Optics and Lasers in Engineering 37 (2002) 643–649

Measurement of electro-optic coefficients oflow-symmetry crystal YbCa4O(Bo3)3

Xin Yin*, Jiyang Wang, Jing-qian Wei, Huai-dong Gang

National Key Laboratory of Crystal Materials, Shandong University, Jinan 250100,

People’s Republic of China

Received 1 January 2001; received in revised form 1 July 2001; accepted 1 August 2001

Abstract

In this paper, we report on all the electro-optic coefficients of the low-symmetry crystalYbCa4O(BO3)3 measured by the interferometric method. The new sample orientations, whichhave not been reported so far, have been used for measuring the skew electro-optic coefficients

g51; g53; g42 and g62 independently. The results obtained are g11 ¼ 0:6; g21 ¼ 0:4; g31 ¼ 0:3;g13 ¼ 0:3; g23 ¼ 0:2; g33 ¼ 2:2; g51 ¼ 0:9; g53 ¼ 4:1; g42 ¼ 0:8 and g62 ¼ 0:4� 10

�12 m/V.r 2002 Elsevier Science Ltd. All rights reserved.

PACS: 42.62.Ky: 42.55.Rz

Keywords: YbCa4O(BO3)3 crystal; Electro-optic coefficient; Interferometric method

1. Introduction

Large and good optical quality single crystals of YbCa4O(BO3)3 (abbreviated asYCOB) have been grown from the melt by the conventional Czohralski pullingmethod. The optical and nonlinear optical properties of YCOB single crystal havebeen studied by a few authors previously [1–12]. However, its electro-optic propertyhas not been reported so far. In this paper, we report on all the electro-opticcoefficients of YCOB single crystal measured by the interferometric method. BecauseYCOB crystal belongs to low symmetry m point group, it has 10 electro-opticcoefficients. The conventional sample orientations have been used for measuring theprincipal axis coefficients g11; g21; g31; g13; g23 and g33: The new ones, which have

*Corresponding author. Tel.: +86-531-856-5174; fax: +86-531-856-5403.

0143-8166/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 1 4 3 - 8 1 6 6 ( 0 1 ) 0 0 1 4 7 - 6

never been seen in previous reports, have been used for measuring the skewcoefficients g51; g53; g42 and g62 independently.

2. Measurement method

Fig. 1 is the diagram of the optical configuration of the interferometric method.A polarized He–Ne laser is divided into two beams with equal intensity by a light-

beam-splitter. One is propagated through the sample, then reflected back by a mirrorwith a piezoelectric quartz crystal adhered on it, and the other is reflected back byanother mirror. After these two beams are propagated back again through light-beam-splitter, the interference occurs.The two sine wave modulating signals, supplied from a generator and amplified

independently, are applied to the sample and the piezoelectric quartz crystal,respectively. The change of the optical path length due to the electro-optic effect ofthe sample is given by

D1 ¼ �n3gijV1l1=d1; ð1Þ

where n and gij are the relative refractive index and the electro-optic coefficient of thecrystal, respectively. V1; l1 and d1 are the voltage applied, the length of the samplealong the optical path and the thickness in the direction of the electric field,respectively. The change of the optical path length due to the anti-piezoelectric effectof the quartz crystal is given by

D2 ¼ 2d11V2l2=d2; ð2Þ

Fig. 1. Optical configuration of the interferometric method.

X. Yin et al. / Optics and Lasers in Engineering 37 (2002) 643–649644

where d11 is the piezoelectric constant of the quartz crystal, and V2 is the voltageapplied, l2 and d2 are the length of the quartz crystal along the strain direction andthe thickness in the direction of the electric field, respectively.When the change of the optical path length due to the electro-optic effect of the

sample is compensated by the anti-piezoelectric effect of the quartz crystal, then theinterference output signal is detected by a photodiode, and amplified by a lock-inamplifier which is minimized. At that time, D1 should be equal to D2: The electro-optic coefficient gij of the sample can be written as

gij ¼ �ð2=n3ÞðV2=V1Þðl2=l1Þðd1=d2Þd11: ð3Þ

In the experimental measurement, the sine wave driving voltages applied on the testsample and the reference sample are at 1 kHz frequency, and the magnitude ofvoltage is adjusted from several volts to several tens of volts. The change of theoptical path length is about l=4 to l=20: At a given point in the sample, the error ofthe measured value is within 5%.

3. Measurement principle

YCOB crystal is a monoclinic biaxial crystal with m point group symmetry [1].The unit cell constants are: a ¼ 8:046 (A, b ¼ 15:959 (A, c ¼ 3:517 (A and b ¼ 101:191.The orientation between crystallophysical axes (X,Y,Z) and crystallographic axes(a,b,c) has been determined as

b8Y ; ða;ZÞ ¼ 23:61; ðc;XÞ ¼ 12:41:

The matrix of the electro-optic coefficients of YCOB crystal are as follows:

g11 0 g13g21 0 g23g31 0 g330 g42 0

g51 0 g510 0 0

0BBBBBBBBB@

1CCCCCCCCCA

:

(a) Principal axis coefficients. g11; g21; g31 and g13; g23; g33 are called principal axiselectro-optic coefficients, because they only cause the change of the principalrefractive indices when an electric field is applied to the crystal. A block of YCOBcrystal cut normal to crystallophysical X-, Y- and Z-axis is used for measuring g11;g21 and g31 by applying an electric field parallel to the X-axis, and by propagatinglight along Y- and Z-axis with optical polarization parallel to X-, Y- and Z-axis,respectively. g13; g23 and g33 are also measured by applying an electric field parallel tothe Z-axis, and by propagating light along X- and Y-axis with optical polarizationparallel to X-, Y- or Z-axis, respectively.(b) Skew coefficients. g51; g53; g42 and g62 are called skew electro-optic coefficients

because the application of an electric field produces a maximum change in refractive

X. Yin et al. / Optics and Lasers in Engineering 37 (2002) 643–649 645

indices when optical polarization is at 451 to the principal axes, and no change inrefractive indices when optical polarization is along the principal axes.The sample’s orientation for measuring g51 of YCOB crystal is shown in Fig. 2.A block of YCOB crystal with d in thickness along the Y-axis is cut normal to Z-

and X-axis. From the corners of the square, four right triangles with l=4 in sidelength are cut away, where l is the length of the square. A pair of faces at the cornersof the square is polished as light propagating faces. The electrodes are deposited onthe X faces. If the optical polarization is in the face of the square, g51 can bemeasured. The effective length of the optical path in the electric field is

l0 ¼ l=2 cos 451 ð4Þ

and the corresponding refractive index is given by

1

n21¼sin2 451

n2zþcos2 451

n2x: ð5Þ

Keeping no change in the directions of the propagating light and opticalpolarization, g53 can also be measured if the electric field is applied along the Z-axis.Another block of YCOB crystal, with the thickness along the X-axis, is cut normal

to Y- and Z-axis. From the corners of the square, four right triangles are cut away,as shown in Fig. 3.If the electric field is applied along the Y-axis, g42 can be measured by propagating

light along the diagonal of the square with the optical polarization located in the faceof the square. The corresponding refractive index is given by

1

n22¼sin2 451

n2yþcos2 451

n2z: ð6Þ

A block of YCOB crystal, with the thickness along the Z-axis, is cut normal to X-and Y-axis. Similarly, four right triangles are cut away from the corners of thesquare, as shown in Fig. 4.

Fig. 2. Sample’s orientation for measuring g51 of YCOB crystal.

X. Yin et al. / Optics and Lasers in Engineering 37 (2002) 643–649646

g62 can be measured by applying an electric field parallel to the Z-axis, and bypropagating light along the diagonal of the square and locating the opticalpolarization in the face of the square. The corresponding refractive index is given by

1

n23¼sin2 451

n2xþcos2 451

n2y: ð7Þ

Ten electro-optic coefficients of YCOB crystal can be measured independently byusing the above sample’s orientations.

4. Measurement and results

The YCOB crystals used for measuring the electro-optic coefficients have beengrown in our laboratory. A square crystal with 5mm in thickness along the X-axis

Fig. 3. Sample’s orientation for measuring g42 of YCOB crystal.

Fig. 4. Sample’s orientation for measuring g62of YCOB crystal.

X. Yin et al. / Optics and Lasers in Engineering 37 (2002) 643–649 647

and 12mm in length along Y- and Z-axis has been manufactured, and used formeasuring g11; g21 and g33: Four right triangles are cut away from its corners, and theremainder of the square has been used for measuring g42: Another square of YCOBcrystal with the same dimensions, with the thickness along the Z-axis, and the lengthalong X- and Y-axis, has been used for measuring g13; g23 and g33: After cutting fourright triangles from the corners of the square, the remainder has been used formeasuring g62:Another square of YCOB crystal with the same dimensions is used, with the

thickness along the Y-axis and the length along Z- and X-axis. Four right trianglesare cut from its corners. The remainder has been used for measuring g51 and g53:In determining the electro-optic coefficients of YCOB crystal, 1 kHz sinusoidal

driving voltage is applied across the test sample and reference sample. The refractiveindex of YCOB crystal at 632.8 nm are [1]: nx ¼ 1:6776; ny ¼ 1:7080 and nz ¼ 1:7182:The results obtained are listed in Table 1.It is shown from Table 1that the electro-optic coefficients of YCOB crystal are

smaller, except g33 and g51:

5. Conclusion

By using the simple sample’s orientations, especially those for measuring the skewcoefficients, all of the electro-optic coefficients of YCOB crystal can be measuredwith the interferometric method. Similarly, the same sample’s orientations can beapplied for measuring the electro-optic coefficients of other crystal materials,especially those which belong to the low-symmetry point group. This may bebeneficial for characterizing the electro-optic crystal materials and investigating thenew ones.

Acknowledgements

This project is supported by the National Science Foundation of China (GrantNo. 68890235).

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Table 1

Electro-optic coefficients of YCOB crystal (pm/V)

g11 g21 g31 g13 g23 g33 g51 g53 g42 g620.6 0.4 0.3 0.3 0.2 2.2 0.9 4.1 0.8 0.4

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