Abstract

The photorefractive properties of semi-insulating AlGaAs–GaAs multiple quantum wells are described for the transverse Franz–Keldysh geometry with the electric field in the plane of the quantum wells. Combining the strong electroabsorption of quantum-confined excitons with the high resistivity of semi-insulating quantum wells yields large nonlinear optical sensitivities. The photorefractive quantum wells have effective nonlinear optical sensitivities of n2 ≈ 103 cm2/W and α2/α0 ≈ 104 cm2/W for applied fields of 10 kV/cm. Photorefractive gains approaching 1000 cm−1 have been observed in two-wave mixing under dc electric fields and stationary fringes. The transverse Franz–Keldysh geometry retains the general transport properties and behavior of conventional bulk photorefractive materials. The resonant excitation of free electrons and holes in the quantum wells leads to novel behavior associated with electron–hole competition. We demonstrate that under resonant excitation of electrons and holes the device resolution is fundamentally limited by diffusion lengths but is insensitive to long drift lengths.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
    [CrossRef]
  2. A. M. Glass, J. Strait, in Photorefractive Materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 237.
    [CrossRef]
  3. V. W. Franz, Z. Naturforsch. A 13, 484 (1958).
  4. L. V. Keldysh, Sov. Phys. JETP 34, 788 (1958).
  5. J. Callaway, Phys. Rev. 130, 549 (1963).
    [CrossRef]
  6. K. Thermalingham, Phys. Rev. 130, 2204 (1963).
    [CrossRef]
  7. J. Callaway, Phys. Rev. 134, A998 (1964).
    [CrossRef]
  8. H. D. Rees, Solid State Commun. 5, 365 (1967).
    [CrossRef]
  9. J. D. Dow, D. Redfield, Phys. Rev. B 1, 3358 (1970).
    [CrossRef]
  10. F. Stern, Phys. Rev. 133, A1653 (1964).
    [CrossRef]
  11. B. O. Seraphin, N. Bottka, Phys. Rev. 139A, 560 (1965).
    [CrossRef]
  12. T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, Appl. Phys. Lett. 48, 451 (1986).
    [CrossRef]
  13. A. Alping, L. A. Coldren, J. Appl. Phys. 61, 2430 (1987).
    [CrossRef]
  14. J. E. Zucker, T. L. Hendrickson, C. A. Burrus, Appl. Phys. Lett. 52, 946 (1988).
    [CrossRef]
  15. J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
    [CrossRef]
  16. A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
    [CrossRef]
  17. D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
    [CrossRef]
  18. D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
    [CrossRef]
  19. E. Yablonovitch, T. Gmitter, J. P. Harbison, R. Bhat, Appl. Phys. Lett. 51, 2222 (1987).
    [CrossRef]
  20. Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
    [CrossRef]
  21. M. B. Johnson, T. C. McGill, N. G. Paulter, Appl. Phys. Lett. 54, 2424 (1989).
    [CrossRef]
  22. H. J. Stein, Appl. Phys. Lett. 57, 792 (1990).
    [CrossRef]
  23. M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
    [CrossRef]
  24. M. Schultz, H. Weiss, in Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, K.-H. Hellwege, A. M. Hellwege, eds. (Springer-Verlag, Berlin, 1984), Vol. 17d, p. 97.
  25. B. Schwartz, L. A. Koszi, P. J. Anthony, R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984).
    [CrossRef]
  26. K. Kenefick, J. Electrochem. Soc. Solid-State Sci. Technol. 129, 2380 (1982).
  27. K. J. K. C. Juang, R. B. Darling, J. Vac. Sci. Technol. B 8, 1122 (1990).
    [CrossRef]
  28. E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
    [CrossRef]
  29. K. Seeger, Semiconductor Physics (Springer-Verlag, Berlin, 1985).
    [CrossRef]
  30. S. M. Sze, Physics of Semiconductor Devices (New York, Wiley-Interscience, 1969).
  31. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
    [CrossRef]
  32. F. L. Lederman, J. D. Dow, Phys. Rev. B 13, 1633 (1976).
    [CrossRef]
  33. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
    [CrossRef]
  34. D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, Phys. Rev. B 33, 6976 (1986).
    [CrossRef]
  35. G. C. Valley, J. F. Lam, in Photorefractive materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 75.
    [CrossRef]
  36. M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 19 (1980).
    [CrossRef]
  37. Q. N. Wang, D. D. Nolte, M. R. Melloch, Opt. Lett. 16, 1944 (1991).
    [CrossRef] [PubMed]
  38. M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, Opt. Commun. 31, 301 (1979).
    [CrossRef]
  39. F. Vachss, L. Hesselink, J. Opt. Soc. Am. A 5, 690 (1988).
    [CrossRef]
  40. D. D. Nolte, Q. N. Wang, M. R. Melloch, Appl. Phys. Lett. 58, 2067 (1991).
    [CrossRef]
  41. Q. N. Wang, D. D. Nolte, M. R. Melloch, Appl. Phys. Lett. 59, 256 (1991).
    [CrossRef]
  42. D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
    [CrossRef]

1991 (4)

M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Opt. Lett. 16, 1944 (1991).
[CrossRef] [PubMed]

D. D. Nolte, Q. N. Wang, M. R. Melloch, Appl. Phys. Lett. 58, 2067 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Appl. Phys. Lett. 59, 256 (1991).
[CrossRef]

1990 (6)

H. J. Stein, Appl. Phys. Lett. 57, 792 (1990).
[CrossRef]

K. J. K. C. Juang, R. B. Darling, J. Vac. Sci. Technol. B 8, 1122 (1990).
[CrossRef]

E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[CrossRef]

D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
[CrossRef]

1989 (1)

M. B. Johnson, T. C. McGill, N. G. Paulter, Appl. Phys. Lett. 54, 2424 (1989).
[CrossRef]

1988 (2)

F. Vachss, L. Hesselink, J. Opt. Soc. Am. A 5, 690 (1988).
[CrossRef]

J. E. Zucker, T. L. Hendrickson, C. A. Burrus, Appl. Phys. Lett. 52, 946 (1988).
[CrossRef]

1987 (2)

A. Alping, L. A. Coldren, J. Appl. Phys. 61, 2430 (1987).
[CrossRef]

E. Yablonovitch, T. Gmitter, J. P. Harbison, R. Bhat, Appl. Phys. Lett. 51, 2222 (1987).
[CrossRef]

1986 (2)

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, Appl. Phys. Lett. 48, 451 (1986).
[CrossRef]

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, Phys. Rev. B 33, 6976 (1986).
[CrossRef]

1985 (3)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

1984 (4)

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

B. Schwartz, L. A. Koszi, P. J. Anthony, R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

1982 (1)

K. Kenefick, J. Electrochem. Soc. Solid-State Sci. Technol. 129, 2380 (1982).

1980 (1)

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 19 (1980).
[CrossRef]

1979 (1)

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, Opt. Commun. 31, 301 (1979).
[CrossRef]

1976 (1)

F. L. Lederman, J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

1970 (1)

J. D. Dow, D. Redfield, Phys. Rev. B 1, 3358 (1970).
[CrossRef]

1967 (1)

H. D. Rees, Solid State Commun. 5, 365 (1967).
[CrossRef]

1965 (1)

B. O. Seraphin, N. Bottka, Phys. Rev. 139A, 560 (1965).
[CrossRef]

1964 (2)

J. Callaway, Phys. Rev. 134, A998 (1964).
[CrossRef]

F. Stern, Phys. Rev. 133, A1653 (1964).
[CrossRef]

1963 (2)

J. Callaway, Phys. Rev. 130, 549 (1963).
[CrossRef]

K. Thermalingham, Phys. Rev. 130, 2204 (1963).
[CrossRef]

1958 (2)

V. W. Franz, Z. Naturforsch. A 13, 484 (1958).

L. V. Keldysh, Sov. Phys. JETP 34, 788 (1958).

Alping, A.

A. Alping, L. A. Coldren, J. Appl. Phys. 61, 2430 (1987).
[CrossRef]

Anthony, P. J.

B. Schwartz, L. A. Koszi, P. J. Anthony, R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984).
[CrossRef]

Axmann, A.

M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
[CrossRef]

Ballman, A. A.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Bhat, R.

E. Yablonovitch, T. Gmitter, J. P. Harbison, R. Bhat, Appl. Phys. Lett. 51, 2222 (1987).
[CrossRef]

Bottka, N.

B. O. Seraphin, N. Bottka, Phys. Rev. 139A, 560 (1965).
[CrossRef]

Burrus, C. A.

J. E. Zucker, T. L. Hendrickson, C. A. Burrus, Appl. Phys. Lett. 52, 946 (1988).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

Callaway, J.

J. Callaway, Phys. Rev. 134, A998 (1964).
[CrossRef]

J. Callaway, Phys. Rev. 130, 549 (1963).
[CrossRef]

Chang, W. S. C.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, Appl. Phys. Lett. 48, 451 (1986).
[CrossRef]

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, Phys. Rev. B 33, 6976 (1986).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Coldren, L. A.

A. Alping, L. A. Coldren, J. Appl. Phys. 61, 2430 (1987).
[CrossRef]

Damen, T. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

Darling, R. B.

K. J. K. C. Juang, R. B. Darling, J. Vac. Sci. Technol. B 8, 1122 (1990).
[CrossRef]

Doran, G. E.

Dow, J. D.

F. L. Lederman, J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

J. D. Dow, D. Redfield, Phys. Rev. B 1, 3358 (1970).
[CrossRef]

Florez, L. T.

E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
[CrossRef]

Franz, V. W.

V. W. Franz, Z. Naturforsch. A 13, 484 (1958).

Garmire, E. M.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[CrossRef]

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 19 (1980).
[CrossRef]

Glass, A. M.

D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

A. M. Glass, J. Strait, in Photorefractive Materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 237.
[CrossRef]

Gmitter, T.

E. Yablonovitch, T. Gmitter, J. P. Harbison, R. Bhat, Appl. Phys. Lett. 51, 2222 (1987).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
[CrossRef]

Gossard, A. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

Harbison, J. P.

E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
[CrossRef]

E. Yablonovitch, T. Gmitter, J. P. Harbison, R. Bhat, Appl. Phys. Lett. 51, 2222 (1987).
[CrossRef]

Hartman, R. L.

B. Schwartz, L. A. Koszi, P. J. Anthony, R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984).
[CrossRef]

Hendrickson, T. L.

J. E. Zucker, T. L. Hendrickson, C. A. Burrus, Appl. Phys. Lett. 52, 946 (1988).
[CrossRef]

Hesselink, L.

Hwang, D. M.

E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
[CrossRef]

Johnson, A. M.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Johnson, M. B.

M. B. Johnson, T. C. McGill, N. G. Paulter, Appl. Phys. Lett. 54, 2424 (1989).
[CrossRef]

Juang, K. J. K. C.

K. J. K. C. Juang, R. B. Darling, J. Vac. Sci. Technol. B 8, 1122 (1990).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 34, 788 (1958).

Kenefick, K.

K. Kenefick, J. Electrochem. Soc. Solid-State Sci. Technol. 129, 2380 (1982).

Klein, M. B.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Knox, W. H.

Koehler, S. D.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Kost, A.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[CrossRef]

Koszi, L. A.

B. Schwartz, L. A. Koszi, P. J. Anthony, R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984).
[CrossRef]

Kuhl, J.

M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
[CrossRef]

Kulikov, V. V.

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, Opt. Commun. 31, 301 (1979).
[CrossRef]

Lam, J. F.

G. C. Valley, J. F. Lam, in Photorefractive materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 75.
[CrossRef]

Lambsdorff, M.

M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
[CrossRef]

Lederman, F. L.

F. L. Lederman, J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

Magnusson, R.

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 19 (1980).
[CrossRef]

McGill, T. C.

M. B. Johnson, T. C. McGill, N. G. Paulter, Appl. Phys. Lett. 54, 2424 (1989).
[CrossRef]

Melloch, M. R.

D. D. Nolte, Q. N. Wang, M. R. Melloch, Appl. Phys. Lett. 58, 2067 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Appl. Phys. Lett. 59, 256 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Opt. Lett. 16, 1944 (1991).
[CrossRef] [PubMed]

Miller, D. A. B.

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, Phys. Rev. B 33, 6976 (1986).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

Millerd, J. E.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Miridonov, S. V.

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, Opt. Commun. 31, 301 (1979).
[CrossRef]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 19 (1980).
[CrossRef]

Nolte, D. D.

D. D. Nolte, Q. N. Wang, M. R. Melloch, Appl. Phys. Lett. 58, 2067 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Appl. Phys. Lett. 59, 256 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Opt. Lett. 16, 1944 (1991).
[CrossRef] [PubMed]

D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
[CrossRef]

Olson, D. H.

D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
[CrossRef]

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Partovi, A.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Paulter, N. G.

M. B. Johnson, T. C. McGill, N. G. Paulter, Appl. Phys. Lett. 54, 2424 (1989).
[CrossRef]

Petrov, M. P.

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, Opt. Commun. 31, 301 (1979).
[CrossRef]

Redfield, D.

J. D. Dow, D. Redfield, Phys. Rev. B 1, 3358 (1970).
[CrossRef]

Rees, H. D.

H. D. Rees, Solid State Commun. 5, 365 (1967).
[CrossRef]

Rosenzweig, J.

M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
[CrossRef]

Schmitt-Rink, S.

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, Phys. Rev. B 33, 6976 (1986).
[CrossRef]

Schneider, J.

M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
[CrossRef]

Schultz, M.

M. Schultz, H. Weiss, in Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, K.-H. Hellwege, A. M. Hellwege, eds. (Springer-Verlag, Berlin, 1984), Vol. 17d, p. 97.

Schwartz, B.

B. Schwartz, L. A. Koszi, P. J. Anthony, R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984).
[CrossRef]

Seeger, K.

K. Seeger, Semiconductor Physics (Springer-Verlag, Berlin, 1985).
[CrossRef]

Seraphin, B. O.

B. O. Seraphin, N. Bottka, Phys. Rev. 139A, 560 (1965).
[CrossRef]

Silverberg, Y.

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

Simpson, W.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Smith, P. W.

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Stein, H. J.

H. J. Stein, Appl. Phys. Lett. 57, 792 (1990).
[CrossRef]

Stepanov, S. I.

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, Opt. Commun. 31, 301 (1979).
[CrossRef]

Stern, F.

F. Stern, Phys. Rev. 133, A1653 (1964).
[CrossRef]

Strait, J.

A. M. Glass, J. Strait, in Photorefractive Materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 237.
[CrossRef]

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices (New York, Wiley-Interscience, 1969).

Tell, B.

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

Thermalingham, K.

K. Thermalingham, Phys. Rev. 130, 2204 (1963).
[CrossRef]

Vachss, F.

Valley, G. C.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[CrossRef]

G. C. Valley, J. F. Lam, in Photorefractive materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 75.
[CrossRef]

Van Eck, T. E.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, Appl. Phys. Lett. 48, 451 (1986).
[CrossRef]

Walpita, L. M.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, Appl. Phys. Lett. 48, 451 (1986).
[CrossRef]

Wang, Q. N.

D. D. Nolte, Q. N. Wang, M. R. Melloch, Appl. Phys. Lett. 58, 2067 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Appl. Phys. Lett. 59, 256 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Opt. Lett. 16, 1944 (1991).
[CrossRef] [PubMed]

Weiss, H.

M. Schultz, H. Weiss, in Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, K.-H. Hellwege, A. M. Hellwege, eds. (Springer-Verlag, Berlin, 1984), Vol. 17d, p. 97.

Wieder, H. H.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, Appl. Phys. Lett. 48, 451 (1986).
[CrossRef]

Wiegmann, W.

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Wood, T. H.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
[CrossRef]

E. Yablonovitch, T. Gmitter, J. P. Harbison, R. Bhat, Appl. Phys. Lett. 51, 2222 (1987).
[CrossRef]

Zucker, J. E.

J. E. Zucker, T. L. Hendrickson, C. A. Burrus, Appl. Phys. Lett. 52, 946 (1988).
[CrossRef]

Appl. Phys. Lett. (13)

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, Appl. Phys. Lett. 48, 451 (1986).
[CrossRef]

J. E. Zucker, T. L. Hendrickson, C. A. Burrus, Appl. Phys. Lett. 52, 946 (1988).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[CrossRef]

E. Yablonovitch, T. Gmitter, J. P. Harbison, R. Bhat, Appl. Phys. Lett. 51, 2222 (1987).
[CrossRef]

Y. Silverberg, P. W. Smith, D. A. B. Miller, B. Tell, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett. 46, 701 (1985).
[CrossRef]

M. B. Johnson, T. C. McGill, N. G. Paulter, Appl. Phys. Lett. 54, 2424 (1989).
[CrossRef]

H. J. Stein, Appl. Phys. Lett. 57, 792 (1990).
[CrossRef]

M. Lambsdorff, J. Kuhl, J. Rosenzweig, A. Axmann, J. Schneider, Appl. Phys. Lett. 58, 1881 (1991).
[CrossRef]

E. Yablonovitch, D. M. Hwang, T. J. Gmitter, L. T. Florez, J. P. Harbison, Appl. Phys. Lett. 56, 2419 (1990).
[CrossRef]

D. D. Nolte, Q. N. Wang, M. R. Melloch, Appl. Phys. Lett. 58, 2067 (1991).
[CrossRef]

Q. N. Wang, D. D. Nolte, M. R. Melloch, Appl. Phys. Lett. 59, 256 (1991).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-21, 1462 (1985).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

J. Appl. Phys. (1)

A. Alping, L. A. Coldren, J. Appl. Phys. 61, 2430 (1987).
[CrossRef]

J. Electrochem. Soc. (1)

B. Schwartz, L. A. Koszi, P. J. Anthony, R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984).
[CrossRef]

J. Electrochem. Soc. Solid-State Sci. Technol. (1)

K. Kenefick, J. Electrochem. Soc. Solid-State Sci. Technol. 129, 2380 (1982).

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Vac. Sci. Technol. B (1)

K. J. K. C. Juang, R. B. Darling, J. Vac. Sci. Technol. B 8, 1122 (1990).
[CrossRef]

Opt. Commun. (2)

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 19 (1980).
[CrossRef]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, Opt. Commun. 31, 301 (1979).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (5)

F. Stern, Phys. Rev. 133, A1653 (1964).
[CrossRef]

B. O. Seraphin, N. Bottka, Phys. Rev. 139A, 560 (1965).
[CrossRef]

J. Callaway, Phys. Rev. 130, 549 (1963).
[CrossRef]

K. Thermalingham, Phys. Rev. 130, 2204 (1963).
[CrossRef]

J. Callaway, Phys. Rev. 134, A998 (1964).
[CrossRef]

Phys. Rev. B (4)

J. D. Dow, D. Redfield, Phys. Rev. B 1, 3358 (1970).
[CrossRef]

F. L. Lederman, J. D. Dow, Phys. Rev. B 13, 1633 (1976).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. B 32, 1043 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, Phys. Rev. B 33, 6976 (1986).
[CrossRef]

Phys. Rev. Lett. (1)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).
[CrossRef]

Solid State Commun. (1)

H. D. Rees, Solid State Commun. 5, 365 (1967).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Keldysh, Sov. Phys. JETP 34, 788 (1958).

Z. Naturforsch. A (1)

V. W. Franz, Z. Naturforsch. A 13, 484 (1958).

Other (5)

A. M. Glass, J. Strait, in Photorefractive Materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 237.
[CrossRef]

G. C. Valley, J. F. Lam, in Photorefractive materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), p. 75.
[CrossRef]

K. Seeger, Semiconductor Physics (Springer-Verlag, Berlin, 1985).
[CrossRef]

S. M. Sze, Physics of Semiconductor Devices (New York, Wiley-Interscience, 1969).

M. Schultz, H. Weiss, in Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, K.-H. Hellwege, A. M. Hellwege, eds. (Springer-Verlag, Berlin, 1984), Vol. 17d, p. 97.

Cited By

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

Alert me when this article is cited.


Figures (26)

Fig. 1
Fig. 1

Multiple-quantum-well structures used in the study. Sample RB-1 differs only in the thickness of the quantum barriers.

Fig. 2
Fig. 2

Room-temperature absorption versus photon energy for sample QW-2 after sample processing. The quantum-confined heavy- and light-hole excitons are the dominant absorption features at 1.478 and 1.495 eV Under an applied field of 10 kV/cm in the plane of the wells, the exciton line shapes broaden.

Fig. 3
Fig. 3

Electroabsorption data plotted versus photon energy for an applied dc field of 10 kV/cm. The solid curve is a fit of the data to Gaussian line shapes. The total oscillator strength is conserved in the Franz–Keldysh effect (HH, heavy hole; LH, light hole).

Fig. 4
Fig. 4

Electroabsorption and electrorefraction for an applied field of 10 kV/cm versus photon energy.

Fig. 5
Fig. 5

Quadratic electro-optic coefficients s1 and s2 versus photon energy for quantum-confined excitons at room temperature.

Fig. 6
Fig. 6

Transverse Franz–Keldysh photorefractive geometry. For two-wave mixing in a thin grating, θ1 = θ2, forcing Kg to lie in the plane of the sample. All measurements are performed under an applied electric field.

Fig. 7
Fig. 7

Space-charge field amplitude versus fringe spacing for varying applied fields from numerical simulations of the quantum wells.

Fig. 8
Fig. 8

Space-charge field amplitude versus fringe spacing for varying defect concentrations from numerical simulations of the quantum wells. The compensation ratio is r = 0.9, with an applied field of 5 kV/cm. The diffusion length determines the device resolution.

Fig. 9
Fig. 9

Electron transition rates versus fringe spacing from numerical simulations. The rates Γle, Γdie, and Γeeh are all negligible compared with the drift, diffusion, and recombination rates. Similar results apply for holes

Fig. 10
Fig. 10

Vertical transport processes. Carriers can escape the quantum wells by tunneling, phonon-assisted tunneling, and thermionic emission. The space-charge trapped at defects in the barriers is expected to play a role in photorefractive properties.

Fig. 11
Fig. 11

First-order diffraction from high spatial harmonic gratings in the semi-insulating multiple quantum wells (SIMQW): M’s, mirrors; BS, beam splitter; ND, neutral-density filter.

Fig. 12
Fig. 12

Diffraction efficiencies for the first, second, and third spatial harmonic gratings as functions of photon energy for m=1.

Fig. 13
Fig. 13

Diffraction signal from the first-harmonic grating versus the square of the modulation index. The dependence is approximately linear, even for m close to 1.

Fig. 14
Fig. 14

Diffraction signal from the second-harmonic grating versus the fourth power of the modulation index. The dependence is approximately linear even for m close to 1.

Fig. 15
Fig. 15

Experimental geometry of nondegenerate four-wave mixing. The gratings are generated by a He–Ne laser and are probed by an infrared beam that is tuned through the exciton absorption. SIMQW, semi-insulating multiple quantum well; ND, neutral-density.

Fig. 16
Fig. 16

Diffraction efficiency verus wavelength of the probe for an applied field of 4 kV/cm and Λ = 2.2 μm. The solid curve is fitted based on Fig. 5.

Fig. 17
Fig. 17

Diffraction efficiency versus electric field for degenerate and nondegenerate four-wave mixing with Λ = 15 μm. Degenerate efficiencies are consistently smaller than nondegenerate efficiencies. At a low field, the diffraction efficiencies vary approximately with the fourth power of the applied field. Above 4 kV/cm there is a significant deviation from ideal behavior.

Fig. 18
Fig. 18

Fringe-spacing dependence of the diffraction efficiency. The roll-off at small fringe spacings matches the behavior predicted in Fig. 7 based on diffusion lengths.

Fig. 19
Fig. 19

Diffracted signal versus probe intensity for varying fringe spacings for sample RB-1 for an applied field of 5 kV/cm.

Fig. 20
Fig. 20

Diffracted signal versus probe intensity for varying fringe spacings for samples QW-2 and RB-1 for 5 kV/cm and Λ = 9.5 μm.

Fig. 21
Fig. 21

Effective electroabsorption compared with differential transmission as functions of probe wavelength for an applied field of 7 kV/cm and a fringe spacing of Λ = 7.3 μm.

Fig. 22
Fig. 22

Photorefractive gain compared with electrorefraction of sample QW-2 for E = 7 kV/cm Λ =7.3μm, and m = 1

Fig. 23
Fig. 23

Photorefractive gain as a function of applied field. The gain approaches 1000 cm−1 for a field of 104 V/cm.

Fig. 24
Fig. 24

Sine of the phase shift as a function of electric field for varying fringe spacings. Above 4 kV/cm the phase shift is close to π/2 with which β ≈ 25 is ideal for maximum photorefractive gain.

Fig. 25
Fig. 25

Simulation of space-charge field amplitude as a function of laser intensity for various defect densities.

Fig. 26
Fig. 26

Experimental values of modulated intensity in two-wave mixing as a function of laser intensity for E = 5 kV/cm. The absorption grating data were obtained for λ = 839 nm, and the refractive-index grating data were obtained for λ = 836 nm. Saturation intensities in the range of 10 μW/cm2 are observed.

Tables (2)

Equations (60)

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

Δ α ( E ) = 1 L ln ( 1 + Δ T T ) , Δ T T = T ( E ) T ( 0 ) T ( 0 ) .
T = n 2 n 0 ( 1 R 1 ) ( 1 R 2 ) exp ( α L ) [ 1 ( R 1 R 2 ) 1 / 2 exp ( α L ) ] 2 + 4 ( R 1 R 2 ) 1 / 2 exp ( α L ) ( sin δ ) 2 ,
δ = ( 2 π / λ ) n 1 L , R 1 = ( n 0 n 1 ) 2 + k 1 2 ( n 0 + n 1 ) 2 + k 1 2 , R 2 = ( n 1 n 2 ) 2 + k 1 2 ( n 1 + n 2 ) 2 + k 1 2 , k 1 = α λ / ( 4 π ) ,
F = π ( R 1 R 2 ) 1 / 4 1 ( R 1 R 2 ) 1 / 2 .
Δ n ( λ ) = λ 2 2 π 2 P 0 Δ α ( λ ) d λ λ 2 λ 2 .
Δ ñ = ( 1 / 2 ) n 3 s E 2 , s = s 1 + i s 2 ,
Δ n ( E ) = ( 1 / 2 ) n 3 s 1 E 2 , Δ α ( E ) = ( 2 π / λ ) n 3 s 2 E 2 .
Λ = λ / ( sin θ 1 + sin θ 2 ) .
I ( x ) = I 0 ( 1 + m sin K x ) ,
n t j e e = I α + β e N D 0 σ e n υ e N D + γ eh n p ,
p t + j h e = I α + β h N D + σ h p υ h N D 0 γ eh n p ,
j e = e μ e n E + k B T μ e n ,
j h = e μ h p E + k B T μ h p ,
t ( n + N A p N D + ) = e ( j e + j h ) ,
E = ( e 0 ) ( n + N A p N D + ) ,
N D = N D 0 + N D + .
n 0 = I 0 α + I 0 s e ( N D N A n 0 + p 0 ) + β e γ e ( N A + n 0 p 0 ) + γ e h p 0 ,
p 0 = I 0 α + I 0 s h ( N A + n 0 P 0 ) + β h γ h ( N D N A n 0 + P 0 ) + γ e h n 0 ,
[ i Γ Ee + Γ De + Γ le + Γ Re + Γ eeh Γ le + Γ ehh Γ die + Γ le Γ lh + Γ eeh i Γ Eh + Γ Dh + Γ lh + Γ Rh + Γ ehh Γ dih Γ lh Γ le + Γ Re + Γ lh Γ le Γ lh Γ Rh Γ le + Γ lh ] [ n 1 p 1 A 1 ] = I 1 [ α + s e ( N D N A + p 0 n 0 ) α + s h ( N A p 0 + n 0 ) s e ( N D N A + p 0 n 0 ) s h ( N A p 0 + n 0 ) ] ,
A 1 = I 0 α [ Γ Rh ( i Γ Ee + Γ De ) + Γ Re ( i Γ Eh + Γ Dh ) Γ dih Γ Rh ( i Γ Ee + Γ De + Γ Re ) + Γ die Γ Re ( i Γ Eh + Γ Dh + Γ Rh ) ] .
E 1 = E 0 [ K L Ee + i K 2 L De 2 + K L Eh + i K 2 L Dh 2 L Eh ( K 2 L De 2 + 1 ) + L Ee ( K 2 L Dh 2 + 1 ) ] ,
L E = μ τ E , L D 2 = μ τ k B T / e .
E 1 = 1 μ h τ h μ e τ e K { μ e τ e ( E 0 + i E D ) + μ h τ h ( E 0 i E D ) 2 E D + [ 1 / ( μ e τ e K ) ] + [ 1 / ( μ h τ h K ) ] } ,
K c 2 L D 2 = 1 ,
L D 2 = ( k B T / e ) μ τ ,
μ τ = 1 1 / 2 [ ( 1 / μ e τ e ) + ( 1 / μ h τ h ) ] .
n p = { n Δ n cos ( K x + ϕ ) for 0 < y < L 1 otherwise ,
| o L d y exp ( i δ k y ) | 2 = | exp ( i δ k L ) 1 δ k | 2 .
δ k = K 2 / ( 2 n k ) ,
Q = 4 δ k L = 2 π L λ / ( n Λ 2 ) ,
Q = 2.93 ( μ m 2 ) / Λ 2
sin ( Q / 8 ) 2 ( Q / 8 ) 2 .
sin θ out = sin θ in + m K λ / 2 π .
δ = ( k Δ n L / cos θ + i Δ α L / 2 cos θ ) ,
E = E t exp [ i ( k 1 x + k 2 y δ ) ] .
exp [ i δ cos ( x + ϕ ) ] = J m ( δ ) exp [ i m ( x + ϕ π / 2 ) ] ,
E = E t J m ( δ ) exp { i [ ( k 1 m K ) x + k 2 y m ( ϕ π / 2 ) ] } .
η m = | J m 2 ( δ ) | = J m 2 ( | 2 π Δ n L λ cos θ + i Δ α L 2 cos θ | ) .
J m ( x ) x m / ( 2 m m ! )
η m = 1 2 2 m m ! 2 [ ( 2 π Δ n L λ cos θ ) 2 + ( Δ α L 2 cos θ ) 2 ] m .
E = E 0 + E sc = E 0 [ E 1 cos ( K x + ϕ 1 ) + E 2 cos ( 2 K x + ϕ 2 ) + E 3 cos ( 3 K x + ϕ 3 ) ] ,
E sc 2 = [ E 0 2 + ½ ( E 1 2 + E 2 2 + E 3 2 ) ] + [ 2 E 0 E 1 cos ( K x + ϕ 1 ) + E 1 E 2 cos ( K x + ϕ 2 ϕ 1 ) + E 2 E 3 cos ( K x + ϕ 3 ϕ 2 ) ] + [ ½ E 1 2 cos ( 2 K x + 2 ϕ 1 ) 2 E 0 E 2 cos ( 2 K x + ϕ 2 ) + E 1 E 3 cos ( 2 K x + ϕ 3 ϕ 1 ) ] + [ 2 E 0 E 3 cos ( 3 K x + ϕ 3 ) + E 1 E 2 cos ( 3 K x + ϕ 1 + ϕ 2 ) ] .
μ ( n E ) = γ I 0 [ 1 + m cos ( K x ) ] ( n n d ) / τ ,
E 2 / E 1 = n 1 / n 0 .
η 1 ( 2 K ) η 1 ( K ) = ( E 2 E 1 E 1 4 E 0 ) 2 1 4 ,
sin θ D = 2 λ p λ HeNe sin θ HeNe ,
I 1 + = I 1 ( 1 α ¯ E L ) + ( I 1 I 2 ) 1 / 2 ( + Δ α L cos ϕ 2 cos θ + 2 π Δ n L sin ϕ λ cos θ ) ,
I 2 + = I 2 ( 1 α ¯ E L ) + ( I 1 I 2 ) 1 / 2 ( + Δ α L cos ϕ 2 cos θ + 2 π Δ n L sin ϕ λ cos θ ) .
1 2 I 1 + ( E ) + I 1 + ( E ) I 1 = 1 Δ α eff L cos θ .
γ = 1 2 I 1 + ( E ) + I 1 + ( E ) I 1 = ( I 2 I 1 ) 1 / 2 2 π Δ n L sin ϕ λ cos θ .
γ = [ β / ( 1 + β ) ] Γ L ,
Γ = 4 π Δ n m sin ϕ λ cos θ
η = π Δ n L / ( λ cos θ ) ,
sin ϕ = 1 2 β ( Δ I / I η ) .
I sat = n d / α τ ,
E sc = m ζ E 0 I / ( I sat + I ) ,
n = n 0 + n 2 I , α = α 0 + α 2 I .
n 2 = Δ n / I sat , α 2 = Δ α / I sat .
Δ n = 0.007 , Δ α = 1400 cm 1
n 2 = 7 × 10 2 cm 2 / W , α 2 / α 0 = 9 × 10 3 cm 2 / W .

Metrics