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Anisotropy of piezo- andelastooptical effect in β-BaB2O4

crystalsA. S. Andrushchak a , V. T. Adamiv a , O. M. Krupycha , I. Yu. Martynyuk-Lototska a , Ya. V. Burak a & R.O. Vlokh aa Institute of Physical Optics , Dragomanov St. 23,Lviv, UkrainePublished online: 09 Mar 2011.

To cite this article: A. S. Andrushchak , V. T. Adamiv , O. M. Krupych , I. Yu.Martynyuk-Lototska , Ya. V. Burak & R. O. Vlokh (2000) Anisotropy of piezo- andelastooptical effect in β-BaB2O4 crystals, Ferroelectrics, 238:1, 299-305, DOI:10.1080/00150190008008796

To link to this article: http://dx.doi.org/10.1080/00150190008008796

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Anisotropy of Piezo- and Elastooptical Effect in P-BaB204 Crystals

A S . ANDRUSHCHAK, V.T. ADAMIV, O.M. KRUPYCH, _-. MARTYNYUK-LOTOTSKA, Ya.V. BURAK and R.O. VLOK

Institute of Physical Optics, Dragomanov St. 23, Lviv, Ukraine

(Received July 12, 1999)

1

At first using the elaborated software the indicative surfaces of the piezooptical tensor and their stereographic projections were constructed for the P-BaB204 crystals. On this basis the spatial distribution of the longitudinal and transverse piezooptical effect was analysed and the extremal values and anisotropy power for each indicative surfaces were determined. The magnitudes and signs of all elastooptical coefficients were calculated and the conclusion about the possibility for use of the P-BaB204 crystals as efficient acoustooptical material was done.

Keywords; P-BaB204 crystals; anisotropy of piezooptical effect; indicative surfaces; stereo- graphic projections; acoustooptical material

INTRODUCTION

The beta barium borate crystals (P-BaB2O4 or shortly BBO crystals) are known as efficient non-linear optical rnaterial.l'.21 But their photoelastical properties have not yet been investigated

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The aim of this paper is to present the analysis of spatial distribution of piezooptical effect and to determine the magnitudes and signs of all elastooptical coefficients for BBO crystals.

CONSTRUCTION OF THE INDICATIVE SURFACES AND THEIR STEREOGRAPHIC PROJECTIONS

For achievement of the paper aim we have measured all piezooptical tensor components for BBO crystals using the interferometric technique and the two-fold diagonal measurements method (in more detail about this method and results of these investigations see in paper, which will be published in Crystal Research Technology, 1999). According to our measurements (for T=20"C temperature and laser wavelength h=0.6328 pm) the piezooptical coefficients values are:

~ ~ ~ = 3 , 7 + 0 , 3 7 ; xI4=-2,O+O,S; ~~~=-2 ,03+0,07; x44=-26,3&0,9 (all values are in B F ~ o - ~ ' mZ/N).

Using these coefficients the indicative surfaces of the piezooptical tensor for BBO crystals were written and constructed. A technique for the construction of indicative surfaces and stereographic projections was developed in our works.i3-51 The equations of the indicative surfaces for the longitudinal (x'ii) and the transverse ( xi$) and xi',")) piezooptical effect were derived in 15.61 (here xi$) and

x$") are the piezooptical indicative surfaces for light polarisation and

mechanical stress respectively). These equations have the following form for the crystals of the 3m point group of symmetry to which BBO crystals belong:

XI I=- 1.7M, 1 5; 7~12=- 1,35f0,07; ~13=1,75M,23; xg I = - 1,6M, 1 5;

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ANISOTROPY OF PIEZOOPTICAL EFFECT IN BBO 18651/301

The Eqs.( 1)-(3) give the complete description of the piezooptical effect for the dim (i,m=1,2,3) main component of the piezooptical tensor. They allow us to construct the piezooptical indicative surfaces (see Figures la, 2a, 3a for x ' , ~ , xi ; ) , x i r ' respectively) and their

stereographic projections (see Figures Ib, 2b, 3b). To plot these surfaces, we use the XI, Xz, X3 crystallophysical coordinate system and the 8 and cp spherical coordinates. The. method for construction these surfaces is described in our work.141 Let us point out that presented indicative surfaces were built by the method of meridian (cp=const) and equatorial (@=const) cuts of these surfaces in frontal dymetric (Figure

2a) or axonometric (Figures 1 a, 3a) representation with following projection on picture plane. In order to lower shadowing the only upper part of surfaces are pictured. Complete special image of every surface can be represented through imaginary reproduction relatively to the centre of coordinate system. The elaborated software allows to take the non-visible part of each separate surface petal and to retain visible through the pictured discrete set of front surface petal the back surface petal, which is shaded by this front surface petal. Besides, on Figures 1-3 the positive parts of figure are pictured by solid line, and negative - by dashed line.

Note that it is of important here to construct the indicative surfaces and stereographic projections in the same coordinate system that was used for the determination of the piezooptical coefficients. This excludes an ambiguity both in determining piezooptical coefficients and in constructing indicative surfaces caused by the choosing rule of positive directions of the crystallophysical axes. 'These problems are considered in more detail in work.171

RESULTS AND DISCUSSION

Let us analyse the results presented in Figures 1-3

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ANISOTROPY OF PIEZOOPTICAL EFFECT IN BBO [867]/303

( I ) As the longitudinal and the transverse piezooptical effect in BBO crystals is characterised by a pronounced anisotropy, including the sign reversal.

( 2 ) In accordance with the German theorem,lsl all aforemen- tioned indicative surfaces for BBO crystals are not surfaces of rotation. Nevertheless, each surface has the symmetry elements characteristic of the 3m point group of symmetry (see Figures I b-3b): a threefold axis and three symmetry planes normal to the (Xl,X2) isotropic plane. This corresponds to well-known Neumann principle. I9J

(3) One extremal value for the piezooptical indicative surfaces of light polarisation and mechanical stress were calculated from the conditions arc/c%=O and &/dcp=O and are equal to -3,5 1 Br and 2,1 Br respectively. They correspond to the following angular coordinates: 8=0.5ar~tan[2x41/(x~2-x31)]~3", (p=9Oo, 21 0'' or 330" and 8 = 0 . 5 a r ~ t a n [ x ~ J ( n , ~ - ~ ~ ~ ) ] ~ l 6 " , (p=30", 150" or 270". Similar values for these extremum and other extremal values (see Table 1 ) were obtained from calculations using our software and also from the measurements on the stereographic projections (Figures 2b, 3b) with the help of the Wulff network. The extremal values (see Table 1) for the indicative surfaces of the longitudinal piezooptical effect were also calculated by elaborated software and were measured on the stereographic projection (Figure 1 b).

TABLE 1 Extremal values and anisotropy power for each indicative surface of the piezooptical effect

Indi- Maxlmal value Minimal value Anisotropy power

cative magni- cp magni- e 'p vSp. Iv+-v-I q, surface tude. Br tude. Br (B$ (Br)3 % n',, 3,7 0" -14.5 49' 30°, 150° 12590 3160 75

or 270' 0 ) 0.56 47" 30". 150" -3.51 43" YOo. 210" 181 33 82

or 270" or 330" '(in) 2.1 16" 30°, 150" -1,65 74" 90'. 210" 35.8 1,s 96

or 270' or 330'

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304/[8681 A S . ANDRUSHCHAK e ta /

(4) The minimal values of the piezooptical effect in BBO crystals are observed for a set of directions corresponding to the zeroth isoline on the stereographic projection (Figures lb-3b) as for longitudinal and for each transverse indicative surfaces.

(5) We suggest to calculate the effect anisotropy power for each indicative surface according to equation:

q=(vsp-/v-q 100% / v,, , (4)

where V,,=4~1f,~~1~/3 - sphere volume with selected radius /fcx,,l= =max(lfm,.l,lfmax)), V+ and V - volume of positive and negative parts of surface, respectively. It is note, when q=O%, then the anisotropy is absent (the effect is isotropy and the indicative surface is sphere) When v+=v-, then the effect have the maximal anisotropy power, which are equal to q=lOO%. According to Eq. (4) we calculate the anisotropy power for each indicative surface (see Table 1)

CALCULATION OF THE ELASTOOPTICAL TENSOR AND CONCLUSION

We have also determined the all values of the elastooptical tensor components pll=-O, 195; p12=-0,197; pl3=-0,059; p31=-0, 1 12; ps3=0,039; p 14=-0,005; p41=-o,oo7; p4.+=-O,078, which were calculated according to known formula pln=x,,,, Sim , where S-', - inverse matrix of elastic compliance coefficients. Thus, BBO crystals have the great values of elastooptical coefficients, especially pI1 and P , ~ . These crystals have the advantage before such acoustooptical materials as LiNbOl and TeOz and their coefficients are commensurate with corresponding coefficients of hsed quartz.ll"l

and acoustic wave velocities (e. g. the measured value of velocity for acoustic wave with directions of [OOI] propagation and [loo] polarization is about v-1000 d s ) provide the high value of M2

acoustooptical quality of this material. As it is known I l O l , the M2 value,

This and relatively small values of density (p=3840 kg/m3)

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ANISOTROPY OF PIEZOOPTICAL EFFECT IN BBO [ 869 ] / 3 O S

according to the well-known formula M:! = pZef n"i / pv3 (where pet: - the effective value of elastooptical coefficient; ni - the refractive index of material), is the main criterion for practical choice of photoelastical material. Besides, the small light absorption in the wide wavelength range, the possibility for obtaining the large samples with high optical quality, chemical inertness, mechanical stiffness and temperature parameters stability make possible the use of BBO crystals as efficient acoustooptical material.

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(1992). [ S ] AS. Andrushchak, B.G. Mytsyk, Ukr: Fiz. Zh. (Ukruin. Ed.), 40, 1216 (1995). [6] B.G. Mytsyk, A S . Andrushchak. Crystulography Reports, 41, 1001 (1996). [7] B.G. Mytsyk, A S . Andrushchak, Uki: Fiz. Zh. (Ukruin. Ed.), 38,49 (1993). 181 V.L. German, Dokl. Akad. Nuuk SSSR, 48,96 (1945). [9] Yu. Sirotin, M.P. Shaskolskaya, Osnovy Kristallofiziki (in Russian), Moskva (1979).

[ I 01 V.1. Balakshiy, V.N. Parygin, L.E. Chirkov, Fizicheskiye (2snovy Akustrioptiki (in Rus- sian), Moskva (1985).

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