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DIRECT MEASUREMENT OF THE NONLINEAR REFRACTIVE INDEX CROSS-SECTION FOR InSb
AT 10.6 µm WAVELENGTH
P. Chua, W. Ji, A. Kar, A. Walker
To cite this version:
P. Chua, W. Ji, A. Kar, A. Walker. DIRECT MEASUREMENT OF THE NONLINEAR REFRAC-
TIVE INDEX CROSS-SECTION FOR InSb AT 10.6 µm WAVELENGTH. Journal de Physique Col-
loques, 1988, 49 (C2), pp.C2-189-C2-192. �10.1051/jphyscol:1988244�. �jpa-00227661�
JOURNAL DE PHYSIQUE
Colloque C 2 , Suppl6ment a u n06, Tome 49, juin 1988
DIRECT MEASUREMENT OF THE NONLINEAR REFRACTIVE INDEX CROSS-SECTION FOR InSb AT 10.6 pm WAVELENGTH
P.L. CHUA, W. JI, A.K. KAR and A.C. WALKER
Department of Physics, Heriot-Watt University, Riccarton, GB- dinb burgh EH14 4AS. Scotland, Great-Britain
Abstract
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A photo-Hall technique has been used to make a direct measurement of the nonlinear refractive index cross-section in room-temperature InSb at 10.6 pmwavelength. The value deduced is a = - (2.3 f 1) x 10-18 cm3.
Optoelectronic optical nonlinearities have been exploited to demonstrate a range of 111-V semiconductor optically bistable devices, e.g. /1-3/. In general, this class of
nonlinearity can be characterised as a dominantly refractive phenomenon arising from modifications to the band-edge spectrum, induced by a photo-excited excess carrier
density, and the consequent change in the dispersion properties of the semiconductor. The absorption changes can be associated with band-filling (the dynamic Moss-Burstein effect) or saturation of exciton features. The change in refractive index, An, for small changes in carrier density, has a linear dependence on the photo-excited population:
where AN is the excess density of electron-hole pairs. Thus, the critical parameter, characterising the magnitude of the nonlinearity, is the nonlinear refractive
cross-section: a. In previous measurements a has been determined indirectly by probing a nonlinear Fabry-Perot cavity, e.g. /1-4/, or by studying other macroscopic nonlinear effects, e.g. /5,6/. In all these cases it was the dependence of refractive index on irradiance (I) that was initially measured, given by
where n, is the nonlinear refractive index. This could then be related to a using the excess carrier density rate equation, as determined by the balance between excitation and recombination processes:
where a is the absorption coefficient, 5 w the photon energy and r the relevant carrier lifetime. Assuming equilibrium conditions, equations (11, (2) and ( 3 ) give:
The accuracy of a, determined in this way, depends on the value for a, at the band-tail wavelength being used, and the carrier lifetime, r. Both these parameters can vary considerably from sample to sample
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depending on crystal defect levels, impurities/doping and temperature. In addition, to deduce a,, an absolute measurement of irradiance is also needed.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988244
C2-190 JOURNAL DE PHYSIQUE
If, instead, the excess carrier density is measured directly while also monitoring An, e.g. by observing changes in transmission through a nonlinear Fabry-Perot cavity, then o can be deduced directly using equation (1).
We have been using a photo-Hall measurement technique to monitor the carrier dynamics in nonlinear InSb etalons. MacKenzie et a1 have exploited this method to make near-band-edge measurements (77 K) at wavelengths around 5.5 p /7/. This paper reports the (room temperature) measurement of o at 10.6 p, at which wavelength carrier excitation in InSb is the result of a two-photon process. Due to the domination of density-dependent Auger recombination processes in room-termpeature InSb and uncertainties regarding
two-photon-ab:;orption coefficients /8,9/, this photo-Hall technique is particularly useful in the way it is independent of both generation and recombination rates.
1
- TO SCOPE TO SCOPE
HALL VOLTAGE
BEAMSPLITTER 2
-
CURRENT SUPPLYFig. 1
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Experimental arrangement: (1) focussing lens, (2) magnetic coil with pole, ( 3 ) sample box, (4) imaging lens.Fig. 2 - Samp1.e configuration with external compensation circuit to eliminate misalignment potential (shaded area reveals exposed region).
Figure 1 shows the experimental layout whereby the nonlinear transmission of an intrinsic InSb etalon was probed by 2 ps (FWHM) GO, laser pulses while a simultaneous measurement was made of the Hall voltage. Figure 2 shows the sample configuration with an external compensation circuit to offset any standing voltage when the magnetic field was off, and hence prevent the appearance of any spurious photoconductive signals. The sample was polished plane/parallel to form a Fabry-Perot etalon 262 p thick and it was illuminated over the central 1.5 nun diameter area by the uniform central region of the weakly focussed
GO, laser beam. The contacts were masked to prevent the edges of the beam inducing photo-voltaic signals. Typically currents of % 10 mA with % 0.3 tesla magnetic fields were used, giving photo-Hall signals of up to 2. 1 mV.
Figure 3 shows a sample set of results. Incident and transmitted pulses were recorded in synchronism with the time dependence of the photo-Hall voltage. From the optical
measurements the variation in transmission was obtained. The changes in refractive index were then dediced by observing the maxima and minima corresponding to the Fabry-Perst
fringes and also from a knowledge of the initial detuning from resonance, previously
Fig. 3
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Time-synchronised results: (a) input pulse (b) output pulse(C) output pulse/input pulse (transmittance) (d) Hall signal.
measured at low powers. The photo-Hall signal AVH is dominated by the contribution of excited electrons, due to the much greater electron mobility compared with hole mobility.
When the excess density is small compared to the equilibrium carrier density, N o , it is given by:
VH is the dark Hall-voltage, related to N o (the intrinsic density in this case) by:
where I is the current through the sample, B the applied magentic field, Q the thickness of the sample and e the magnitude of the electron charge. The parameter f is a correction factor that takes into account sample and illumination geometry (in this case 2.2). The linearity of the dark Hall-voltage, VH, with applied magnetic field and current was confirmed and its magnitude was shown to closely correspond to that expected for intrinsic InSb: N o = 1.7 X 1016 cm-'. Thus equation ( 5 ) could be used to deduce the time variation of AN from the observed photo-Hall signal.
Figure 4 shows a compilation of results obtained from different pulse records. The dependence of An upon AN over this region can be seen to be linear, as expected, and the nonlinear refractive cross-section, given by the slope of this plot, is determined to be o = - (2.3
+
1) X 10-l8 cm3.Theoretical calculations of the expected magnitude of a agree well with -this value. Two distinct contributions can be identified: the free carrier (plasma)
JOURNAL DE PHYSIQUE
PHOTO-GENERATED DENSITY (xE14 cm-3)
Fig. 4
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Compiled result showing linear relationship between photogenerated density AN and refractive index change An.term and the band-filling term [lo]. The former is readily calculated as
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0.9~10-" cm3 at the wavelength 10.6 pm. The latter can be calculated on the basis of Boltzmann statistics, allowing for blocking of electronic transitions from both light- andheavy-hole valence bands, to be
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0 . 4 ~ 1 0 - ~ ~ cm3. More complete calculations using Fermi- Dirac statist:ics and including non-parbolicity of the bands give a somewhat larger contribution, suggesting a total theoretical value a =-
2x10-18 cm3.We acknowledge the excellent preparation of the sample by Mr. N. Ross.
REFERENCES
/1/ Miller, D.A.B., Smith, S.D. and Johnston, A.M., Appl. Phys. Lett.
35
(1979) 658./2/ Gibbs, H.M., McCall, S.L., Venkatesan, T.N.C., Gossard, A.C., Passner, A. and Wiegmann, W., Appl. Phys. Lett.
35
(1979) 451./3/ Kar, A.K., Mathew, J.G.H., Smith, S.D., Davis, B. and Prettl, W., Appl. Phys. Lett.
42 (1983) 334.
/4/ Eole, C.D. and Garmire, E., Opt. Lett. 9 (1984) 356.
/5/ Miller, D.A.B., Seaton, C.T., Prise, M.E, and Smith, S.D., Phys. Rev. Lett.
47
(1981) 197./6/ Mackenzie, H.A., Hagan, D.J. and Al-Attar, H.A., Opt. Corn.
3
(1984) 352./7/ Mackenzie, H.A., Allan, G.R., Hunter, J.J., and Whet-rett, B.S., "XIV International Quantum Electronics Conference (IQEC '86) Technical Digest" (1986) 174.
/8/ Gibson, A.F., Hatch, C.B., Maggs, P.N.D., Tilley, D.R. and Walker A.C., J. Phys. C:
Solid state Phys. 9 (1976) 3259.
/9/ Johnston, A.M., piZgeon, C.R. and Dempsey, J., Phys. rev. B,
22
(1980) 825./lo/ Walker, A.C. and Tooley, F.A.P., "From Optical Bistability Towards Optical Computing"
Ed. Mandel, P., Smith, S.D and Wherrett, B.S., Elsevier, Amersterdam (1987) 49.
