High photorefractive gain at counterpropagatinggeometry in CdTe:Ge at 1:064 μm and 1:55 μm

Konstantin ShcherbinInstitute of Physics, National Academy of Sciences, Prospekt Nauki 46, 03028 Kiev, Ukraine

(kshcherb@iop.kiev.ua)

Received 9 October 2008; revised 26 November 2008; accepted 5 December 2008;posted 8 December 2008 (Doc. ID 102599); published 8 January 2009

Recording of efficient reflection holograms is achieved in CdTe:Ge at λ ¼ 1:064 μm and λ ¼ 1:55 μm. Thegain factor measured at both wavelengths for counterpropagating two-beam coupling considerably ex-ceeds the absorption constant and transcends all values previously reported for semiconductors with noexternal field. The dependences of the gain factor on intensity and grating spacing are studied. Somecrystal characteristics are estimated in the frame of a single band, one mobile species approximationof space-charge formation. The homogeneity of photorefractive properties in the crystal volume is demon-strated. © 2009 Optical Society of America

OCIS codes: 160.5320, 190.5330, 190.7070.

1. Introduction

Photorefractive semiconductor crystals, such asGaAs, CdTe, and InP, are well suited for telecommu-nication systems because they are sensitive in theinfrared region of the spectrum. An additional signif-icant advantage of these materials is a fast responsewhen compared with photorefractive wide-band-gapcrystals. On the other hand, the smaller electro-opticcoefficients of semiconductors result in a smallerrefractive index modulation and, therefore, in asmaller diffraction efficiency and a two-beam cou-pling gain factor. Furthermore, the latter importantcharacteristics decrease with the wavelength for afixed refractive index change, as the nonlinear phaseshift is inversely proportional to the wavelength. Inother words, the photorefractive response of semicon-ductors in the infrared wavelength range is reducedwhen compared with the response of crystals with si-milar characteristics in the visible region of the spec-trum. This unfavorable feature, along with smallerelectro-optic coefficients, makes any improvementto the response of photorefractive semiconductorsvery important.

The photorefractive response can be improvedwhen the space-charge field is increased by an exter-nal electric field. A dc field [1,2], a high frequency[2,3], or a low-frequency [4] ac field may be used,but these techniques have particular difficulties.The use of a dc field requires the homogeneous illu-mination of the crystal to prevent an undesirable for-mation of the large-scale space-charge distribution ofthe field across the cross section of the crystal withhigh photoconductivity. Quite often, it is almost im-possible to apply a field with high amplitude to semi-conductors with relatively high conductivity of theorder of 10−6–10−9 ðΩ × cmÞ−1. When an ac field isused, the frequency of the field must be much largerthan the reciprocal relaxation time of the crystal,which falls to microsecond range or even less. Appli-cation of a high voltage with such a high frequency isa difficult engineering task. This is why the increaseof the photorefractive response of semiconductorswith no external field remains an important task.

For the diffusion process of recording (when noexternal field is applied to the crystal), the maximumspace-charge field may be reached in the reflectiongeometry [2] when nearly counterpropagating re-cording beams are directed into the sample throughopposite faces. This is possible if the effective trapconcentration is high enough to ensure efficientspace-charge formation at small grating spacing.

0003-6935/09/020371-04$15.00/0© 2009 Optical Society of America

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However, the photorefractive semiconductors oftendo not meet this requirement. In this work it isdemonstrated that doping of CdTe with germaniumallows the effective recording of reflection gratingsat two important wavelengths, λ ¼ 1:064 μm andλ ¼ 1:55 μm. The two-beam coupling gain factor mea-sured at both wavelengths is, to the best of ourknowledge, the largest ever reported for any photo-refractive semiconductor with no electric field andexceeds the values previously reported for CdTe bymore than two times for λ ¼ 1:064 μm [5] and bynearly 1.5 times for λ ¼ 1:55 μm [6].

2. Experimental Setup

Cadmium telluride is the most promising semicon-ductor for photorefractive recording with no electricfield as it exhibits the largest electro-optic coefficientamongst other semiconductors [7]. In this workCdTe:Ge, which is a particularly promising semicon-ductor [8], has been studied. The crystal was grownby a modified Bridgman process at ChernivtsyNational University, Ukraine. The CdTe is deliber-ately germanium-doped to ensure a high effectivetrap concentration: germanium was added in themelt in a concentration of the order of 1019 cm−3.The single-crystal sample is cut along the ½1�10�,½001�, and ½110� crystallographic axis and has dimen-sions 3:8mm× 3:5mm × 6:8mm, respectively. Eachface of the crystal is optically finished. The absorp-tion constant of the sample α ≈ 1:7 cm−1 is measuredat λ ¼ 1:064 μm and α ≈ 0:6 cm−1 at λ ¼ 1:55 μm.The experimental setup is shown schematically in

Fig. 1. Either a YAG: Nd3þ laser operating at 1:06 μmor a laser diode emitting at 1:55 μm, both continuouswave single frequency, serves as a light source. Theoutput laser radiation is divided by a beam splitter(BS) into two beams, I0S0 and I0P0, with intensity ratio

β ≈ 1∶20. The shutter (SH) allows control of the pre-sence of the pump beam. To study gratings recordedwith copropagating beams, both beams are sentto the crystal through the same input face parallelto the ð110Þ crystallographic plane as shown inFig. 1(a). The plane of incidence corresponds to theð1�10Þ plane. For recording of reflection gratings,two nearly counterpropagating beams, I0S0 and I0P0,are sent to the sample through opposite faces paral-lel to the ð001Þ plane [see Fig. 1(b)]. In such a man-ner, the grating vector K is always kept parallel tothe ½001� direction. The polarization of the light isperpendicular to the plane of incidence, i.e., it is par-allel to the ½1�10� direction. The effective electro-opticcoefficient is equal to the handbook electro-optic coef-ficient r41 in this case for two-beam coupling in codir-ectional as well as in counterdirectional geometry.

The unexpanded beams of half-width Gaussianintensity distribution w ≈ 2:4mm are used in theexperiment. To ensure grating recording with betterhomogeneity of intensity, the diaphragm D with dia-meter d ¼ 1:4mm is placed in the path of a signalbeam in front of the crystal at a distance of 4 cm.In this way the grating recording by beams at thetop of the Gaussian distribution is achieved. Theuse of a wider pump beam as compared to the signalalso ensures the complete overlap of the beams atcopropagating geometry when beams intersect inthe crystal at a relatively large angle.

3. Experiment and Discussion

The two-beam coupling gain factor Γ ¼ ð1=lÞlnðIS=IS0Þ is measured in the experiment, where ISand IS0 is the intensity of the transmitted signalbeam in the presence of a pump beam and with ablocked pump, respectively, and l is the interactionlength. First, the dependence of the gain factor onincident light intensity was measured at both wave-lengths for counterdirectional two-beam coupling.The results are presented in Fig. 2. The gain factorincreases as intensity increases and nearly reaches asaturated value at intensity I ¼ 1500mW=cm2 forλ ¼ 1:064 μm and I ¼ 500mW=cm2 for λ ¼ 1:55 μm.The direction of energy transfer is unchanged at bothwavelengths, which indicates that the main chargecarriers are the same. They are the holes, accordingto the charge transport model for CdTe:Ge [9,10].When the crystal is rotated by 180° in such a waythat the ½001� axis reverses direction, the directionof energy transfer is inverted, i.e., the weak signalbeam is attenuated and the negative gain factor ismeasured. The modulus of the gain is the same foramplification and attenuation geometry with thesame experimental conditions. This indicates thephotorefractive recording with no contribution froman absorption grating.

For a simple one-band, one-level model of thephotorefractive effect, the intensity dependence ofthe gain factor is given as [11]

Fig. 1. Experimental setup for (a) copropagating and (b) counter-propagating two-beam coupling.

372 APPLIED OPTICS / Vol. 48, No. 2 / 10 January 2009

Γ ¼ Γ0

1þ σD=ðκIÞ; ð1Þ

where Γ0 is the saturated value of the gain factor, σDis the dark conductivity, and κ is the specific photo-conductivity. The solid curves in Fig. 2 represent thebest fit to the experimental data by Eq. (1) with Γ0 ¼2:8 cm−1 and σD=κ ¼ 66mW=cm2 for λ ¼ 1:064 μmand Γ0 ¼ 1:28 cm−1 and σD=κ ¼ 17:8mW=cm2 forλ ¼ 1:55 μm. It could be expected that the ratioσD=κ is larger for the longer wavelength as photocon-ductivity typically decreases with wavelength. Thelarger ratio σD=κ at λ ¼ 1:064 μm observed in theexperiment can be explained by electron-hole compe-tition when secondary charge carriers are photoex-cited and partially compensate the primary gratingrecorded by the main charge carriers. Secondarycharge carriers are photoexcited more effectively atλ ¼ 1:064 μm. Hence the larger intensity is necessaryto reach saturation of the gain factor on intensity. Inspite of the fact that electron-hole competition is in-herent to CdTe:Ge and several species are involvedin space-charge formation [9,10], the dependence(1) describes well the experimental data. The estima-tions made for the ratio σD=κ should be consideredas an “effective” ratio of the dark conductivity andspecific conductivity made in the frame of a single

charge carrier model for the crystal with bipolarconductivity.

To determine the grating spacing dependence ofthe gain factor, the intensity dependences of the gainfactor were measured in copropagating geometry fordifferent crossing angle between recording beams.The gain factor for intensity saturation conditionswas evaluated from these dependences. The gratingspacing dependences of the gain factor for intensitysaturation conditions are presented in Fig. 3 for λ ¼1:064 μm and λ ¼ 1:55 μm.

According to the theory [2], the gain factor de-creases at large grating spacing as

Γ ¼ 4π2n3reff ξkBTλe

ΛΛ2 þ ℓ2S

; ð2Þ

where Λ is the grating spacing, reff is the effectiveelectro-optic coefficient (reff ¼ r41 in the presenttwo-beam coupling geometry), kB is the Boltzmannconstant, T is the absolute temperature, n is therefractive index, e is the electron charge, ξ is the elec-tron-hole competition factor taking into account apossible compensation of the main grating by theminority carriers, and the Debye screening lengthℓS is given by ℓ2S ¼ ð4π2εε0kBTÞ=ðe2Neff Þ, where εis the dielectric constant of the material, ε0 is the

Fig. 2. Intensity dependences of the gain factor measured forcounterpropagating geometry at (a) λ ¼ 1:064 μm and (b) λ ¼1:55 μm; circles—experimental data, solid lines—best fit by Eq. (1).

Fig. 3. Grating spacing dependences of the gain factor measuredat (a) λ ¼ 1:064 μm and (b) λ ¼ 1:55 μm; circles—experimentaldata, solid lines—best fit by Eq. (2).

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electric permittivity of free space, and Neff is theeffective trap density.The solid lines in Fig. 3 represent the best fit to the

experimental data by Eq. (2) with ℓS ¼ 0:15 μm(Neff ≈ 2:4 × 1016) and ξ ¼ 0:66 for λ ¼ 1:064 μmand with ℓS ¼ 0:22 μm (Neff ≈ 1:1 × 1016) and ξ ¼0:7 for λ ¼ 1:55 μm. The electro-optic coefficientr41 ¼ 6:1pm=V [7] and the refractive indexes n ¼2:82 at λ ¼ 1:064 μm and n ¼ 2:74 at λ ¼ 1:55 μm [12]were used to get fitting parameters. As for intensitydependences of the gain factor, the estimatedcharacteristics should be considered as “effective”characteristics because several defect and impuritycenters and both types of charge carriers are involvedin space-charge redistribution in differently dopedCdTe [9,10,13]. At the same time, the simplestapproximation of charge transport considering onetype of carrier and one photorefractive center quali-tatively perfectly explains the experimental results.Cadmium telluride usually exhibits nonuniformity

of photorefractive properties in the crystalvolume, which introduces significant limitationsfor practical applications. To determine the distribu-tion of photorefractive properties in the studied sam-ple, the crystal was mounted on a translation stageallowing translational displacement along the z axisparallel to the ½110� crystallographic direction [seeFig. 1(b)]. The gain factor as a function of displace-ment measured at λ ¼ 1:064 μm for the counterpro-pagating geometry is shown in Fig. 4. The gainfactor remains nearly the same within experimentalerror. The experimental data demonstrate the homo-geneity of the excellent photorefractive properties inthe volume of studied CdTe:Ge crystal.

4. Conclusion

In conclusion, it has been demonstrated that dopingof cadmium telluride with germanium may ensure ahigh effective trap concentration sufficient for the re-cording of efficient reflection holograms. To the best

of our knowledge, the gain factor reached for counter-propagated two-beam coupling exceeds previouslyreported results by more than two times for1:064 μm recording and nearly 1.5 times for1:55 μm recording. The gain factor at both wave-lengths considerably transcends the absorptionconstant: Γ ≈ 2:8 cm−1 and α ≈ 1:7 cm−1 at 1:064 μm;Γ ≈ 1:3 cm−1 and α ≈ 0:6 cm−1 at 1:55 μm. The unifor-mity of the photorefractive properties in the crystalvolume is demonstrated experimentally. The crystalswith such characteristics are perfect candidates forapplications such as laser ultrasonics receivers, laserintracavity filters, and others.

TheCdTe:Ge crystalwas supplied byZ. I. Zakharukand I. M. Rarenko. The author is grateful toS. Bozhko and K. Eveson for technical assistance.

References1. J. P. Huignard and A. Marrakchi, “Coherent signal beam am-

plification in two-wave mixing experiments with photorefrac-tive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).

2. M.P.Petrov,S. I.Stepanov,andA.V.Khomenko,PhotorefractiveCrystals in Coherent Optical Systems (Springer-Verlag, 1991).

3. S. I. Stepanov and M. P. Petrov, “Efficient unstationary holo-graphic recording inphotorefractive crystalsunderan externalalternating electric field,” Opt. Commun. 53, 292–295 (1985).

4. A. V. Khomenko, A. López Navarro, M. García-Zárate, andK. Shcherbin, “Optically stimulated electron-hole resonancein photorefractive CdTe with a low frequency ac field,”J. Opt. Soc. Am. B 24, 2172–2176 (2007).

5. K. Shcherbin, A. Shumeljuk, S. Odoulov, P. Fochuk, andG. Brost, “Relaxation of photorefractive gratings in cadmiumtelluride crystals,” Proc. SPIE 2795, 236–243 (1996).

6. A. Godard, G. Pauliat, G. Roosen, and É. Ducloux, “Relaxationof the single-mode emission conditions in extended-cavitysemiconductor lasers with a self-organizing photorefractivefilter,” Appl. Opt. 43, 3543–3547 (2004).

7. K. Tada and M. Aoki, “Linear electro-optic properties of ZnTeat 10.6 microns,” Jpn. J. Appl. Phys. 10, 998–1001 (1971).

8. K. Shcherbin, “Recent progress in semiconductor photorefrac-tive crystals,” in Photorefractive Materials and Their Applica-tions II, P. Günter and J.-P. Huignard, eds. (Springer, 2007),pp. 391–418.

9. B. Briat, K. Shcherbin, B. Farid, and F. Ramaz, “Optical andmagnetooptical study of photorefractive germanium-dopedcadmium telluride,” Opt. Commun. 156, 337–340 (1998).

10. B. Briat, F. Ramaz, B. Farid, K. Shcherbin, and H. J. vonBardeleben, “Spectroscopic characterization of photorefrac-tive CdTe:Ge,” J. Cryst. Growth 197, 724–728 (1999).

11. N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, andV. L. Vinetskii, “Holographic storage in electro-optic crystals.II. Beam coupling—light amplification,” Ferroelectrics 22,961–964 (1979).

12. D. T. F. Marple, “Refractive indexes of ZnSe, ZnTe, and CdTe,”J. Appl. Phys. 35, 539–542 (1964).

13. L. A. de Montmorillon, Ph. Delaye, G. Roosen, H. Bou Rjeily,F. Ramaz, B. Briat, J. G. Gies, J. P. Zielinger, M. Tapiero,H. J. von Bardeleben, T. Arnoux, and J. C. Launay, “Correla-tion between microscopic properties and the photorefractiveresponse for vanadium-doped CdTe,” J. Opt. Soc. Am. B 13,2341–2351 (1996).

Fig. 4. Scan of the gain factor along z axis parallel to ½110� direc-tion measured at λ ¼ 1:064 μm for counterpropagating geometry.

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