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276 J. Opt. Soc. Am. B/Vol. 23, No. 2 /February 2006 Juvalta et al.

Electro-optical properties of near-stoichiometricand congruent lithium tantalate

at ultraviolet wavelengths

Flurin Juvalta, Mojca Jazbinšek, and Peter Günter

Nonlinear Optics Laboratory, ETH Zurich, CH-8093 Zurich, Switzerland

Kenji Kitamura

Advanced Materials Laboratory, National Institute for Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan

Received June 15, 2005; accepted September 10, 2005

We measured the unclamped electro-optic coefficients r13 and r33 of near-stoichiometric and congruent lithiumtantalate �LiTaO3� from �=633 nm down to the absorption edge at �275 nm. Electro-optical coefficients up tor33=52±1 pm/V have been determined at �=275 nm. The reduced half-wave voltage at 275 nm isv�=300±10 V for r33 and v�=560±20 V for the configuration employing rc=r33− �no /ne�3r13. We propose a two-oscillator polarization potential model that well describes our data in the UV. In the investigated wavelengthrange the values for stoichiometric and congruent LiTaO3 differ by less than 3%, which is below the accuracyof our measurements. In addition, the refractive indices in the UV were measured, and more precise Sellmeierparameters for the UV and visible were determined based on the previous and new refractive-index data.© 2006 Optical Society of America

OCIS codes: 120.4530, 160.2260, 160.2100, 260.7190.

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. INTRODUCTIONhe electro-optic effect is widely used in scientific andechnical applications for modulation, deflection, or pro-essing of optical signals. There are many electro-opticalaterials that are used at visible or infrared wave-

engths, but only a few of them are suitable for applica-ions in the UV. Since laser sources in the UV are becom-ng available, there is an increasing interest in such low-avelength applications. Using UV light, a resolutionroportional to � can be achieved in applications such asolographic interferometry or lithography. For volume ho-

ographic data storage, the storage density increases pro-ortional to �−3 when going to smaller wavelengths. An-ther important advantage of using lower wavelengths ishe smaller divergence of such light beams.

A promising material for applications at UV wave-engths is stoichiometric lithium tantalate �LiTaO3�. It isransparent down to 260 nm where most of the standardlectro-optical materials, e.g., LiNbO3 or KNbO3, showarge light absorption. At 320 nm, congruent LiTaO3 ex-ibits an absorption constant of �20 cm−1 while in con-ruent LiTaO3 this value is reached at 275 nm.1 We haveemonstrated earlier that in stoichiometric materialsany physical properties are substantially different from

onventionally used congruent materials.1–3 For example,he absorption edge is shifted deeper into the UV down to00 nm for stoichiometric LiNbO3 and down to 260 nm fortoichiometric LiTaO3.1 Therefore the refractive indicesnd electro-optic coefficients are also excepted to be differ-nt.

There is an increasing interest in use of LiTaO3 forhotorefractive and other applications at UV wave-

0740-3224/06/020276-6/$15.00 © 2

engths. In addition to a lower absorption edge, stoichio-etric LiTaO3 as compared with LiNbO3 shows higherurie temperature, higher dark resistivity,1 smaller opti-al damage in the visible,1,4,5 smaller coercive fields,6 1 or-er of magnitude longer dark storage time of holograms,7

nd smaller birefringence, which can even be adjusted toero by controlling the stoichiometry and/or theemperature.8

Recent investigations such as dynamic holography athe deep-UV wavelength of 257 nm (Refs. 3 and 9) andwo-beam coupling at 364 nm (Ref. 1) or two-color holo-raphic recording with gating light at 350 nm (Ref. 7)howed the potential of near-stoichiometric LiTaO3 foreveral applications in the UV, such as tunable opticallters,9 nonvolatile holographical data storage,10 high-peed optical processing with high resolution,11 light-nduced waveguides,12 or frequency doubling into the UVsing periodically poled crystals.13 For all these applica-ions, the material properties such as refractive indicesnd electro-optic coefficients are required.Up to now, there exist no data on these coefficients at

V wavelengths in LiTaO3. For congruent LiTaO3, thelectro-optical coefficients have been known at 633 nmRef. 14) and have recently been measured at near-nfrared wavelengths up to 1558 nm.15 Also, refractive in-ices were known only down to 400 nm (Refs. 16 and 17)nd not in the UV wavelength range.In this paper we determine the optical properties of

ongruent and near-stoichiometric LiTaO3, namely, thelectro-optic coefficients and the refractive indices par-icularly in the UV. We describe the dispersion of thelectro-optic coefficients with a polarization potential

006 Optical Society of America

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Juvalta et al. Vol. 23, No. 2 /February 2006 /J. Opt. Soc. Am. B 277

odel. This model was developed by Wemple and DiDo-enico in the long-wavelength approximation.18 We

resent here an extended version of this model to describeur experimental data for low-frequency (unclamped)lectro-optic coefficients r13 and r33 near the absorptiondge. We use an interferometric measurement techniqueor the evaluation of the electro-optic coefficients, whichlso requires the precise knowledge of the refractive indi-es. Therefore we extend the previous measurements ofefractive indices16,17 to the deep-UV wavelength rangeear 275 nm.

. LITHIUM TANTALATEongruent LiTaO3 crystals can be grown by the tradi-

ional Czochralski method.19 These crystals are intrinsi-ally nonstoichiometric due to a shift of the melt compo-ition from the stoichiometry toward the Ta side.onsequently, to grow stoichiometric crystals, the meltomposition has to be kept Li rich. This is achieved bydding stoichiometric powder to the melt at a rate equalo the crystal growth. This so-called double-crucible Czo-hralski method is described in detail in Ref. 20.

In this paper one congruent (CLT) and one near-toichiometric (SLT) lithium tantalate crystal grown byne of the authors at the National Institute for Materialcience, Tsukuba, have been investigated. The degree oftoichiometry of the SLT crystal was Li/ �Ta+Li�=49.9%ith a Curie temperature of 684 °C. The absorption edgef our SLT crystal is slightly shifted from75 to 270 nm.21 The properties of the two investigatedrystals are summarized in Table 1.

Below the Curie temperature, the point-group symme-ry of LiTaO3 is uniaxial 3m with the optical axis (therystallographic c axis) along the threefold symmetryxis. It therefore has two different refractive indicesa=nb=no for ordinary and nc=ne for extraordinary polar-

zation, which we determined for the two crystals. Accord-ng to the 3m point-group symmetry, LiTaO3 has eightonzero elements of the electro-optic tensor in the re-uced notation, with only four independent values:12=−r22=r61, r51=r42, r13=r23, and r33. When applying aeld in the c direction, we are able to measure the highestoefficient r33 as well as r13.

. REFRACTIVE INDICESnterferometric refractive-index measurements have beenerformed using a standard Michelson interferometer (asepicted in Fig. 1) and vertically polarized light. The crys-al was mounted onto a rotation stage in one arm of thenterferometer. It can be rotated around an axis perpen-icular to the light beam and parallel to the light polar-zation. When the crystal is rotated by an angle � away

Table 1. Crystals Investigated in This Paper

rystalDimension

a�b�c �mm3�Curie Temperature

(°C)Li/ �Ta+Li�

(%)

LT 7.3�0.975�10.2 605±1 48.6LT 1.958�7.9�8.2 684±1 49.9

rom the position of normal incidence, the optical pathength can be determined by counting the number m of in-erference fringes at the interferometer output. With �nd m we can calculate the refractive index n using22

n =�2 + 2�1 − cos ���1 − ��

2�1 − cos � − ��, �1�

here �= �m�� / �2L�, � is the wavelength at which the re-ractive index was measured, and L is the crystal thick-ess. Using this technique, refractive indices could beeasured with a preciseness of �0.01. The refractive in-

ices were measured at five different wavelengths be-ween 275 and 364 nm using an Ar++ laser (Spectra-hysics) for the ordinary and the extraordinary waves.he results are shown in Fig. 2 for the CLT and SLT crys-

als. The data above 400 nm had been reported previ-usly, and the wavelength dispersion of the refractive in-ex was described by the Sellmeier equation16,17:

n2��� = A +B

�2 − C− D�2. �2�

his function is plotted in Fig. 2 (dashed curves) using theellmeier coefficients A, B, C, and D from Refs. 16 and 17

or CLT and SLT, respectively. The measured data in theV deviates from these curves. Therefore we adjusted the

oefficients to match the data also at smaller wavelengthssolid curves). To give the Sellmeier coefficients a morehysical meaning, we have also rewritten Eq. (2) as ex-lained in the following.DiDomenico and Wemple23 introduced a simple oscilla-

or model for describing the dispersion of the refractivendex:

n2��� − 1 = �i

fi

�i2 − �2

. �3�

quation (3) separates all interband transitions into indi-idual oscillators with frequency �i and strength fi. En-rgy band calculations showed that the conduction band

ig. 1. Interferometric setup used to measure the refractive in-ices and electro-optical coefficients (eo-coeff.). For the determi-ation of refractive indices, the crystal was mounted onto a rota-ion stage. The unclamped electro-optic coefficients wereeasured by applying a low-frequency sine voltage.

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278 J. Opt. Soc. Am. B/Vol. 23, No. 2 /February 2006 Juvalta et al.

f oxygen-octahedra ferroelectrics such as LiTaO3 can beescribed by considering two subbands that can be re-ated to the two main oscillators.23 This leads to the two-scillator Sellmeier equation:

n2 − 1 =S���

2

1 − ���/��2 +S���

2

1 − ���/��2 =Ed�

E�

E�2 − E2

+Ed�

E�

E�2 − E2

.

�4�

ere, Si= fi / �2�c�2 are the oscillator strength factors andi=2�c /�i are the resonant light wavelengths for the twoscillators �i=� ,��. The expression on the right-hand sides the energy description of Wemple and DiDomenico withhe oscillator energies Ei=�i and the dispersion energyarameters Edi

=Sih2c2 /Ei. Since one oscillator is reso-ant far in the UV at �9 eV and one at �5 eV, i.e.,�����,23 one can simplify the first term of Eq. (4) by aonstant A=S���

2=Ed�/E� and leaving the second term,

hich corresponds to the dominating oscillator, un-hanged.

With this simplification, Eq. (4) describes the measuredata well in the wavelength range below 500 nm. In thisodel only interband transitions are considered; we do

ot consider optical lattice vibrations that occur at far-nfrared wavelengths. We can include these vibrations bynother oscillator SIR�IR

2 / �1− ��IR/��2�. Since the latticeibrations occur at higher wavelengths, �IR��, we can re-uce this additional term to −D�2 with D=SIR�IR

2 and ob-ain

ig. 2. Refractive indices of (a) CLT and (b) SLT. The dashedurves and the data above 400 nm are taken from literature.16,17

he solid curves correspond to the new coefficients (Table 2).here is a small correction at lower wavelengths due to the newata in the UV.

n2��� − 1 = A +S���

2

1 − ���/��2 − D�2. �5�

t is easy to assign the coefficients A, S�, ��, D to the co-fficients A, B, C, D of Eq. (2). In the energy description,q. (5) can be rewritten as

n2�E� − 1 =Ed�

E�

+Ed�

E�

E�2 − E2

−EIR

2

E2 . �6�

his form of the Sellmeier equation is used in Section 4or the derivation of the polarization potential model toescribe the dispersion of the electro-optic coefficient.The Sellmeier coefficients in Table 2 correspond to the

scillator description in Eq. (5) with the oscillator energy�=hc /��. They were evaluated taking into account theeasured data in the UV and the literature data fromefs. 16 and 17 for CLT and SLT, respectively. The values

n Table 2 are fit parameters used to calculate the refrac-ive indices at any wavelength, but the physical proper-ies exhibit an error of �12%.

Note that the empirical law of Wemple andiDomenico18,23 that the ratio E0 /S0 is a constant forost inorganic crystals is valid only for the one-oscillatorellmeier equation, where all oscillators are considered inmean oscillator with strength S0 and energy E0.If we compare the new Sellmeier parameters (solid

urves in Fig. 2) with the old ones (dashed curves), theres a small variation at lower wavelengths. This is becausehe old parameters have been evaluated from refractive-ndex data above 400 nm only, not considering the mainispersion range in the UV. We have used the newly de-ermined Sellmeier parameters to evaluate electro-opticoefficients from the measurements as described in Sec-ion 4.

. ELECTRO-OPTIC COEFFICIENTShe electro-optic coefficients were measured with theame Michelson interferometer as was used for the deter-ination of refractive indices. The setup is depicted inig. 1. Similar measurements have been performed inther materials such as LiNbO3,24 2-cycloactylamino-5-itropyridine, 2-(N-prolinol)-5-nitropyridine,25 orn2P2S6.26 For the measurement, the crystal was orien-ated with the c axis in the propagation plane and perpen-icular to the incoming laser beam. An electric field waspplied along the c axis using silver-paste electrodes. Theeld-induced phase shift is then given by

Table 2. Sellmeier Parameters Used to Describethe Dispersion of no and ne in CLT

and SLT Crystalsa

oefficient A S� � m−2� E� (eV) D � m−2�

LT, no 1.08 68.66 6.59 0.0241LT, no 1.72 43.45 6.05 0.0327LT, ne 1.22 62.02 6.43 0.0242LT, ne 1.68 45.57 6.16 0.0320

aThe given values are the fit parameters used to calculate the electro-optic coef-cient with Eq. �5� and E�=hc /��.

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Juvalta et al. Vol. 23, No. 2 /February 2006 /J. Opt. Soc. Am. B 279

� = −2�L

�n3reffE +

4�L

��n − 1�deffE, �7�

here L is the length of the crystal, n is the refractive in-ex, reff is the electro-optic coefficient of the correspondingight polarization (ne and r33 for horizontally polarizedight, no and r13 for vertically polarized light), and deff ishe effective piezoelectric coefficient. The first term of Eq.7) is the phase shift due to the electro-optic effect and theecond term describes the contribution due to the piezo-lectric change of the crystal length. With the knownalue of deff=−1.3 pm/V,27 this piezoelectric effect repre-ents a small correction of the order of �1% to r33 and5% to the smaller coefficient r13.If the applied field is a low-frequency-modulated sine-

ave signal ���1 kHz� with a small amplitude �V, thenduced phase shift is also modulated with this frequencys well as the measured intensity at the interferometerutput. Using a lock-in amplifier, we are then able to mea-ure very small intensity modulations �I. The workingoint of the interferometer was adjusted by means of a pi-zoelectric movable mirror as depicted in Fig. 1. If theorking point is set to maximum modulation, the electro-ptic coefficient can be determined using

reff = −�I

�V

d

L

�

�n3�I+ 2

n − 1

n3 deff. �8�

ere d is the distance between the electrodes andI=Imax−Imin is the intensity contrast of the interferom-ter that was determined by moving the piezoelectric mir-or to detect minimum and maximum intensity at the in-erferometer output. This configuration allows us toetermine the unclamped electro-optic coefficients r33 and13. The measurements were performed at different wave-engths between 275 and 528 nm (Ar++ laser) and at33 nm (He–Ne laser). The absorption at 275 nm was1 cm−1 in SLT and �15 cm−1 in CLT. Therefore trans-ission experiments were still possible since the crystalsere relatively thin (CLT, 1 mm; SLT, 2 mm). By measur-

ng the field-induced absorption, we found that the elec-roabsorption did not influence the electro-optic measure-ents. At low frequencies of the applied electric field ��500 Hz� we observed a significant photoconductive

creening of the applied field, which disappeared if thelectric field frequency was increased to ��1 kHz. There-ore all the measurements were performed at ��1 kHznd low light intensities �10 W/cm2−1 mW/cm2�. Thexperimental results for the two crystals are depicted inig. 3.Wemple and DiDomenico presented a polarization po-

ential model for describing the dispersion of the electro-ptic coefficient18: In one dimension, the electro-optic co-fficient can be calculated by a differentiation withespect to the induced polarization P:

r = �0�� − 1�d

dP� 1

n2 , �9�

here � is the low-frequency dielectric constant in the cor-esponding direction. Starting from the single-oscillatorellmeier equation for the dispersion of n,

n2 − 1 =S0�0

1 − ��0/��2 =EdE0

E02 − E2

, �10�

he electro-optic coefficient can be derived using Eq. (9) as

reff��� = �0�� − 1�1 −1

n���2�2dE0/dP

Ed

��1 − K� + �1 + K���0

�2� , �11�

ith the dispersion energy Ed=S0h2c2 /E0, the polariza-ion potential dE0 /dP, and the dispersion parameter Kd�ln Ed� /d�ln E0�.Comparing this model with the measured electro-optic

oefficients, the polarization potential model of Eq. (11)annot describe the data at shorter wavelengths. This isecause the single-oscillator Sellmeier equation is a long-avelength approximation and cannot be applied near

he absorption edge. For comparison with other materi-ls, K and dE0 /dP that describe the data at wavelengthsbove 350 nm are listed in Table 3 and the slopes are plot-ed in Fig. 3 as dashed curves.

To better describe the data near the absorption edge,e extend here the derivation of the electro-optical coeffi-

ient with the simplified two-oscillator Sellmeier equation6) where we considered an additional contribution of theecond oscillator in a constant A=Ed�

/E�. Since we are in-erested in the description of electro-optic coefficientsear the absorption edge, i.e., E�EIR, we can neglect the

nfrared term. Using Eq. (9), we obtain

ig. 3. Measured dispersion of the electro-optic coefficients r33nd r13 of CLT and SLT. The solid curves correspond to Eq. (12),hile the dashed curves correspond to Eq. (11) that describes theispersion at longer wavelengths. The parameters for the theo-etical curves are listed in Table 3.

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280 J. Opt. Soc. Am. B/Vol. 23, No. 2 /February 2006 Juvalta et al.

reff��� = �0�� − 1�1 −1 + A

n���2�2dE�/dP

Ed�

�1 − K1 − K2�

+ �1 + K1 + 2K2����

�2

− K2���

�4� . �12�

1 and K2 are dispersion parameters, where

K1 =d ln Ed�

d ln E�

�13�

escribes interband transition strength changes of theominating oscillator induced by the polarization, and

K2 =d ln�Ed�

/E��

d ln E�

R �14�

escribes polarization-induced changes of the second os-illator. The quantity R= �E�Ed�

� / �E�Ed�� was previously

ntroduced by DiDomenico and Wemple to describe thewo-oscillator model and was expected to be R�0.5 forost of the inorganic crystals.23 If we calculate this quan-

ity from the Sellmeier parameters (Table 2), we obtainalues between 0.4 and 0.9, which is in good agreementith that approximation. Figure 3 shows that the ex-

ended model (solid curves) well describes our data in theV region. The parameters for the slopes are listed inable 3. For wavelengths above 400 nm, the r33 value is inLT by �0.5 pm/V higher than in CLT, which is belowhe accuracy of our measurements. Below 350 nm it be-omes slightly higher for CLT, which could be attributedo the shifted absorption edge; however, the difference istill within the experimental error.

An important quantity for the application of electro-ptic materials is the half-wave voltage that is defined as

V� =�

n3r

d

L= v�

d

L, �15�

here d is the distance between the electrodes, L is theength of the beam path in the crystal, n is the refractivendex, r is the electro-optic coefficient, and � is the wave-ength of the light. It defines the applied voltage neededo rotate the beam polarization by 90°. A quantity that isndependent of the crystal geometry (i.e., d and L) is theeduced half-wave voltage v�=� / �n3r�. This quantity isepicted in Fig. 4 for the SLT crystal as a function of the

Table 3. Parameters Used to Describe theDispersion of the Electro-Optic Coefficienta

oefficient

Eq. (11) Eq. (12)

KdE0 /dP

�eV m2/As� K1 K2

dE� /dP�eV m2/As�

LT, r13 0.51 0.92 2.70 −2.03 3.54LT, r13 0.56 0.80 1.53 −1.27 1.66LT, r33 −0.31 1.54 2.01 −2.00 4.65LT, r33 −0.39 1.40 1.18 −1.98 3.04

aThe given values are the fit parameters used to calculate the electro-optic coef-cient with Eq. �11� and Eq. �12�.

avelength using Eqs. (5) and (12) and the parametersrom Tables 2 and 3 for n��� and r���, respectively. Theispersion of v� is similar in both investigated crystals,ut the absorption edge of SLT is shifted toward shorteravelengths. At �=275 nm, the absorption in CLT is al-

eady 15 cm−1 while in SLT it is only �1 cm−1. The re-uced half-wave voltage at the deep-UV wavelength=275 nm is �300 V for the larger coefficient r33 and560 V for rc=r33− �no /ne�3r13.

. CONCLUSIONSe have determined the dispersion of the unclamped

lectro-optic coefficients r13 and r33 in congruent andear-stoichiometric lithium tantalate down to �=275 nm.lectro-optic coefficients up to 52±1 pm/V were mea-ured at �=275 nm. The measured wavelengths cover theange from the deep-UV absorption edge at 270 nm overearly the whole visible spectrum to 633 nm. We have ex-ended the polarization potential model from Wemple andiDomenico to describe the dispersion of the coefficients

n the UV. The theoretical curve describes well the experi-ental data within the error of the measurements. In the

nvestigated wavelength range the values for SLT andLT differ by less than 3%, which is below the accuracy ofur measurements. The reduced half-wave voltage at75 nm was found to be �300 V for r33 and �560 V forhe configuration employing rc=r33− �no /ne�3r13 for bothrystal compositions.

In addition, the refractive indices at UV wavelengthsrom 275 to 400 nm were determined and the Sellmeieroefficients for the UV and visible wavelengths were re-valuated.

CKNOWLEDGMENTShis work has been supported by the Swiss National Sci-nce Foundation (NF 2-777416-04).

ig. 4. Absorption �c in CLT and SLT for the extraordinary po-arization and reduced half-wave voltage v� for the higherlectro-optic coefficient r33 and for the configuration employing rc.ince v� is similar for both investigated crystals, only the one ofLT is plotted. To compare the absorption, a vertical dotted line

s plotted at �=275 nm.

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1

1

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2

2

2

2

2

2

2

2

Juvalta et al. Vol. 23, No. 2 /February 2006 /J. Opt. Soc. Am. B 281

The e-mail address for F. Juvalta isurin@phys.ethz.ch.

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