Abstract

The nonlinear optical properties of, and phase conjugation in, the bulk semiconductor GaSb were investigated at 2.1 µm by use of the Z-scan and the degenerate four-wave mixing techniques. Measurements were also carried out near the fundamental bandgap of the quaternary compound Ga0.87In0.13As0.11Sb0.89. Z-scan measurements as a function of sample temperature, in conjunction with theoretical modeling, identified the predominant sources of the medium nonlinearity to be nonequilibrium free carriers generated through two-photon absorption in GaSb, while it is saturation of real transitions near the fundamental band edge in Ga0.87In0.13As0.11Sb0.89 that was identified as the primary cause of this nonlinearity. Degenerate four-wave mixing phase-conjugate reflectivity of as much as 14% has been achieved in GaSb.

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  1. 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]
  2. A. A. Borsch, M. Brodlin, and V. Volkov, Refractive Nonlinearity of Wide-Band Semiconductors and Applications (Harwood Academic, Chur, Switzerland, 1990), pp. 7–16.
  3. B. S. Wherrett, “A comparison of theories of resonant nonlinear refraction in semiconductors,” Proc. R. Soc. London Ser. A 390, 397–409 (1983).
    [CrossRef]
  4. R. K. Jain and M. B. Klein, “Degenerate four-wave mixing in semiconductors,” Optical Phase Conjugation, R. L. Fisher, ed. (Academic, New York, 1983), pp. 332–345.
  5. A. F. Gibson, “Two-photon absorption in indium antimonide and germanium,” J. Phys. C 9, 3259–3274 (1976).
    [CrossRef]
  6. D. K. Schroder, Semiconductor Material and Device Characterization (Wiley, New York, 1990), pp. 205–206.
  7. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge Univ. Press, Cambridge, UK, 1986), pp. 550–560.
  8. Ref. 2, p. 24.
  9. 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]
  10. C. R. Pigdoen, “Two-photon absorption in zincblende semiconductors,” Phys. Rev. Lett. 42, 1785–1787 (1979).
    [CrossRef]
  11. V. Nathan, “Review of multiphoton absorption in crystalline solids,” J. Opt. Soc. Am. B 2, 294–316 (1985).
    [CrossRef]
  12. 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]
  13. R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992), pp. 159–164.
  14. E. W. Van Stryland, M. 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).
  15. R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high resolution spectroscopy by resonant degenerate four-wave mixing,” Optical Phase Conjugation, R. L. Fisher, ed. (Academic, New York, 1983), pp. 215–264.
  16. P. L. Landsberg, Recombination in Semiconductors (Cambridge Univ. Press, Cambridge, UK, 1990), pp. 315–316.
  17. Ref. 4, pp. 369–401.
  18. M. D. Turner, “Degenerate four-wave mixing of Cr, Tm, Ho:YAG laser output at 2.1 μm in semiconductor compounds,” Ph.D. dissertation (Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1996), pp. 125–126.
  19. S. Adachi, Physical Properties of III–V Semiconductor Compounds (Academic, Boston, Mass., 1992), pp. 178–180.

1992 (2)

1990 (1)

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]

1985 (2)

E. W. Van Stryland, M. 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).

V. Nathan, “Review of multiphoton absorption in crystalline solids,” J. Opt. Soc. Am. B 2, 294–316 (1985).
[CrossRef]

1983 (1)

B. S. Wherrett, “A comparison of theories of resonant nonlinear refraction in semiconductors,” Proc. R. Soc. London Ser. A 390, 397–409 (1983).
[CrossRef]

1979 (1)

C. R. Pigdoen, “Two-photon absorption in zincblende semiconductors,” Phys. Rev. Lett. 42, 1785–1787 (1979).
[CrossRef]

1976 (1)

A. F. Gibson, “Two-photon absorption in indium antimonide and germanium,” J. Phys. C 9, 3259–3274 (1976).
[CrossRef]

Boggess, T. F.

E. W. Van Stryland, M. 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).

Gibson, A. F.

A. F. Gibson, “Two-photon absorption in indium antimonide and germanium,” J. Phys. C 9, 3259–3274 (1976).
[CrossRef]

Guha, S.

E. W. Van Stryland, M. 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.

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]

Hutchings, D. C.

Nathan, V.

Pigdoen, C. R.

C. R. Pigdoen, “Two-photon absorption in zincblende semiconductors,” Phys. Rev. Lett. 42, 1785–1787 (1979).
[CrossRef]

Said, A. A.

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]

Sheik-Bahae, M.

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]

Smirl, A. L.

E. W. Van Stryland, M. 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).

Soileau, M. J.

E. W. Van Stryland, M. 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).

Van Stryland, E. W.

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, 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, M. 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).

Vanherzeele, M.

E. W. Van Stryland, M. 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).

Wang, J.

Wei, T. H.

Wei, T.-H.

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]

Wherrett, B. S.

B. S. Wherrett, “A comparison of theories of resonant nonlinear refraction in semiconductors,” Proc. R. Soc. London Ser. A 390, 397–409 (1983).
[CrossRef]

Woodall, M. A.

E. W. Van Stryland, M. 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).

Young, J.

IEEE J. Quantum Electron. (1)

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]

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

J. Phys. C (1)

A. F. Gibson, “Two-photon absorption in indium antimonide and germanium,” J. Phys. C 9, 3259–3274 (1976).
[CrossRef]

Opt. Eng. (1)

E. W. Van Stryland, M. 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).

Phys. Rev. Lett. (1)

C. R. Pigdoen, “Two-photon absorption in zincblende semiconductors,” Phys. Rev. Lett. 42, 1785–1787 (1979).
[CrossRef]

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

B. S. Wherrett, “A comparison of theories of resonant nonlinear refraction in semiconductors,” Proc. R. Soc. London Ser. A 390, 397–409 (1983).
[CrossRef]

Other (11)

R. K. Jain and M. B. Klein, “Degenerate four-wave mixing in semiconductors,” Optical Phase Conjugation, R. L. Fisher, ed. (Academic, New York, 1983), pp. 332–345.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992), pp. 159–164.

D. K. Schroder, Semiconductor Material and Device Characterization (Wiley, New York, 1990), pp. 205–206.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge Univ. Press, Cambridge, UK, 1986), pp. 550–560.

Ref. 2, p. 24.

A. A. Borsch, M. Brodlin, and V. Volkov, Refractive Nonlinearity of Wide-Band Semiconductors and Applications (Harwood Academic, Chur, Switzerland, 1990), pp. 7–16.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, and P. F. Liao, “Phase conjugation and high resolution spectroscopy by resonant degenerate four-wave mixing,” Optical Phase Conjugation, R. L. Fisher, ed. (Academic, New York, 1983), pp. 215–264.

P. L. Landsberg, Recombination in Semiconductors (Cambridge Univ. Press, Cambridge, UK, 1990), pp. 315–316.

Ref. 4, pp. 369–401.

M. D. Turner, “Degenerate four-wave mixing of Cr, Tm, Ho:YAG laser output at 2.1 μm in semiconductor compounds,” Ph.D. dissertation (Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1996), pp. 125–126.

S. Adachi, Physical Properties of III–V Semiconductor Compounds (Academic, Boston, Mass., 1992), pp. 178–180.

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Figures (20)

Fig. 1
Fig. 1

Schematic of the experimental system used for the Z-scan measurements. The laser is an acousto-optically Q-switched Cr, Tm, Ho:YAG laser manufactured by Schwartz Electro-Optics. The commercial system was extensively modified to improve its temporal and spectral properties. NLR, nonlinear dispersion.

Fig. 2
Fig. 2

Phase conjugation setup in which the delay leg allows for accurate adjustment of the temporal overlap of the beams involved in the FWM process. The energy in the pump beams was balanced to within a few percent, and the probe beam energy could be adjusted over a wide range. RjP devices, detectors; pol., polarizer.

Fig. 3
Fig. 3

Steady-state solution to the equations governing the excess carrier density as a function of intensity. The inset is a log10 versus log10 plot of the same data.

Fig. 4
Fig. 4

NLA in the AR-coated GaSb substrates. The spot size of the beam incident upon the sample was w=414 µm, and the 1/e2 time of the pulse was 74.7 ns (88.4-ns FWHM).

Fig. 5
Fig. 5

Intensity-dependent absorption coefficient of the uncoated GaInAsSb/n-GaSb. The spot size of the beam incident upon the sample was w=283 µm, and the 1/e2 time of the pulse was 71.1 ns.

Fig. 6
Fig. 6

Three sets of Z-scan data taken at three average input energy levels, 30.7, 54.4, and 74.4 µJ. The solid curves are the results of the time-dependent numerical model coupled with the Huygens–Fresnel propagation equations. The top two data sets are purposely offset along the vertical axis for clarity.

Fig. 7
Fig. 7

Z-scan measurements of AR-coated n-GaSb of 415-µm thickness. Scans represent the ratio of the apertured to the unapertured signal, with average incident energy levels of 17.8 and 30.7 µJ.

Fig. 8
Fig. 8

Normalized ratio of the apertured to the unapertured detector measurements for Ga0.87In0.13As0.11Sb0.89/n-GaSb at three different temperatures.

Fig. 9
Fig. 9

Unapertured signal recorded during the Z-scan measurements at a particular energy level for several different temperatures. The lower-temperature measurements simply reflect the linear absorption and the NLA in the substrate. At the higher temperatures the saturation behavior of the epitaxial layer is readily apparent.

Fig. 10
Fig. 10

|χeff(3)| plotted as a function of the peak on-axis intensity at the focus of the beam, I0, where the observed ΔTpv is ascribed to a single material (the GaSb substrate) of 340-µm thickness. Also shown are results of room-temperature measurements made with the 415-µm-thick substrate sample. The spline fits to the data points serve only as a guide for the eye.

Fig. 11
Fig. 11

Estimated third-order nonlinearity of the epitaxial layer calculated by removal of the contributions to ΔTpv, attributed to the substrate. χeff(3) rises rapidly with temperature as the bandgap energy shifts with respect to the laser photon energy. Also shown is the effective absorption coefficient of the epilayer, which was determined from the transmission measurements.

Fig. 12
Fig. 12

Phase-conjugate reflectivity for n-GaSb, plotted against the peak intensity of the incident pump pulses. The solid curve shows the fit to the room-temperature data with -3.48±0.5×10-7 esu.

Fig. 13
Fig. 13

Temperature-dependence reflectivity in n-GaSb. Temperature dependence of the phase-conjugate reflectivity in n-GaSb at three different average incident peak intensity levels with a fixed value for EPump/EProbe=6.1. All the levels were recorded as the temperature was raised at a constant rate of 10 K/min.

Fig. 14
Fig. 14

Estimates of the achievable phase-conjugate reflectivity as a function of n-GaSb sample length for three peak intensity levels. Note that the sample on hand was 415 µm thick but that the intensities achieved were limited to ∼2.5 MW/cm2.

Fig. 15
Fig. 15

Phase-conjugate reflectivity measured as a continuous function of temperature at several average incident energy levels. With τ=74 ns and ω=1.12 mm, the on-axis peak intensity is I0=1.50 MW/cm2 with EPump=2.75 mJ and I0=0.95 MW/cm2 with EPump=1.73 mJ.

Fig. 16
Fig. 16

Temperature-dependent DFWM reflectivity comparing the performance of the substrate material and the epilayer–substrate sample. Data taken at approximately the same average incident energy levels are compared above. Note the differences in thickness between the samples.

Fig. 17
Fig. 17

Temperature dependence of the estimated χeff(3) of the epitaxial layer and of the substrate as a function of temperature.

Fig. 18
Fig. 18

Comparison of the time-dependent and steady-state solutions at two incident intensity levels (offset from each other for comparison). The peak excess carrier density is 1013/cm3 for the low-intensity pulse and 1017/cm3 for the high-intensity pulse.

Fig. 19
Fig. 19

Transmission of Ga0.87In0.13As0.11Sb0.89 as a function of sample temperature, taken at 30 K increments from 90 to 300 K. The transmission data were compensated for substrate absorption.

Fig. 20
Fig. 20

Bandgap energy and the linear absorption of the Ga0.87In0.13As0.11Sb0.89 epitaxial layer and of the n-type GaSb substrate as a function of temperature.

Tables (3)

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Table 1 Nonlinear Susceptibility Due to Nonequilibrium Free Carriersa

Tables Icon

Table 2 Summary of Experimental Resultsa

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Table 3 Material Properties of GaSb, GaInAsSb, and Gea

Equations (15)

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

Δ=-σsΔN,
σs=4πe2meh*ω2,
I(r,t)=2Eπw22π1τexp(-2r2/w2)exp(-2t2/τ2).
dIdz=-[αI+βI2+ΔN(σp+σn)I].
d(ΔN)dt=βI22ω-r(ΔN)ΔN.
r(ΔN)=BRad(N0+ΔN)+CAug(N0+ΔN)2,
dΔϕdz=-kσsΔN,
ΔTpv=(Δn0)0.406(1-S)1/4kLeff/2,
χ(3)=γn02c12π2(inesu).
η=Ec(0)Ep(0)2=|κ sin ξL|2|ξ cos ξL+α sin ξL|2.
κ*=(3ω/8n0c)χeff(3)Epump2 exp(-αL),
αeff=-ln(Eout/Ein)/L.
dIdz=-[αI+βI2+ΔN(σp+σn)I],
d(ΔN)dt=βI22ω-r(ΔN)ΔN.
r(ΔN)=BRad(N0+ΔN)+CAug(N0+ΔN)2,

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