Beam coupling in undoped GaAs at 1.06 Azm using thephotorefractive effect
M. B. Klein
Hughes Research Laboratories, 3011 Malibu Canyon Road, Malibu, California 90265
Received March 19, 1984; accepted May 21, 1984
We have observed beam coupling and degenerate four-wave mixing in high-resistivity, undoped GaAs at 1.06 'mthat is due to the photorefractive effect. The photorefractive species is thought to be the deep donor EL2. Themeasured values of two-wave gain are comparable with those measured in Bi12SiO2 0. The response time is mea-sured to be 20 gsec at an intensity of 4 W/cm2. This exceptionally fast photorefractive response time (comparedwith that of oxide electro-optic materials) is due primarily to the large mobility of GaAs.
There is an ongoing need for efficient nonlinear mate-rials at wavelengths in the near infrared for a variety ofapplications. Whereas typical photorefractive mate-rials [such as BaTiO 3 , Bi12SiO2 0 (BSO), KNbO 3 , andLiNbO3] have proven to be useful in the visible, theirspectral response typically cuts off at 600-700 nm. Inthis Letter initial results are presented of experimentson the photorefractive effect in undoped, semi-insu-lating GaAs, with a spectral response peaked near 1.06Aim. Our experiments represent the first reported ob-servation of the photorefractive effect in undoped GaAsand thus open up the potential use of the III-V semi-conductors as fast, sensitive photorefractive materials 1
for operation at wavelengths throughout the near in-frared. GaAs, in particular, appears to have promisefor optical data processing (ODP) and phase conjuga-tion at diode- and Nd:YAG-laser wavelengths. Byexploiting the photorefractive effect, we have observeddegenerate two-wave mixing (beam coupling) and de-generate four-wave mixing (DFWM) at 1.06 gim in un-doped semi-insulating GaAs grown at Hughes ResearchLaboratories. Similar results in Cr-doped GaAs andFe-doped InP have been obtained by Glass et al. 2
GaAs has several important characteristics that leadto favorable photorefractive properties, especially forODP applications using DFWM. First, it is availablein semi-insulating form, so the dark carrier concentra-tion does not mask the effect of the photoinduced car-riers. Second, it is noncentrosymmetric, with a singlenonvanishing electro-optic tensor component r4l = 1.43pm/V at 1.15 um.3 Third, it has significant extrinsicabsorption between 0.95 and 1.35 gim because of tran-sitions from deep donors to the conduction band. Thefourth favorable characteristic of GaAs is its large valueof mobility. Room-temperature values are typically5000-8000 cm2/V sec, compared with values of 0.1-1.0cm2/V see in oxide photorefractive materials, such asLiNbO3 , BaTiO3 , and BSO. The large value of mobilityin GaAs leads to an enhancement in photoconductivity,and thus in sensitivity and speed, as described below.
Deep levels in GaAs can result from the presence ofintentional dopants (such as Cr) or from defects in un-
doped samples. In both cases, the deep levels play animportant role in providing charge compensation,leading to semi-insulating samples. It is reasonable toassume that these deep levels could contribute to pho-torefractive behavior, as they are present in an ad-mixture of neutral and ionized (filled and unfilled)forms in typical samples. In undoped GaAs the dom-inant deep level is a donor state designated as EL2,which lies 0.82 eV below the conduction band (i.e., nearthe middle of the band gap). This state is thought tobe due to an antisite defect4 and is typically present inconcentrations of the order of 10' 6/cc. The absorptionspectrum of the undoped GaAs sample used in our ex-periments is shown in Fig. 1. Note the broad extrinsicfeature centered near 1.06 gm, which is characteristicof EL2.
There are several figures of merit that can be used tocharacterize the performance of a photorefractive ma-terial.5' 6 For operation in the steady state, the impor-tant parameter is the refractive-index change, givenby
An = 1 /2 n3reffEsv, (1)
where n is the background refractive index, reff is theeffective electro-optic coefficient, and Esc is the inter-nally generated space-charge electric field. thesteady-state refractive-index change (and thus thegrating diffraction efficiency) is an important perfor-mance parameter in phase-conjugate-resonator ex-
6 I I .I
5 GaAs M043T
4 06 pm
o - ; U
6000 7000 8000 9000 10000
PHOTON ENE RGY, - I'
1100D
Fig. 1. Absorption spectrum of undoped semi-insulatingGaAs sample used for beam-coupling experiments.
periments, in which large values of four-wave mixingreflectivity are required. The most favorable materialsfor this application are BaTiO3 (Ref. 7) andSri-,BaNb 2O6 (SBN),8 which have exceptionally largevalues of n3reff. The value of n3reff for GaAs is -200times smaller than those for BaTiO3 and SBN but iscomparable in magnitude with that for BSO. In BSOthe use of an applied electric field9 and moving gratingtechniques 1 0 has to a considerable degree overcome thesmall value of n3reff; we expect that these techniqueswill also be applicable to GaAs.
The sensitivity for ODP operations is dependentmore on response time than on the steady-state indexchange. The response time of an elemental grating (foreither writing or erasure) is given by6' 11
T = Tdif (Ag, Eo), (2)
where Tdi is the dielectric relaxation time, Ag is thegrating period, and E0 is the applied electric field. Thefunction f (Ag, Eo) accounts for the fact that the spacecharge is spatially modulated; its importance as a cor-rection to Tdi depends on the material chosen and theparameters of the particular experiment.6 The di-electric relaxation time may be written as Tdi = E/470-,where E is the relative dielectric constant and a is theconductivity. When photoconductivity dominates, itcan be shown 6 that
T di = E/47recaxTRIO, (3)
where a is the absorption coefficient, TR is the recoin-bination time into empty traps, and Io is the averageirradiance.
The well-known variation of rdi with (MTR)-1 is fre-
quently used to support the selection of materials withlarge values of M-TR. However, in materials such as BSO(large -R) and especially GaAs (very large ,), the cor-rection factor in Eq. (2) must be taken into account. Inthe absence of an applied field and for grating periodslarge compared with the Debye screening length,12 thisfactor can be approximated as
4Ir 2MTrRkBTf(Ag, °) 1+ I eA 2 (4)
where kB is Boltzmann's constant. For values of gTR
> eAg2/47 2kBT, expressions (2)-(4) can be combinedto yield
- 7rskBT/e 2 acIoAg2 . (5)
In this limit, the response time becomes independentof 1-rR and strongly dependent on Ag. Using expres-sion (5) with Ag = 1 ,um, e = 12.9, a = 1.2 cm-', and Io= 4 W/cm 2 , we calculate r = 28 ,usec. This responsetime is much larger than the dielectric relaxation time(di = 1.9 nsec), thus illustrating the importance of thecorrection factor f(Ag, 0). Note, however, that shorterresponse times are predicted for larger values of irra-diance or grating period.
The technique that we have used to study the pho-torefractive effect in GaAs is two-wave mixing, or beamcoupling.'2 In this technique, two beams are incidentupon a sample, thereby producing a spatially periodicirradiance pattern. If the resultant refractive-index
05oM | 1 IRIL)
I0WO) R~ ~ IS IM(00?1
(I0) (t110)
Fig. 2. Beam notation and crystal orientation for beam-coupling experiments in undoped GaAs.
pattern (or grating) is not in phase with the irradiancepattern, then energy is transferred from one beam to theother, in a direction determined by the crystal orien-tation and the sign of the charge carriers but not by therelative power in the beams. The theory for two-wavemixing has been developed by Kukhtarev et al. 12 Forthe beam notation shown in Fig. 2 and the crystal or-ientation that provides gain for the weak beam, thetransmission of the signal beam is given by
IS (L) = IR (0)exp(L) , 7Is(O) IR(O) + Is(O)exp(TL) (7)
where r is the gain coefficient and L is the interactionlength. For negligible depletion of the signal wave[Is (O)exp(rL) << IR(O)], Eq. (7) reduces to
(8)
When absorption is significant, Eq. (8) is modified toread
Is(L) = Is(O)exp[(r- a)L]. (9)
In our experiment, we measure the effective gain9 yo,defined as
(10)- Is (L) with reference waveIs (L) without reference wave
When depletion of the reference wave can be neglected,-yo = exp(FL). In the absence of an applied electricfield, the phase of the periodic space-charge electric fieldis shifted from that of the irradiance by 7r/2. For thiscase, the gain r is given by
r = 27rn 3r 4lE,,/X cos 0, (11)
where 0 is the Bragg angle inside the crystal. Thus,from a measurement of r, we can directly determine thespace-charge electric field. In the case of GaAs, ourknowledge of all required material parameters (deter-mined by independent measurement) is completeenough for us to compare calculated values of r (as afunction of grating period) with those determined bydirect measurement.
In our two-wave mixing experiments, we used asample of undoped GaAs (grown by the liquid-encap-sulated Gochralski technique) with a dark resistivity p= 6.3 X 107 Q cm and an electron Hall mobilityu = 5800cm2/V sec. The concentration of ionized EL2 donorswas obtained from measurements of conductivity as afunction of temperature; we find that NEL2 = 1.4 X1015/cc at room temperature.' 4 The concentration ofneutral (filled) EL2, as determined from the measured
Is (L) = Is (0) exp (n).
352 OPTICS LETTERS / Vol. 9, No. 8 / August 1984
0.4
0.3
0.2
0.1
0 0.5 1.0 1.5 2.0 2.5
GRATING PERIOD A,. pm
3.0
Fig. 3. Two-wave gain coefficient versus grating spacing inundoped GaAs.
absorption coefficient and the photoionization crosssection,13 was found to be NEL2 = 1.0 X 10' 6/cc. Thecrystal was oriented as shown in Fig. 2. The cross sec-tion of the crystal was 6 mm X 5 mm, and the thicknessL was 4 mm.
The laser source for our experiments was a cw Nd:YAG laser operating in the fundamental transversemode and having a coherence length of -1 cm. Theoutput beam from the laser was divided at a beamsplitter, and the two resulting beams were recombinedat the sample in such a way that the input angle couldbe varied while the path lengths of the two beams werekept equal. Both input beams were s polarized [i.e.,along (110)] to exploit the refractive-index change in-duced through the electro-optic tensor component r41.9The signal beam had an intensity of 10 mW and a di-ameter of -2 mm. The reference beam was expandedwith a telescope to a diameter of -5 mm in order tomaintain a uniform interaction region over the lengthof the crystal as the angle of incidence is varied. Theintensity of this beam was made sufficiently large [IR (0)A 10IO (0)] to ensure that it would remain undepleted inour experiments. A typical plot of signal-beam gainversus grating period is shown in Fig. 3. The curvepeaks at a value of Ag equal to the Debye screeninglength LT = rEkBT/e 2NEL2.12 Thus, from the mea-sured value of LT, we can determine the value of NEL2-We find that NEL2 = 1.3 X 1015, in good agreement withthe value determined from conductivity measurements.The measured values of gain are close to those measuredat 5145 nm in BSO (Ref. 9) (with no applied field).When we account for the difference in the measurementwavelength, we find that the figure of merit n3 r41 forGaAs is a factor of 2 larger than the effective value forBSO.
We have also made a direct measurement of gratingefficiency using DFWM. A third input beam wasgenerated with a beam splitter and was incident uponthe crystal in a direction counterpropagating the strongforward wave. The intensity of this backward beamwas reduced to avoid depletion of either forward wave.In this situation, the ratio of diffracted to undiffractedbackward wave is a direct measure of the grating dif-fraction efficiency. Our measured values of diffraction
efficiency were of the order of 0.1% and were consistentwith our measured values of signal-beam gain.
Finally, we have studied the transient response of thesignal-beam gain by chopping the reference beam withan electro-optic switch and monitoring the time re-sponse of the transmitted signal beam by using a fastphotodiode. When the switch is opened, the signal-beam intensity increases to a new steady state with aresponse time (for small values of rL) that is compa-rable in magnitude with the grating response time givenin Eq. (2). When the switch is closed, the signal decaysto its original level with a response time limited only bythe detection circuitry. In our experiment (Io = 4W/cm 2 , Ag = 1 gim), we measure a rise time of 20 gisec,in reasonable agreement with the value (28 gsec) cal-culated earlier by using Eq. (5).
In summary, GaAs (and other III-V materials) showsgreat promise for a number of DFWM applications atwavelengths in the near infrared, especially those re-quiring high speed or sensitivity. Large steady-statevalues of weak-beam gain and DFWM reflectivityshould also be obtainable by using an applied electricfield and techniques to induce a spatial phase shift inthe space-charge field pattern.
I would like to acknowledge helpful discussions withG. C. Valley, A. T. Hunter, A. M. Glass, and R. A. Mul-len and technical assistance by R. H. Sipman. TheGaAs samples were provided by H. Kimura, C. Afable,and H. M. Olsen. J. P. Baukus provided the EL2 ab-sorption curve. I am grateful to G. C. Valley for hiscritical reading of this manuscript.
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