Abstract

We suggest the use of the refractive-index changes associated with the intersubband transitions in quantum wells for phase matching in nonlinear materials. An improvement in the conversion efficiency of mid-IR second-harmonic generation by almost 2 orders of magnitude over non-phase-matched bulk GaAs is predicted. We also show that the linear phase contributions of intersubband transitions used for resonant enhancement of second-harmonic generation must be considered, as they could limit the conversion efficiency by increasing the phase mismatch on one hand or offset the bulk’s dispersion and lead to phase matching on the other.

© 1994 Optical Society of America

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  2. S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
    [CrossRef]
  3. G. Almogy, A. Shakouri, A. Yariv, Appl. Phys. Lett. 63, 2720 (1993).
    [CrossRef]
  4. E. Dupont, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 29, 2313 (1993).
    [CrossRef]
  5. F. H. Julien, P. Vagos, J.-M. Lourtioz, D. D. Yang, Appl. Phys. Lett. 59, 2645 (1991).
    [CrossRef]
  6. A possible exception is suggested byM. O. Scully, T. W. Hänsch, M. Fleischhauer, C. H. Keitel, S. Y. Zhu, in Physics and Probability, W. T. Grandy, P. W. Millonni, eds. (Cambridge U. Press, Cambridge, 1993), p. 73.
    [CrossRef]
  7. T. A. DeTemple, L. A. Bahler, J. Osmundsen, Phys. Rev. A 24, 1950 (1981).
    [CrossRef]
  8. A. Yariv, Quantum Electronics (Wiley, New York, 1988).
  9. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1991), Vol. 2, p. 534.
  10. F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
    [CrossRef]
  11. R. J. Pressley, ed., Handbook of Lasers (CRC, Cleveland, Ohio, 1971), p. 504(the crystal growth direction must correspond to a bulk SHG coefficient).
  12. D. F. G. Gallagher, IEEE J. Quantum Electron. 28, 1785 (1992).
    [CrossRef]
  13. M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
    [CrossRef]
  14. M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
    [CrossRef] [PubMed]
  15. P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, Opt. Lett. 16, 199 (1991).
    [CrossRef] [PubMed]

1993 (2)

G. Almogy, A. Shakouri, A. Yariv, Appl. Phys. Lett. 63, 2720 (1993).
[CrossRef]

E. Dupont, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 29, 2313 (1993).
[CrossRef]

1992 (1)

D. F. G. Gallagher, IEEE J. Quantum Electron. 28, 1785 (1992).
[CrossRef]

1991 (2)

1989 (2)

M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
[CrossRef]

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

1988 (1)

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

1981 (1)

T. A. DeTemple, L. A. Bahler, J. Osmundsen, Phys. Rev. A 24, 1950 (1981).
[CrossRef]

1972 (1)

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Almogy, G.

G. Almogy, A. Shakouri, A. Yariv, Appl. Phys. Lett. 63, 2720 (1993).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bahler, L. A.

T. A. DeTemple, L. A. Bahler, J. Osmundsen, Phys. Rev. A 24, 1950 (1981).
[CrossRef]

Bar-Joseph, I.

M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bois, P.

Boucaud, P.

Byer, R. L.

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Chang, T. Y.

M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
[CrossRef]

Chemla, D. S.

M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
[CrossRef]

Delacourt, D.

E. Dupont, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 29, 2313 (1993).
[CrossRef]

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

DeTemple, T. A.

T. A. DeTemple, L. A. Bahler, J. Osmundsen, Phys. Rev. A 24, 1950 (1981).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Dupont, E.

E. Dupont, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 29, 2313 (1993).
[CrossRef]

Fejer, M. M.

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Fleischhauer, M.

A possible exception is suggested byM. O. Scully, T. W. Hänsch, M. Fleischhauer, C. H. Keitel, S. Y. Zhu, in Physics and Probability, W. T. Grandy, P. W. Millonni, eds. (Cambridge U. Press, Cambridge, 1993), p. 73.
[CrossRef]

Gallagher, D. F. G.

D. F. G. Gallagher, IEEE J. Quantum Electron. 28, 1785 (1992).
[CrossRef]

Hänsch, T. W.

A possible exception is suggested byM. O. Scully, T. W. Hänsch, M. Fleischhauer, C. H. Keitel, S. Y. Zhu, in Physics and Probability, W. T. Grandy, P. W. Millonni, eds. (Cambridge U. Press, Cambridge, 1993), p. 73.
[CrossRef]

Harris, J. S.

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Harwit, A.

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Herschkorn, N.

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

Julien, F. H.

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

F. H. Julien, P. Vagos, J.-M. Lourtioz, D. D. Yang, Appl. Phys. Lett. 59, 2645 (1991).
[CrossRef]

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

Keitel, C. H.

A possible exception is suggested byM. O. Scully, T. W. Hänsch, M. Fleischhauer, C. H. Keitel, S. Y. Zhu, in Physics and Probability, W. T. Grandy, P. W. Millonni, eds. (Cambridge U. Press, Cambridge, 1993), p. 73.
[CrossRef]

Kuo, J. M.

M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
[CrossRef]

Leroux, G.

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

Lourtioz, J. M.

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

Lourtioz, J.-M.

F. H. Julien, P. Vagos, J.-M. Lourtioz, D. D. Yang, Appl. Phys. Lett. 59, 2645 (1991).
[CrossRef]

Osmundsen, J.

T. A. DeTemple, L. A. Bahler, J. Osmundsen, Phys. Rev. A 24, 1950 (1981).
[CrossRef]

Papuchon, M.

E. Dupont, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 29, 2313 (1993).
[CrossRef]

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Planel, R.

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

Pocholle, J. P.

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

Rosencher, E.

Scully, M. O.

A possible exception is suggested byM. O. Scully, T. W. Hänsch, M. Fleischhauer, C. H. Keitel, S. Y. Zhu, in Physics and Probability, W. T. Grandy, P. W. Millonni, eds. (Cambridge U. Press, Cambridge, 1993), p. 73.
[CrossRef]

Shakouri, A.

G. Almogy, A. Shakouri, A. Yariv, Appl. Phys. Lett. 63, 2720 (1993).
[CrossRef]

Somekh, S.

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

Vagos, P.

F. H. Julien, P. Vagos, J.-M. Lourtioz, D. D. Yang, Appl. Phys. Lett. 59, 2645 (1991).
[CrossRef]

Wegner, M.

M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
[CrossRef]

Yang, D. D.

Yariv, A.

G. Almogy, A. Shakouri, A. Yariv, Appl. Phys. Lett. 63, 2720 (1993).
[CrossRef]

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

A. Yariv, Quantum Electronics (Wiley, New York, 1988).

Yoo, S. J. B.

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Zhu, S. Y.

A possible exception is suggested byM. O. Scully, T. W. Hänsch, M. Fleischhauer, C. H. Keitel, S. Y. Zhu, in Physics and Probability, W. T. Grandy, P. W. Millonni, eds. (Cambridge U. Press, Cambridge, 1993), p. 73.
[CrossRef]

Appl. Phys. Lett. (5)

S. Somekh, A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

G. Almogy, A. Shakouri, A. Yariv, Appl. Phys. Lett. 63, 2720 (1993).
[CrossRef]

F. H. Julien, P. Vagos, J.-M. Lourtioz, D. D. Yang, Appl. Phys. Lett. 59, 2645 (1991).
[CrossRef]

F. H. Julien, J. M. Lourtioz, N. Herschkorn, D. Delacourt, J. P. Pocholle, M. Papuchon, R. Planel, G. Leroux, Appl. Phys. Lett. 53, 116 (1988).
[CrossRef]

M. Wegner, T. Y. Chang, I. Bar-Joseph, J. M. Kuo, D. S. Chemla, Appl. Phys. Lett. 55, 583 (1989).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. F. G. Gallagher, IEEE J. Quantum Electron. 28, 1785 (1992).
[CrossRef]

E. Dupont, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 29, 2313 (1993).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. A (1)

T. A. DeTemple, L. A. Bahler, J. Osmundsen, Phys. Rev. A 24, 1950 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, J. S. Harris, Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Other (4)

A. Yariv, Quantum Electronics (Wiley, New York, 1988).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1991), Vol. 2, p. 534.

R. J. Pressley, ed., Handbook of Lasers (CRC, Cleveland, Ohio, 1971), p. 504(the crystal growth direction must correspond to a bulk SHG coefficient).

A possible exception is suggested byM. O. Scully, T. W. Hänsch, M. Fleischhauer, C. H. Keitel, S. Y. Zhu, in Physics and Probability, W. T. Grandy, P. W. Millonni, eds. (Cambridge U. Press, Cambridge, 1993), p. 73.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Waveguide phase matched by the ISBT contributions to the susceptibility, consisting of the following layers: 1-μm AlAs, 5-μm Al0.5GaAs cladding, a multiple-quantum-well (MQW) stack of 150 periods of 6.2-nm GaAs wells with 11.3-nm Al0.4GaAs barriers, n-doped to 6 × 1011 cm−2 surface density, and a second, 3-μm Al0.5GaAs cladding. The wave functions of the 10.6- and 5.3-μm modes and the corresponding refractive indices are also shown.

Fig. 2
Fig. 2

Refractive-index (n) dispersion of GaAs: n(λ) − n(10.6 μm) with a single correcting ISBT at 1.5ω is shown versus frequency (the solid curves). Also shown are the refractive-index dispersion of bulk GaAs (the dashed–dotted curve) and the propagation length, defined as the inverse of the energy-dependent ISBT-induced absorption coefficient (the dotted curve).

Fig. 3
Fig. 3

Refractive-index (n) dispersion of GaAs: n(λ) − n(10.6 μm) with two ISBT’s used for resonant enhancement of the SHG as well as for phase matching shown versus frequency (solid curve). Also shown are the refractive-index dispersion of bulk GaAs (the dashed–dotted curve) and the resultant double-peaked SHG coefficient (the dashed curve). The transitions in the asymmetric well are depicted in the inset. A confinement factor of ~1/30 in the quantum wells is needed for phase matching for ω̃ = 40 and Δω̃ = 3.

Equations (13)

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

d E ω d z = - α ω E ω - i ω 2 ɛ 0 n ω c d E 2 ω E ω * exp ( - i Δ k z ) ,
d E 2 ω d z = - α 2 ω E 2 ω - i ω ɛ 0 n 2 ω c d E ω 2 exp ( i Δ k z ) ,
χ ( ω ) χ ( ω ) - i χ ( ω ) = N μ 2 ɛ 0 T 2 ( Δ ω T 2 - i ) ( Δ ω T 2 ) 2 + 1 ,
k ω 2 = ω 2 c 2 [ n ω 2 + χ ( ω ) ] ,
α ω = ω 2 n ω c χ ( ω ) .
n ω 2 - n 2 ω 2 2 n ω n ω - n 2 ω Δ n = χ res 2 n ω [ Δ ω ˜ Δ ω ˜ 2 + 1 - ( Δ ω ˜ - ω ˜ ) ( Δ ω ˜ - ω ˜ ) 2 + 1 ] ,
E 2 ω ( z ) = - i ω ɛ 0 n 2 ω c d ( α 2 ω - 2 α ω ) × [ exp ( - 2 α ω z ) - exp ( - α 2 ω z ) ] E ω ( 0 ) 2 ,
z max = 1 α 2 ω - 2 α ω ln ( α 2 ω 2 α ω ) ,
η ( z max ) I 2 ω ( z max ) I ω ( 0 ) = 2 ( μ 0 ɛ 0 ) 3 / 2 ω 2 d 2 n 2 ω n ω 2 [ 1 α 2 ω ( 2 α ω α 2 ω ) 2 α ω α 2 ω - 2 α ω ] 2 I ω ( 0 ) ,
η max = 1 2 e 2 ( μ 0 ɛ 0 ) 3 / 2 d 2 c 2 η ω 2 n 2 ω I ω ( ω ˜ Δ n ) 2 ,
z max = c T 2 2 Δ n = ω ˜ π λ 4 Δ n = ω ˜ π l c ,
Δ n = 2 n ω N μ 2 ω ɛ 0 2 1 + 4 / ω ˜ 2 1 n ω N μ 2 ω ɛ 0 ,
Δ n ISBT = n ( ω ) - n ( 2 ω ) 1 n χ res Δ ω ˜ Δ ω ˜ 2 + 1 .

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