Abstract

An ellipsometric picosecond pump–probe technique is used to measure the birefringence and dichroism induced in the zinc blende semiconductors ZnSe, GaAs, and CdTe by an intense linearly polarized pump pulse at 950 nm. We show that the induced birefringence and dichroism depend strongly on sample orientation (i.e., they are anisotropic). Furthermore, we demonstrate that by measuring the induced birefringence and dichroism for the pump polarized along the [100] and [110] crystal axes we can determine the sign and the magnitude of the intrinsic anisotropy both in the bound-electronic nonlinear refractive index and in the two-photon absorption coefficient; and, finally, we can extract the anisotropy in both the real and the imaginary parts of the product of the anisotropy parameter σ and the diagonal element of χ(3), the third-order susceptibility tensor. The latter product is a measure of the intrinsic anisotropy of the material. We find that the induced birefringence varies by roughly a factor of 2 with sample orientation in all three materials. The induced birefringence is, however, roughly an order of magnitude larger in size and opposite in sign for excitation above half the band gap (in GaAs and CdTe) than it is for excitation below half the band gap (in ZnSe). As expected, no dichroism is observed in ZnSe, but it is large in GaAs and CdTe, and, as with the birefringence, the dichroism varies by roughly a factor of 2 with crystal orientation. In order to test the effect of the measured anisotropy on device performance, we construct a simple on–off optical switch that exploits the measured birefringence and dichroism. Figures of merit are defined, and switch performance is investigated as a function of crystal orientation for excitation above and below the two-photon resonance (i.e., half the band gap). The figures of merit are shown to be extremely sensitive to crystal anisotropies for excitation below half the band gap and less so for excitation above half the band gap.

© 1995 Optical Society of America

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    [CrossRef]
  27. N. Pfeffer, F. Charra, and J. M. Nunzi, “Phase and frequency resolution of picosecond optical Kerr nonlinearities,” Opt. Lett. 16, 1987–1989 (1991).
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  28. M. A. Duguay and J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
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  29. P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
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  31. M. D. Dawson, W. A. Schroeder, D. P. Norwood, A. L. Smirl, J. Weston, R. N. Ettelbrick, and R. Aubert, “Characterization of a high-gain picosecond flash-lamp-pumped Nd:YAG regenerative amplifier,” Opt. Lett. 13, 990–992 (1988).
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  32. A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
    [CrossRef]
  33. T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
    [CrossRef]
  34. G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump-probe technique to measure deep-level, free-carrier, and two-photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
    [CrossRef]
  35. See, for example, P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
    [CrossRef]
  36. See, for example, C. Flytzanis, “Third-order optical susceptibilities in IV–IV and III–V semiconductors,” Phys. Lett. 31A, 273–274 (1970).
  37. In the notation used in this paper χijkl(−ω, ω, ω) specifically refers to those terms in the nonlinear susceptibility that resonate whenever 2ω is equal to a transition frequency (two-photon-resonant terms). Similarly, χijkl(ω,−ω, ω) refers to one-photon-resonant terms and χijkl(ω, ω,−ω) to nonresonant terms. An alternative notation also appears in the literature (e.g., in Ref. 35) in which one guarantees intrinsic permutation symmetry by defining the susceptibility as a permutation over all frequency/polarization pairings. The relationshipχi jkl(3)(−ω;−ω,ω,ω)=⅓[χi jkl(−ω,ω,ω)+χi jkl(ω,−ω,ω)+χi jkl(ω,ω,−ω)]allows one to make the connection between the notation of Ref. 35 (on the left-hand side) and that used in this study. The frequency ordering on the left-hand side has no physical significance. Accounting for this relationship, thenχT∥≡6χxxxx(3)(−ω;−ω,ω,ω),χT∥≡6χxyyx(3)(−ω;−ω,ω,ω).These results are a special case of the relationshipχeffective=|e·p|2χxyyx(3)(−ω;−ω,ω,ω)+χxyxy(3)(−ω;−ω,ω,ω)+|e·p*|2χxyyx(3)(−ω;−ω,ω,ω)for two-beam experiments in the isotropic limit.38
  38. D. C. Hutchings and B. S. Wherrett, “Polarization dichroism of nonlinear refraction in zinc-blende semiconductors,” Opt. Commun. (to be published).
  39. R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
    [CrossRef]
  40. E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).
  41. G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
    [CrossRef]
  42. V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
    [CrossRef] [PubMed]
  43. K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063–2064 (1990).
    [CrossRef]
  44. Data taken from Landolt–Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, K.-H. Hellwege, ed., Group III, Physics of IV and III–V Compounds and Physics of II–VI and I–VII Compounds, Semimagnetic Semiconductors (Springer-Verlag, Berlin, 1982), Vols. 17a and 17b.
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    [CrossRef]
  47. A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
    [CrossRef]
  48. J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, “All-optical switching in a nonlinear GaAlAs X junction,” Opt. Lett. 18, 1153–1155 (1993).
    [CrossRef] [PubMed]
  49. K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
    [CrossRef]
  50. H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
    [CrossRef]
  51. A. Migus, C. V. Shank, E. P. Ippen, and R. L. Fork, “Amplification of subpicosecond optical pulses: theory and experiment,” IEEE J. Quantum Electron. QE-18, 101–109 (1982).
    [CrossRef]

1994 (2)

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

1993 (2)

1992 (4)

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe”, J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

D. C. Hutchings and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc-blende semiconductors,” J. Opt. Soc. Am. B 9, 2065–2074 (1992).
[CrossRef]

1991 (3)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

N. Pfeffer, F. Charra, and J. M. Nunzi, “Phase and frequency resolution of picosecond optical Kerr nonlinearities,” Opt. Lett. 16, 1987–1989 (1991).
[CrossRef] [PubMed]

J. S. Aitchison, A. H. Kean, C. N. Ironside, A. Villeneuve, and G. I. Stegeman, “An ultrafast light gate,” Electron. Lett. 27, 1709–1710 (1991).
[CrossRef]

1990 (5)

K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063–2064 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. J. LaGasse, K. K. Anderson, C. A. Wang, H. A. Haus, and J. G. Fujimoto, “Femtosecond measurements of the non-resonant nonlinear index in AlGaAs,” Appl. Phys. Lett. 56, 417–419 (1990).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
[CrossRef] [PubMed]

G. I. Stegeman and E. M. Wright, “All optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

1989 (5)

1988 (3)

1987 (1)

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
[CrossRef]

1986 (1)

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

1985 (3)

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
[CrossRef] [PubMed]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488–494 (1985).
[CrossRef]

1982 (4)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[CrossRef]

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

A. Migus, C. V. Shank, E. P. Ippen, and R. L. Fork, “Amplification of subpicosecond optical pulses: theory and experiment,” IEEE J. Quantum Electron. QE-18, 101–109 (1982).
[CrossRef]

1979 (2)

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

1978 (1)

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

1976 (1)

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[CrossRef]

1975 (1)

W. L. Smith, J. H. Bechtel, and N. Bloembergen, “Dielectric-breakdown threshold and nonlinear-refractive-index measurements with picosecond laser pulses,” Phys. Rev. B 12, 706–714 (1975).
[CrossRef]

1970 (1)

See, for example, C. Flytzanis, “Third-order optical susceptibilities in IV–IV and III–V semiconductors,” Phys. Lett. 31A, 273–274 (1970).

1969 (2)

M. A. Duguay and J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
[CrossRef]

J. M. Ralston and R. K. Chang, “Optical limiting in semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[CrossRef]

1966 (1)

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[CrossRef]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

Adhav, R. S.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

Aitchison, J. S.

J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, “All-optical switching in a nonlinear GaAlAs X junction,” Opt. Lett. 18, 1153–1155 (1993).
[CrossRef] [PubMed]

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

J. S. Aitchison, A. H. Kean, C. N. Ironside, A. Villeneuve, and G. I. Stegeman, “An ultrafast light gate,” Electron. Lett. 27, 1709–1710 (1991).
[CrossRef]

Alfano, R. R.

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Al-hemyari, K.

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

Andersen, D. R.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Anderson, K. K.

M. J. LaGasse, K. K. Anderson, C. A. Wang, H. A. Haus, and J. G. Fujimoto, “Femtosecond measurements of the non-resonant nonlinear index in AlGaAs,” Appl. Phys. Lett. 56, 417–419 (1990).
[CrossRef]

Andrejco, M. J.

Aubert, R.

Bechtel, J. H.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[CrossRef]

W. L. Smith, J. H. Bechtel, and N. Bloembergen, “Dielectric-breakdown threshold and nonlinear-refractive-index measurements with picosecond laser pulses,” Phys. Rev. B 12, 706–714 (1975).
[CrossRef]

Bloembergen, N.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

W. L. Smith, J. H. Bechtel, and N. Bloembergen, “Dielectric-breakdown threshold and nonlinear-refractive-index measurements with picosecond laser pulses,” Phys. Rev. B 12, 706–714 (1975).
[CrossRef]

Boggess, T. F.

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump-probe technique to measure deep-level, free-carrier, and two-photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[CrossRef]

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488–494 (1985).
[CrossRef]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

Bohnert, K. M.

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

Boyd, I. W.

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488–494 (1985).
[CrossRef]

Butcher, P. N.

See, for example, P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
[CrossRef]

Chang, R. K.

J. M. Ralston and R. K. Chang, “Optical limiting in semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[CrossRef]

Charra, F.

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[CrossRef]

Cotter, D.

See, for example, P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
[CrossRef]

Cullen, T. J.

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
[CrossRef]

Dawson, M. D.

DeLong, K. W.

K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063–2064 (1990).
[CrossRef]

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

Dempsey, J.

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

DeSalvo, R.

Dubard, J.

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump-probe technique to measure deep-level, free-carrier, and two-photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[CrossRef]

Duguay, M. A.

M. A. Duguay and J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
[CrossRef]

Dvorak, M. D.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

Ettelbrick, R. N.

Flytzanis, C.

See, for example, C. Flytzanis, “Third-order optical susceptibilities in IV–IV and III–V semiconductors,” Phys. Lett. 31A, 273–274 (1970).

Fork, R. L.

A. Migus, C. V. Shank, E. P. Ippen, and R. L. Fork, “Amplification of subpicosecond optical pulses: theory and experiment,” IEEE J. Quantum Electron. QE-18, 101–109 (1982).
[CrossRef]

Fujimoto, J. G.

M. J. LaGasse, K. K. Anderson, C. A. Wang, H. A. Haus, and J. G. Fujimoto, “Femtosecond measurements of the non-resonant nonlinear index in AlGaAs,” Appl. Phys. Lett. 56, 417–419 (1990).
[CrossRef]

Garmire, E.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Gossard, A. C.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Grant, R. S.

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

Guha, S.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Hagan, D. J.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18, 194–196 (1993).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe”, J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1980–1989 (1988).
[CrossRef]

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, and Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. 13, 315–317 (1988).
[CrossRef] [PubMed]

Hansen, J. W.

M. A. Duguay and J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
[CrossRef]

Haus, H. A.

M. J. LaGasse, K. K. Anderson, C. A. Wang, H. A. Haus, and J. G. Fujimoto, “Femtosecond measurements of the non-resonant nonlinear index in AlGaAs,” Appl. Phys. Lett. 56, 417–419 (1990).
[CrossRef]

Ho, P. P.

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Holah, G. D.

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Hopf, F. A.

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

Hutchings, D. C.

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

D. C. Hutchings and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc-blende semiconductors,” J. Opt. Soc. Am. B 9, 2065–2074 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of ultrafast nonlinear refraction in zinc blende semiconductors at frequencies below the band edge,” submitted to Phys. Rev. B.

D. C. Hutchings and B. S. Wherrett, “Polarization dichroism of nonlinear refraction in zinc-blende semiconductors,” Opt. Commun. (to be published).

Ippen, E. P.

A. Migus, C. V. Shank, E. P. Ippen, and R. L. Fork, “Amplification of subpicosecond optical pulses: theory and experiment,” IEEE J. Quantum Electron. QE-18, 101–109 (1982).
[CrossRef]

Ironside, C. N.

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

J. S. Aitchison, A. H. Kean, C. N. Ironside, A. Villeneuve, and G. I. Stegeman, “An ultrafast light gate,” Electron. Lett. 27, 1709–1710 (1991).
[CrossRef]

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
[CrossRef]

Islam, M. N.

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992).

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[CrossRef]

Jewell, J. L.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Johnson, A. M.

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Kean, A. H.

J. S. Aitchison, A. H. Kean, C. N. Ironside, A. Villeneuve, and G. I. Stegeman, “An ultrafast light gate,” Electron. Lett. 27, 1709–1710 (1991).
[CrossRef]

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[CrossRef]

Kennedy, G. T.

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

Koch, S. W.

N. Peyghambarian and S. W. Koch, “Semiconductor nonlinear materials,” in Nonlinear Photonics, H. Gibbs, G. Khitrova, and N. Peyghambarian, eds. (Springer, New York, 1990), pp. 7–89.
[CrossRef]

LaGasse, M. J.

M. J. LaGasse, K. K. Anderson, C. A. Wang, H. A. Haus, and J. G. Fujimoto, “Femtosecond measurements of the non-resonant nonlinear index in AlGaAs,” Appl. Phys. Lett. 56, 417–419 (1990).
[CrossRef]

Liu, P.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

Lotem, H.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

Mansour, K.

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1980–1989 (1988).
[CrossRef]

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

McCall, S. L.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Migus, A.

A. Migus, C. V. Shank, E. P. Ippen, and R. L. Fork, “Amplification of subpicosecond optical pulses: theory and experiment,” IEEE J. Quantum Electron. QE-18, 101–109 (1982).
[CrossRef]

Miller, A.

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

G. I. Stegeman and A. Miller, “Physics of all-optical switching devices,” in Photonics in Switching, J. E. Midwinter, ed. (Academic, San Diego, Calif., 1993), Vol. I.
[CrossRef]

Mizrahi, V.

Moss, S. C.

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488–494 (1985).
[CrossRef]

Norwood, D. P.

Nunzi, J. M.

Passner, A.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

Peyghambarian, N.

N. Peyghambarian and S. W. Koch, “Semiconductor nonlinear materials,” in Nonlinear Photonics, H. Gibbs, G. Khitrova, and N. Peyghambarian, eds. (Springer, New York, 1990), pp. 7–89.
[CrossRef]

Pfeffer, N.

Pidgeon, C. R.

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Ralston, J. M.

J. M. Ralston and R. K. Chang, “Optical limiting in semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[CrossRef]

Said, A. A.

Saifi, M. A.

Schroeder, W. A.

Seaton, C. T.

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
[CrossRef]

Shank, C. V.

A. Migus, C. V. Shank, E. P. Ippen, and R. L. Fork, “Amplification of subpicosecond optical pulses: theory and experiment,” IEEE J. Quantum Electron. QE-18, 101–109 (1982).
[CrossRef]

Sheik-Bahae, M.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18, 194–196 (1993).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe”, J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Sibbett, W.

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

Smirl, A. L.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump-probe technique to measure deep-level, free-carrier, and two-photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[CrossRef]

M. D. Dawson, W. A. Schroeder, D. P. Norwood, and A. L. Smirl, “Wavelength-tunable synchronous amplification of picosecond dye-laser pulses near 1 μmm,” Opt. Lett. 14, 364–366 (1989).
[CrossRef] [PubMed]

M. D. Dawson, W. A. Schroeder, D. P. Norwood, A. L. Smirl, J. Weston, R. N. Ettelbrick, and R. Aubert, “Characterization of a high-gain picosecond flash-lamp-pumped Nd:YAG regenerative amplifier,” Opt. Lett. 13, 990–992 (1988).
[CrossRef] [PubMed]

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488–494 (1985).
[CrossRef]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

Smith, J.

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Smith, W. L.

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[CrossRef]

W. L. Smith, J. H. Bechtel, and N. Bloembergen, “Dielectric-breakdown threshold and nonlinear-refractive-index measurements with picosecond laser pulses,” Phys. Rev. B 12, 706–714 (1975).
[CrossRef]

Soileau, M. J.

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, and Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. 13, 315–317 (1988).
[CrossRef] [PubMed]

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
[CrossRef] [PubMed]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

Stegeman, G. I.

J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, “All-optical switching in a nonlinear GaAlAs X junction,” Opt. Lett. 18, 1153–1155 (1993).
[CrossRef] [PubMed]

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

J. S. Aitchison, A. H. Kean, C. N. Ironside, A. Villeneuve, and G. I. Stegeman, “An ultrafast light gate,” Electron. Lett. 27, 1709–1710 (1991).
[CrossRef]

K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063–2064 (1990).
[CrossRef]

G. I. Stegeman and E. M. Wright, “All optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
[CrossRef]

G. I. Stegeman, “Material figures of merit and implications to all-optical switching,” in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 75–89 (1993).
[CrossRef]

G. I. Stegeman and A. Miller, “Physics of all-optical switching devices,” in Photonics in Switching, J. E. Midwinter, ed. (Academic, San Diego, Calif., 1993), Vol. I.
[CrossRef]

Tai, K.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Tarng, S. S.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Valley, G. C.

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump-probe technique to measure deep-level, free-carrier, and two-photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[CrossRef]

Van Stryland, E. W.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18, 194–196 (1993).
[CrossRef] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe”, J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

D. C. Hutchings and E. W. Van Stryland, “Nondegenerate two-photon absorption in zinc-blende semiconductors,” J. Opt. Soc. Am. B 9, 2065–2074 (1992).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, and Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. 13, 315–317 (1988).
[CrossRef] [PubMed]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1980–1989 (1988).
[CrossRef]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488–494 (1985).
[CrossRef]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
[CrossRef] [PubMed]

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

Vanherzeele, H.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
[CrossRef] [PubMed]

Villeneuve, A.

J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, “All-optical switching in a nonlinear GaAlAs X junction,” Opt. Lett. 18, 1153–1155 (1993).
[CrossRef] [PubMed]

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

J. S. Aitchison, A. H. Kean, C. N. Ironside, A. Villeneuve, and G. I. Stegeman, “An ultrafast light gate,” Electron. Lett. 27, 1709–1710 (1991).
[CrossRef]

Walker, A. C.

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
[CrossRef]

Wang, C. A.

M. J. LaGasse, K. K. Anderson, C. A. Wang, H. A. Haus, and J. G. Fujimoto, “Femtosecond measurements of the non-resonant nonlinear index in AlGaAs,” Appl. Phys. Lett. 56, 417–419 (1990).
[CrossRef]

Wang, J.

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe”, J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Weinberger, D. A.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Weston, J.

Wherrett, B. S.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

D. C. Hutchings and B. S. Wherrett, “Polarization dichroism of nonlinear refraction in zinc-blende semiconductors,” Opt. Commun. (to be published).

D. C. Hutchings and B. S. Wherrett, “Theory of ultrafast nonlinear refraction in zinc blende semiconductors at frequencies below the band edge,” submitted to Phys. Rev. B.

Wiegmann, W.

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

Wigley, P. J.

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Woodall, M. A.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
[CrossRef] [PubMed]

Wright, E. M.

G. I. Stegeman and E. M. Wright, “All optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

Wu, Y. Y.

Yang, C. C.

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Young, J.

Appl. Phys. B (1)

E. W. Van Stryland, A. L. Smirl, T. F. Boggess, M. J. Soileau, B. S. Wherrett, and F. A. Hopf, “Weak-wave retardation and phase-conjugate self-defocusing in Si,” Appl. Phys. B 29, 159–160 (1982).

Appl. Phys. Lett. (7)

G. I. Stegeman, C. T. Seaton, C. N. Ironside, T. J. Cullen, and A. C. Walker, “Effects of saturation and loss on nonlinear directional couplers,” Appl. Phys. Lett. 50, 1035–1037 (1987).
[CrossRef]

K. W. DeLong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063–2064 (1990).
[CrossRef]

A. Villeneuve, J. S. Aitchison, C. C. Yang, P. J. Wigley, C. N. Ironside, and G. I. Stegeman, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, “Room temperature excitonic optical bistability in a GaAs-GaAlAs superlattice etalon,” Appl. Phys. Lett. 41, 221–222 (1982).
[CrossRef]

J. M. Ralston and R. K. Chang, “Optical limiting in semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[CrossRef]

M. J. LaGasse, K. K. Anderson, C. A. Wang, H. A. Haus, and J. G. Fujimoto, “Femtosecond measurements of the non-resonant nonlinear index in AlGaAs,” Appl. Phys. Lett. 56, 417–419 (1990).
[CrossRef]

M. A. Duguay and J. W. Hansen, “An ultrafast light gate,” Appl. Phys. Lett. 15, 192–194 (1969).
[CrossRef]

Electron. Lett. (2)

J. S. Aitchison, A. H. Kean, C. N. Ironside, A. Villeneuve, and G. I. Stegeman, “An ultrafast light gate,” Electron. Lett. 27, 1709–1710 (1991).
[CrossRef]

K. Al-hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, “Ultrafast all-optical switching in GaAlAs integrated spectrometer in 1.55 μm spectral region,” Electron. Lett. 28, 1090–1093 (1992).
[CrossRef]

IEEE J. Quantum Electron. (7)

A. Migus, C. V. Shank, E. P. Ippen, and R. L. Fork, “Amplification of subpicosecond optical pulses: theory and experiment,” IEEE J. Quantum Electron. QE-18, 101–109 (1982).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[CrossRef]

T. F. Boggess, K. M. Bohnert, K. Mansour, S. C. Moss, I. W. Boyd, and A. L. Smirl, “Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the band gap of crystalline silicon,” IEEE J. Quantum Electron. QE-22, 360–368 (1986).
[CrossRef]

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1982).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, “Optical limiting in GaAs,” IEEE J. Quantum Electron. QE-21, 488–494 (1985).
[CrossRef]

J. Appl. Phys. (1)

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump-probe technique to measure deep-level, free-carrier, and two-photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[CrossRef]

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

J. Phys. C (1)

A. Miller, A. M. Johnson, J. Dempsey, J. Smith, C. R. Pidgeon, and G. D. Holah, “Two-photon absorption in InSb and Hg1−x Cdx Te,” J. Phys. C 12, 4839–4849 (1979).
[CrossRef]

Opt. Eng. (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, “Two-photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Opt. Lett. (9)

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, and Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. 13, 315–317 (1988).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

M. D. Dawson, W. A. Schroeder, D. P. Norwood, and A. L. Smirl, “Wavelength-tunable synchronous amplification of picosecond dye-laser pulses near 1 μmm,” Opt. Lett. 14, 364–366 (1989).
[CrossRef] [PubMed]

M. D. Dawson, W. A. Schroeder, D. P. Norwood, A. L. Smirl, J. Weston, R. N. Ettelbrick, and R. Aubert, “Characterization of a high-gain picosecond flash-lamp-pumped Nd:YAG regenerative amplifier,” Opt. Lett. 13, 990–992 (1988).
[CrossRef] [PubMed]

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18, 194–196 (1993).
[CrossRef] [PubMed]

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
[CrossRef] [PubMed]

N. Pfeffer, F. Charra, and J. M. Nunzi, “Phase and frequency resolution of picosecond optical Kerr nonlinearities,” Opt. Lett. 16, 1987–1989 (1991).
[CrossRef] [PubMed]

J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, “All-optical switching in a nonlinear GaAlAs X junction,” Opt. Lett. 18, 1153–1155 (1993).
[CrossRef] [PubMed]

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

Opt. Quantum Electron. (1)

G. I. Stegeman and E. M. Wright, “All optical waveguide switching,” Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

Phys. Lett. (1)

See, for example, C. Flytzanis, “Third-order optical susceptibilities in IV–IV and III–V semiconductors,” Phys. Lett. 31A, 273–274 (1970).

Phys. Rev. A (1)

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Phys. Rev. B (5)

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

J. H. Bechtel and W. L. Smith, “Two-photon absorption in semiconductors with picosecond laser pulses,” Phys. Rev. B 13, 3515–3522 (1976).
[CrossRef]

P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav, “Absolute two-photon absorption coefficients at 355 and 266 nm,” Phys. Rev. B 17, 4620–4632 (1978).
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

W. L. Smith, J. H. Bechtel, and N. Bloembergen, “Dielectric-breakdown threshold and nonlinear-refractive-index measurements with picosecond laser pulses,” Phys. Rev. B 12, 706–714 (1975).
[CrossRef]

Phys. Rev. Lett. (2)

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96–99 (1990).
[CrossRef] [PubMed]

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158–1161 (1966).
[CrossRef]

Other (9)

In the notation used in this paper χijkl(−ω, ω, ω) specifically refers to those terms in the nonlinear susceptibility that resonate whenever 2ω is equal to a transition frequency (two-photon-resonant terms). Similarly, χijkl(ω,−ω, ω) refers to one-photon-resonant terms and χijkl(ω, ω,−ω) to nonresonant terms. An alternative notation also appears in the literature (e.g., in Ref. 35) in which one guarantees intrinsic permutation symmetry by defining the susceptibility as a permutation over all frequency/polarization pairings. The relationshipχi jkl(3)(−ω;−ω,ω,ω)=⅓[χi jkl(−ω,ω,ω)+χi jkl(ω,−ω,ω)+χi jkl(ω,ω,−ω)]allows one to make the connection between the notation of Ref. 35 (on the left-hand side) and that used in this study. The frequency ordering on the left-hand side has no physical significance. Accounting for this relationship, thenχT∥≡6χxxxx(3)(−ω;−ω,ω,ω),χT∥≡6χxyyx(3)(−ω;−ω,ω,ω).These results are a special case of the relationshipχeffective=|e·p|2χxyyx(3)(−ω;−ω,ω,ω)+χxyxy(3)(−ω;−ω,ω,ω)+|e·p*|2χxyyx(3)(−ω;−ω,ω,ω)for two-beam experiments in the isotropic limit.38

D. C. Hutchings and B. S. Wherrett, “Polarization dichroism of nonlinear refraction in zinc-blende semiconductors,” Opt. Commun. (to be published).

See, for example, P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
[CrossRef]

N. Peyghambarian and S. W. Koch, “Semiconductor nonlinear materials,” in Nonlinear Photonics, H. Gibbs, G. Khitrova, and N. Peyghambarian, eds. (Springer, New York, 1990), pp. 7–89.
[CrossRef]

G. I. Stegeman and A. Miller, “Physics of all-optical switching devices,” in Photonics in Switching, J. E. Midwinter, ed. (Academic, San Diego, Calif., 1993), Vol. I.
[CrossRef]

G. I. Stegeman, “Material figures of merit and implications to all-optical switching,” in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 75–89 (1993).
[CrossRef]

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992).

Data taken from Landolt–Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, K.-H. Hellwege, ed., Group III, Physics of IV and III–V Compounds and Physics of II–VI and I–VII Compounds, Semimagnetic Semiconductors (Springer-Verlag, Berlin, 1982), Vols. 17a and 17b.

D. C. Hutchings and B. S. Wherrett, “Theory of ultrafast nonlinear refraction in zinc blende semiconductors at frequencies below the band edge,” submitted to Phys. Rev. B.

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Figures (7)

Fig. 1
Fig. 1

Experimental geometry for the Kerr ellipsometry measurement. P1 and P2 are, respectively, the polarizer and the analyzer; L1 and L2 are lenses, QWP is a quarter-wave plate, and HWP is a half-wave plate. The excitation (pump) pulse, indicated by ê, is vertically polarized, and the probe pulse, p ̂, is polarized at 45° with respect to it. The transmission axis of the analyzer is indicated by â; δ = 0 corresponds to the transmission axis of the analyzer perpendicular to the transmission axis of the polarizer.

Fig. 2
Fig. 2

Orientation of the excitation pulse polarization with respect to the crystallographic axes. The polarization of the excitation pulse remains vertical while the sample is rotated such that the excitation polarization lies along (a) the [100] axis and (b) the [110] axis.

Fig. 3
Fig. 3

Probe transmission as a function of analyzer angle for the pump pulse polarized along (a) the [100] axis and (b) the [110] axis of the ZnSe sample. The filled (open) symbols indicate data taken without (with) the quarter-wave plate. The peak-on-axis pump irradiance was (a) 3 × 1013 W/m2 and (b) 1 × 1013 W/m2.

Fig. 4
Fig. 4

Transmission of probe pulse through the [110]-oriented ZnSe sample as a function of delay between the pump and the probe pulses for analyzer angle δ=0.

Fig. 5
Fig. 5

Probe transmission as a function of analyzer angle for the pump pulse polarized along (a) the [100] axis and (b) the [110] axis of the GaAs sample. The filled (open) symbols indicate data taken without (with) the quarter-wave plate. The peak on-axis pump irradiance was 2.5 × 1012 W/m2 in both (a) and (b).

Fig. 6
Fig. 6

Probe transmission as a function of analyzer angle for the pump pulse polarized along (a) the [100] axis and (b) the [110] axis of the CdTe sample. The filled (open) symbols indicate data taken without (with) the quarter-wave plate. The peak on-axis pump irradiance was 2.1 × 1012 W/m2 in both (a) and (b).

Fig. 7
Fig. 7

Transmission of the polarization rotation switch as a function of peak on-axis pump pulse irradiance for ZnSe (filled circles), CdTe (filled squares), and GaAs (filled triangles) with the pump pulse polarized along the [110] axis and for ZnSe (open circles) with the pump polarized along the [100] axis. The ZnSe and CdTe crystals are each 2 mm long, and the GaAs crystal is 0.5 mm long. For the purposes of comparison, the GaAs data have been scaled to a 2-mm crystal length. The original data for GaAs were obtained at four times higher irradiance than indicated by the points on the graph. The solid lines are fits to expression (45) for the values of Δn2 and Δβ quoted in Table 1. There is no depletion evident in the ZnSe data, whereas depletion associated with two-photon absorption is apparent in the GaAs and CdTe data.

Tables (2)

Tables Icon

Table 1 Measured Induced Birefringence Δn2 and Dichroism Δβ of the Zinc Blende Semiconductors ZnSe, GaAs, and CdTe for the Exciting Pulse Polarized along the [100] and [110]Crystal Axes

Tables Icon

Table 2 Measured Values of Real and Imaginary Components of D [Eqs. (24) and (25)] for the Zinc Blende Semiconductors ZnSe, GaAs, and CdTe

Equations (50)

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T ( δ ) = ( 1 C ) sin 2 δ + C ,
P i ( 3 ) ( ω i , k i ) = 0 4 jkl χ i jkl ( 3 ) ( ω j , ω k , ω l ) j ( ω j , k j ) k ( ω k , k k ) × l ( ω l , k l ) ,
P a ( 3 ) ( ω a , k a ) = 0 4 bcd i jkl χ i jkl ( 3 ) ( ω b , ω c , ω d ) a i * b j c k d l × b ( ω b , k b ) c ( ω c , k c ) d ( ω d , k d ) ,
P a ( 3 ) ( ω a , k a ) = 0 4 bcd χ eff ( ω b , ω c , ω d ) b ( ω b , k b ) × c ( ω c , k c ) d ( ω d , k d ) ,
χ eff ( ω b , ω c , ω d ) = χ xxyy ( ω b , ω c , ω d ) ( â * · b ̂ ) ( ĉ · d ̂ ) + χ xyyx ( ω b , ω c , ω d ) ( â * · d ̂ ) ( b ̂ · ĉ ) + χ xyxy ( ω b , ω c , ω d ) ( â * · ĉ ) ( b ̂ · d ̂ ) + S ( ω b , ω c , ω d ) i a i * b i c i d i ,
S ( ω b , ω c , ω d ) = χ xxxx ( ω b , ω c , ω d ) [ χ xxyy ( ω b , ω c , ω d ) + χ xyxy ( ω b , ω c , ω d ) + χ xyyx ( ω b , ω c , ω d ) ] = σ 1 ( ω b , ω c , ω d ) Re [ χ xxxx ( ω b , ω c , ω d ) ] + i σ 2 ( ω b , ω c , ω d ) Im [ χ xxxx ( ω b , ω c , ω d ) ]
p ( ω , k p ) = p ( ω , k p ) ê + p ( ω , k p ) q ̂ ,
P e ( ω , k p ) = 0 4 [ χ T e * ( ω , k e ) e ( ω , k e ) p ( ω , k p ) + χ C e * ( ω , k e ) e ( ω , k e ) p ( ω , k p ) ] ,
P q ( ω , k p ) = 0 4 [ χ T e * ( ω , k e ) e ( ω , k e ) p ( ω , k p ) + χ C e * ( ω , k e ) e ( ω , k e ) p ( ω , k p ) ] ,
χ T = 2 A 2 D ( 1 i e i 4 ) , χ T = 2 B + 2 D i e i 2 q i 2 , χ C = 2 D i e i 3 q i
A = χ xxxx ( ω , ω , ω ) + χ xxxx ( ω , ω , ω ) + χ xxxx ( ω , ω , ω ) ,
B = χ xyyx ( ω , ω , ω ) + χ xxyy ( ω , ω , ω ) + χ xyxy ( ω , ω , ω ) ,
D = S ( ω , ω , ω ) + S ( ω , ω , ω ) + S ( ω , ω , ω ) .
A z = ω 4 n 2 c 2 0 Im χ T I e A = 1 2 α 2 I e A ,
ϕ z = ω 4 n 2 c 2 0 Re χ T I e = 2 π λ 0 n 2 I e
A z = ω 4 n 2 c 2 0 Im χ T I e A = 1 2 α 2 I e A ,
ϕ z = ω 4 n 2 c 2 0 Re χ T I e = 2 π λ 0 n 2 I e
I ( n 0 λ / 4 ) = I p ( 0 , r , t ) ( 1 R 1 ) ( 1 R 2 ) × { [ δ + Δ α 2 ( 1 R 1 ) I e ( 0 , r , t ) L 4 ] 2 + [ π Δ n 2 ( 1 R 1 ) I e ( 0 , r , t ) L λ 0 ] 2 } ,
Δ n 2 = n 2 n 2 = 1 4 n 2 c 0 Re ( Δ χ ) ,
Δ α 2 = α 2 α 2 = ω 2 n 2 c 2 0 Im ( Δ χ ) ,
Δ χ = χ T χ T = 2 [ A B D ( 1 i e i 4 + i e i 2 q i 2 ) ] .
T ( n 0 λ / 4 ) = ( 1 R 1 ) ( 1 R 2 ) × ( { δ + 2 3 [ ( 1 R 1 ) Δ α 2 I e 0 L 4 ] } 2 + 8 15 { [ π ( 1 R 1 ) Δ n 2 I e 0 L λ 0 ] 2 + 1 6 [ ( 1 R 1 ) Δ α 2 I e 0 L 4 ] 2 } ) ,
T ( λ / 4 ) = ( 1 R 1 ) ( 1 R 2 ) × ( { δ 2 3 [ π ( 1 R 1 ) Δ n 2 I e 0 L λ 0 ] } 2 + 8 15 { [ ( 1 R 1 ) Δ α 2 I e 0 L λ 0 ] 2 + 1 6 [ π ( 1 R 1 ) Δ n 2 I e 0 L λ 0 ] 2 } ) .
Δ n 2 [ 100 ] Δ n 2 [ 110 ] = 1 4 n 2 c 0 Re ( 2 D ) = 1 2 n 2 c 0 { σ 1 ( ω , ω , ω ) Re [ χ xxxx ( ω , ω , ω ) ] + σ 1 ( ω , ω , ω ) Re [ χ xxxx ( ω , ω , ω ) ] + σ 1 ( ω , ω , ω ) Re [ χ xxxx ( ω , ω , ω ) ] } ,
Δ α 2 [ 100 ] Δ α 2 [ 110 ] = ω 2 n 2 c 2 0 Im ( 2 D ) = ω n 2 c 2 0 { σ 2 ( ω , ω , ω ) Im [ χ xxxx ( ω , ω , ω ) ] + σ 2 ( ω , ω , ω ) Im [ χ xxxx ( ω , ω , ω ) ] + σ 2 ( ω , ω , ω ) Im [ χ xxxx ( ω , ω , ω ) ] } .
Δ n 2 [ ê ] = Δ n 2 [ 110 ] + ( Δ n 2 [ 100 ] Δ n 2 [ 110 ] ) × [ i ( e i 4 e i 2 q i 2 ) ] .
Δ α 2 [ ê ] = Δ α 2 [ 110 ] + ( Δ α 2 [ 100 ] Δ α 2 [ 110 ] ) × [ i ( e i 4 e i 2 q i 2 ) ] .
n 2 = 1 4 n 2 c 0 Re [ χ T ] = 1 4 n 2 c 0 Re [ A D ( 1 i e i 4 ) ] ,
α 2 = ω 2 n 2 c 2 0 Im [ χ T ] = ω 2 n 2 c 2 0 Im [ A D ( 1 i e i 4 ) ] ,
n 2 [ ê ] = n 2 [ 100 ] ½ ( Δ n 2 [ 100 ] Δ n 2 [ 110 ] ) ( 1 i e i 4 ) .
α 2 [ ê ] = α 2 [ 100 ] ½ ( Δ α 2 [ 100 ] Δ α 2 [ 110 ] ) ( 1 i e i 4 ) .
Δ n 2 [ ê ] = [ 0.34 0.20 i ( e i 4 e i 2 q i 2 ) ] × 10 4 cm 2 / GW .
n 2 [ ê ] = n 2 [ 100 ] + ( 0.1 × 10 4 cm 2 / GW ) ( 1 i e i 4 ) = n 2 [ 100 ] σ 1 ( ω , ω , ω ) n 2 [ 100 ] ( 1 i e i 4 )
Re [ D ] = 2 n 2 c 0 ( Δ n 2 [ 100 ] Δ n 2 [ 110 ] ) = σ 1 ( ω , ω , ω ) Re [ χ xxxx ( ω , ω , ω ) ] ,
Δ β [ ê ] = 32 20 [ i ( e i 4 e i 2 q i 2 ) ] cm / GW .
β [ ê ] = β [ 100 ] + 10 ( 1 i e i 4 ) cm / GW = β [ 100 ] σ 2 ( ω , ω , ω ) β [ 100 ] ( 1 i e i 4 ) .
Im ( D ) = n 2 c 2 0 ω ( Δ β [ 100 ] Δ β [ 110 ] ) = σ 2 ( ω , ω , ω ) Im [ χ xxxx ( ω , ω , ω ) ] .
Δ n 2 [ ê ] = [ 5.0 + 1.7 i ( e i 4 e i 2 q i 2 ) ] × 10 4 cm 2 / GW ,
n 2 [ ê ] = n 2 [ 100 ] ( 0.9 × 10 4 cm 2 / GW ) ( 1 i e i 4 ) .
Re ( D ) = 2 n 2 c 0 ( Δ n 2 [ 100 ] Δ n 2 [ 110 ] ) = σ 1 ( ω , ω , ω ) Re [ χ xxxx ( ω , ω , ω ) ] + σ 1 ( ω , ω , ω ) Re [ χ xxxx ( ω , ω , ω ) ] + σ 1 ( ω , ω , ω ) Re [ χ xxxx ( ω , ω , ω ) ] .
Δ n 2 [ ê ] = [ 2.4 + 1.0 i ( e i 4 e i 2 q i 2 ) ] × 10 4 cm 2 / GW ,
Δ β [ ê ] = 20 11 [ i ( e i 4 e i 2 q i 2 ) ] cm / GW .
n 2 [ ê ] = n 2 [ 100 ] ( 0.5 × 10 4 ) ( 1 i e i 4 ) cm 2 / GW ,
β [ ê ] = β [ 100 ] + 5.5 ( 1 i e i 4 ) cm / GW = β [ 100 ] σ 2 ( ω , ω , ω ) β [ 100 ] ( 1 i e i 4 ) .
R 8 15 C × { [ π ( 1 R 1 ) Δ n 2 I e 0 L λ 0 ] 2 + [ ( 1 R 1 ) Δ β I e 0 L 4 ] 2 } ,
M 8 [ π ( 1 R 1 ) Δ n 2 I e 0 L ] 2 15 C λ 0 2 α 0 L I e 0 τ .
M 8 { [ π ( 1 R 1 ) Δ n 2 I e 0 L λ 0 ] 2 + [ ( 1 R 1 ) Δ β I e 0 L 4 ] 2 } 15 C β I e 0 2 L τ .
χi jkl(3)(ω;ω,ω,ω)=[χi jkl(ω,ω,ω)+χi jkl(ω,ω,ω)+χi jkl(ω,ω,ω)]
χT6χxxxx(3)(ω;ω,ω,ω),χT6χxyyx(3)(ω;ω,ω,ω).
χeffective=|e·p|2χxyyx(3)(ω;ω,ω,ω)+χxyxy(3)(ω;ω,ω,ω)+|e·p*|2χxyyx(3)(ω;ω,ω,ω)

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