Abstract

The nonlinear refractive-index (n2) spectrum of ZnSe near the band gap (λgap ~ 450 nm) at 77 K was measured for the first time to our knowledge by using self-bending of a pulsed laser beam. The maximum nonlinearity, n2 ~ 1.9 × 10−8 cm2/W, measured by us is anomalously large, which cannot be explained by conventional thermally induced band-gap shrinkage.

© 1990 Optical Society of America

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References

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  1. D. R. Andersen, S. H. Park, S. W. Koch, A. Jeffery, Appl. Phys. Lett. 48, 1559 (1986); N. Peyghambarian, L. A. Kolodziejski, R. L. Gunshor, S. Datta, A. E. Kaplan, Appl. Phys. Lett. 52, 182 (1988).
    [CrossRef]
  2. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
    [CrossRef]
  3. B. S. Wherrett, A. K. Darzi, Y. T. Chow, B. T. McGuckin, E. W. Van Stryland, J. Opt. Soc. Am. B 7, 215 (1990).
    [CrossRef]
  4. Y. Y. Wu, D. J. Hagan, E. W. Van Stryland, M. J. Soileau, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 44.
  5. Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 43.
  6. D. Weaire, B. S. Wherrett, D. A. B. Miller, S. D. Smith, Opt. Lett. 4, 331 (1979).
    [CrossRef] [PubMed]
  7. M. Sheik-bahae, A. A. Said, E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
    [CrossRef] [PubMed]
  8. A. E. Kaplan, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 869 (1969) [Sov. Radiophys. 12, 692 (1969)].
  9. A. E. Kaplan, Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969) [JETP Lett. 9, 33 (1969)].
  10. M. S. Brodin, A. M. Kamuz, Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969) [JETP Lett. 9, 351 (1969)].
  11. I. Golub, Y. Beaudoin, S. L. Chin, Opt. Lett. 13, 488 (1988).
    [CrossRef] [PubMed]
  12. G. A. Swartzlander, H. Yin, A. E. Kaplan, Opt. Lett. 13, 1011 (1988); J. Opt. Soc. Am. B 6, 1317 (1989).
    [CrossRef] [PubMed]
  13. G. A. Swartzlander, A. E. Kaplan, J. Opt. Soc. Am. B 5, 765 (1988).
    [CrossRef]
  14. V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989), Chap. 8.
    [CrossRef]
  15. B. S. Wherrett, N. A. Higgins, Proc. R. Soc. London Ser. A 379, 67 (1982).
    [CrossRef]
  16. S. Colak, B. J. Fitzpatrick, R. N. Bhargava, J. Cryst. Growth 72, 504 (1985).
    [CrossRef]
  17. The most recent measurements of absorption spectra done at Phillips Laboratories (Briarcliff Manor, N.Y.) by J. B. Khurgin are consistent with our measurements.
  18. H. Haug, S. Schmitt-Rink, J. Opt. Soc. Am. B 2, 1135 (1985); L. Banyai, S. W. Koch, Z. Phys. B 63, 283 (1986).
    [CrossRef]
  19. P. V. Gul’tyaev, A. V. Petrov, Sov. Phys. Solid State 1, 330 (1959).
  20. B. Ray, II–VI Compounds (Pergamon, New York, 1969).
  21. T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 48.
  22. The difference between results3 due to TIBS and our measurements may be related to the exceptionally high quality of single-crystal ZnSe material that we used compared with the polycrystalline material used in Ref. 3.
  23. J. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971), pp. 92–93; C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976), p. 289.
  24. J. E. Bjorkholm, P. W. Smith, W. J. Tomlinson, A. E. Kaplan, Opt. Lett. 6, 345 (1981); A. E. Kaplan, Opt. Lett. 6, 360 (1981).
    [CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (3)

1986 (1)

D. R. Andersen, S. H. Park, S. W. Koch, A. Jeffery, Appl. Phys. Lett. 48, 1559 (1986); N. Peyghambarian, L. A. Kolodziejski, R. L. Gunshor, S. Datta, A. E. Kaplan, Appl. Phys. Lett. 52, 182 (1988).
[CrossRef]

1985 (2)

1984 (1)

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
[CrossRef]

1982 (1)

B. S. Wherrett, N. A. Higgins, Proc. R. Soc. London Ser. A 379, 67 (1982).
[CrossRef]

1981 (1)

1979 (1)

1969 (3)

A. E. Kaplan, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 869 (1969) [Sov. Radiophys. 12, 692 (1969)].

A. E. Kaplan, Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969) [JETP Lett. 9, 33 (1969)].

M. S. Brodin, A. M. Kamuz, Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969) [JETP Lett. 9, 351 (1969)].

1959 (1)

P. V. Gul’tyaev, A. V. Petrov, Sov. Phys. Solid State 1, 330 (1959).

Andersen, D. R.

D. R. Andersen, S. H. Park, S. W. Koch, A. Jeffery, Appl. Phys. Lett. 48, 1559 (1986); N. Peyghambarian, L. A. Kolodziejski, R. L. Gunshor, S. Datta, A. E. Kaplan, Appl. Phys. Lett. 52, 182 (1988).
[CrossRef]

Beaudoin, Y.

Bhargava, R. N.

S. Colak, B. J. Fitzpatrick, R. N. Bhargava, J. Cryst. Growth 72, 504 (1985).
[CrossRef]

Bjorkholm, J. E.

Brodin, M. S.

M. S. Brodin, A. M. Kamuz, Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969) [JETP Lett. 9, 351 (1969)].

Butylkin, V. S.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989), Chap. 8.
[CrossRef]

Chin, S. L.

Chow, Y. T.

Colak, S.

S. Colak, B. J. Fitzpatrick, R. N. Bhargava, J. Cryst. Growth 72, 504 (1985).
[CrossRef]

Darzi, A. K.

Ding, Y. J.

Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 43.

Fitzpatrick, B. J.

S. Colak, B. J. Fitzpatrick, R. N. Bhargava, J. Cryst. Growth 72, 504 (1985).
[CrossRef]

Gibbs, H. M.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
[CrossRef]

Golub, I.

Gul’tyaev, P. V.

P. V. Gul’tyaev, A. V. Petrov, Sov. Phys. Solid State 1, 330 (1959).

Guo, C. L.

Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 43.

Hagan, D. J.

Y. Y. Wu, D. J. Hagan, E. W. Van Stryland, M. J. Soileau, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 44.

Haug, H.

Higgins, N. A.

B. S. Wherrett, N. A. Higgins, Proc. R. Soc. London Ser. A 379, 67 (1982).
[CrossRef]

Jeffery, A.

D. R. Andersen, S. H. Park, S. W. Koch, A. Jeffery, Appl. Phys. Lett. 48, 1559 (1986); N. Peyghambarian, L. A. Kolodziejski, R. L. Gunshor, S. Datta, A. E. Kaplan, Appl. Phys. Lett. 52, 182 (1988).
[CrossRef]

Kamuz, A. M.

M. S. Brodin, A. M. Kamuz, Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969) [JETP Lett. 9, 351 (1969)].

Kaplan, A. E.

G. A. Swartzlander, A. E. Kaplan, J. Opt. Soc. Am. B 5, 765 (1988).
[CrossRef]

G. A. Swartzlander, H. Yin, A. E. Kaplan, Opt. Lett. 13, 1011 (1988); J. Opt. Soc. Am. B 6, 1317 (1989).
[CrossRef] [PubMed]

J. E. Bjorkholm, P. W. Smith, W. J. Tomlinson, A. E. Kaplan, Opt. Lett. 6, 345 (1981); A. E. Kaplan, Opt. Lett. 6, 360 (1981).
[CrossRef] [PubMed]

A. E. Kaplan, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 869 (1969) [Sov. Radiophys. 12, 692 (1969)].

A. E. Kaplan, Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969) [JETP Lett. 9, 33 (1969)].

Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 43.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989), Chap. 8.
[CrossRef]

Khronopulo, Yu. G.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989), Chap. 8.
[CrossRef]

Khurgin, J. B.

Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 43.

Koch, S. W.

D. R. Andersen, S. H. Park, S. W. Koch, A. Jeffery, Appl. Phys. Lett. 48, 1559 (1986); N. Peyghambarian, L. A. Kolodziejski, R. L. Gunshor, S. Datta, A. E. Kaplan, Appl. Phys. Lett. 52, 182 (1988).
[CrossRef]

Macleod, H. A.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
[CrossRef]

McGuckin, B. T.

Miller, D. A. B.

Moss, T. S.

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 48.

Olbright, G. R.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
[CrossRef]

Pankove, J.

J. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971), pp. 92–93; C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976), p. 289.

Park, S. H.

D. R. Andersen, S. H. Park, S. W. Koch, A. Jeffery, Appl. Phys. Lett. 48, 1559 (1986); N. Peyghambarian, L. A. Kolodziejski, R. L. Gunshor, S. Datta, A. E. Kaplan, Appl. Phys. Lett. 52, 182 (1988).
[CrossRef]

Petrov, A. V.

P. V. Gul’tyaev, A. V. Petrov, Sov. Phys. Solid State 1, 330 (1959).

Peyghambarian, N.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
[CrossRef]

Ray, B.

B. Ray, II–VI Compounds (Pergamon, New York, 1969).

Said, A. A.

Schmitt-Rink, S.

Sheik-bahae, M.

Smith, P. W.

Smith, S. D.

Soileau, M. J.

Y. Y. Wu, D. J. Hagan, E. W. Van Stryland, M. J. Soileau, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 44.

Swartzlander, G. A.

G. A. Swartzlander, A. E. Kaplan, J. Opt. Soc. Am. B 5, 765 (1988).
[CrossRef]

G. A. Swartzlander, H. Yin, A. E. Kaplan, Opt. Lett. 13, 1011 (1988); J. Opt. Soc. Am. B 6, 1317 (1989).
[CrossRef] [PubMed]

Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 43.

Tomlinson, W. J.

Van Milligen, F.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
[CrossRef]

Van Stryland, E. W.

B. S. Wherrett, A. K. Darzi, Y. T. Chow, B. T. McGuckin, E. W. Van Stryland, J. Opt. Soc. Am. B 7, 215 (1990).
[CrossRef]

M. Sheik-bahae, A. A. Said, E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Y. Y. Wu, D. J. Hagan, E. W. Van Stryland, M. J. Soileau, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 44.

Weaire, D.

Wherrett, B. S.

Wu, Y. Y.

Y. Y. Wu, D. J. Hagan, E. W. Van Stryland, M. J. Soileau, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 44.

Yakubovich, E. I.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989), Chap. 8.
[CrossRef]

Yin, H.

Appl. Phys. Lett. (2)

D. R. Andersen, S. H. Park, S. W. Koch, A. Jeffery, Appl. Phys. Lett. 48, 1559 (1986); N. Peyghambarian, L. A. Kolodziejski, R. L. Gunshor, S. Datta, A. E. Kaplan, Appl. Phys. Lett. 52, 182 (1988).
[CrossRef]

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. Van Milligen, Appl. Phys. Lett. 45, 1031 (1984); I. Freund, I. Janossy, M. R. Taghizadeh, J. G. H. Mathew, S. D. Smith, IEEE J. Quantum Electron. QE-21, 1447 (1985).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (1)

A. E. Kaplan, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 12, 869 (1969) [Sov. Radiophys. 12, 692 (1969)].

J. Cryst. Growth (1)

S. Colak, B. J. Fitzpatrick, R. N. Bhargava, J. Cryst. Growth 72, 504 (1985).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (5)

Pis’ma Zh. Eksp. Teor. Fiz. (2)

A. E. Kaplan, Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969) [JETP Lett. 9, 33 (1969)].

M. S. Brodin, A. M. Kamuz, Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969) [JETP Lett. 9, 351 (1969)].

Proc. R. Soc. London Ser. A (1)

B. S. Wherrett, N. A. Higgins, Proc. R. Soc. London Ser. A 379, 67 (1982).
[CrossRef]

Sov. Phys. Solid State (1)

P. V. Gul’tyaev, A. V. Petrov, Sov. Phys. Solid State 1, 330 (1959).

Other (8)

B. Ray, II–VI Compounds (Pergamon, New York, 1969).

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 48.

The difference between results3 due to TIBS and our measurements may be related to the exceptionally high quality of single-crystal ZnSe material that we used compared with the polycrystalline material used in Ref. 3.

J. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971), pp. 92–93; C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976), p. 289.

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, New York, 1989), Chap. 8.
[CrossRef]

Y. Y. Wu, D. J. Hagan, E. W. Van Stryland, M. J. Soileau, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 44.

Y. J. Ding, C. L. Guo, G. A. Swartzlander, J. B. Khurgin, A. E. Kaplan, in Digest of the OSA 1989 Annual Meeting (Optical Society of America, Washington, D.C., 1989), p. 43.

The most recent measurements of absorption spectra done at Phillips Laboratories (Briarcliff Manor, N.Y.) by J. B. Khurgin are consistent with our measurements.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the experiment. The inset shows a razor blade inserted into the beam to form a semi-Gaussian beam profile, which is then imaged onto the ZnSe sample plane. The beam is self-deflected toward the razor image because n2 > 0. P’s, pinholes; ND, neutral-density filter; BS, beam splitter; D’s, photodiodes; OSC, oscilloscope; MTS, motorized translation stage; Im, image.

Fig. 2
Fig. 2

Spatial intensity profiles of a laser beam in the far-field area after it passes through ZnSe plotted versus the deflection angles for linear and nonlinear cases.

Fig. 3
Fig. 3

Measured spectra of SB angles θNL (filled circles, experimental data; solid curve, least-square fitting) and of the nonlinear refractive index n2 (open circles, recalculated experimental data; dashed curve, least-square fitting) versus the laser wavelength. For illustration, intensity profiles in the far-field area are plotted for some specific wavelengths at left. Inset: the measured spectra of absorption α (curve 1) and of the SB angle due to TIBS (θNL)T (curve 2) for I0 ~ 1.5 × 105 W/cm2. The shaded area corresponds to strong absorption of the laser beam.

Equations (3)

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θ NL = n 2 L I 0 / a 0 ,
( Δ T ) max = ( Δ T ) 0 exp ( αx ) , ( Δ T ) 0 J laser α / π c p a 0 2 ,
( θ NL ) T = J laser n 0 ( d E g / d T ) × { 1 exp [ α ( λ ) L ] } / 4 π E g c p a 0 3 ,

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