossRef]

Phys. Rep.

F. Cooper, A. Khare, and U. Sukhatme, "Supersymmetry and quantum mechanics," Phys. Rep. 251, 267-385 (1995).
[CrossRef]

Phys. Rev. B

S. Tomić, V. Milanović, and Z. Ikonić, "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]

G. D. Sanders and Y. C. Chang, "Effects of uniaxial stress on the electronic and optical properties of GaAs-AlxGa1-xAs quantum wells," Phys. Rev. B 32,4282-4285 (1985).
[CrossRef]

Other

O. Madelung, Semiconductors—Basic Data, (Springer, New York, 1996), Chap. 2.
[CrossRef]

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 2003), Chap. 12.

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Figures (6)

Fig. 1.
Fig. 1.

Computed band structure for the structure in Ref. [2].

Fig. 2.
Fig. 2.

Dependence of DMEP on λ .

Fig. 3.
Fig. 3.

Optimized potential and original potential.

Fig. 4.
Fig. 4.

Energy levels and squared moduli of wavefunctions for the modified potential shape.

Fig. 5.
Fig. 5.

Net modal gain versus current for the original and optimized structures.

Fig. 6.
Fig. 6.

Linear and nonlinear power output vs. current.

Equations (3)

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

χ ( 2 ) ( 2 ω ) e 3 ħ 2 [ M 23 M 34 M 24 Γ 42 ( N 3 N 4 Γ 43 + N 3 N 2 Γ 32 ) + M 34 M 45 M 35 Γ 53 ( N 4 N 5 Γ 54 + N 4 N 3 Γ 43 ) ] ,
m wnp * ( E ) = m wp * [ 1 + 2 γ m wp * ( E E cbm ) ħ 2 ] ,
V s ( z ) = V o ( z ) ħ 2 m ( z ) d dz [ 1 m ( z ) d dz { In [ λ + I ( z ) ] } ] ,

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