Measurement of electrooptic constant with the reflection intensity method

Optics Communications 101 ( 1993) 347-349 North-Holland

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Measurement of electrooptic constants with the reflection intensity method L.P. Shi a n d J.Y. W a n g The Institute of CrystalMaterials, Universityof Shandong, Shandong, China

Received 26 February 1993

A new method to measure electrooptic constants is introduced. The advantages and the weak points of this method are discussed. The new method has been compared with the other methods. The electrooptic constant r333of Ko.TRbo.3TPcrystal has been measured with this method.

1. Introduction

Electrooptic constants o f crystals are the most important parameters for an electrooptic application. Although there are some methods to measure electrooptic constants [ 1,2 ], it is always attractive to develop new measurement methods to determined electrooptic constants more precisely. In this paper we introduce a new measurement method. Potassium titanium oxide phosphate, KTiOPO4 (in the following abbreviated K T P ) is a relatively new nonlinear optical material [3,4]. It has many substantial advantages in second harmonic generation ( S H G ) applications. Besides its application in SHG, its large electrooptic constants and low dielectric constants make it attractive for various electrooptic applications such as modulators and switches in integrated optics [ 5 ]. In 1987, Bierlein reported on planar and channel optical waveguides in K T P fabricated by an ion-exchange method [6]. The waveguide layers are K~_x-RbxTiOPO4 and so on, with refractive indices that are larger than those o f KTP. In order to study the properties o f these guidewave layers, we have grown Ko.7Rbo.3TP. We have measured the electrooptic constant r333 o f a grown crystal with this method.

2. Measurement method An experimental arrangement is shown in fig. 1. A linear polarized HeNe laser beam passes through a semi-mirror and is reflected by the front and back surface o f a sample. The reflected light beams are again reflected by the semi-mirror and their interference pattern is detected by a diode. The signal is amplified by a lock-in amplifier. We use a crystal physics coordinate [ 7 ]. The wave vector and polarization are along ei and ej, respectively. The amplitude coefficients o f reflection and transmission on the front surface and back surface are

I•Laser

Semi-~ p m i r ~ 0Lens

~

Pin-Diode Lock-In

Amplifer

2 Sample Fig. 1. The reflection intensity method. 0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All riots reserved.

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Volume 101, number 5,6

l -- nj

nj -- I

rol= l + n j '

r12= l + n / '

2 tol-- l + n / '

2 tL2- l + n j "

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(1)

R=rol + tol horl2 exp(--i2fl) -I-tol tlo( rlorl2 ) 2 e x p ( - - i 4 / f l ) + ... =rol + {tot hot12 exp(--i2fl) ] × [ 1 -- (rlor12)" exp(--i2nfl) ]}

X [ 1 --rlor12 exp(--i2fl) 1-1 ,

(2a)

fl= (27tL,/2)n/.

(2b)

I f n--,oo, we obtain the following equation (3)

,

2rtL, (

n=

----7-12zcLi[ n 3 rjjk V~ + d~ikV~(nj- 1 )) \nj-- 2 Lk Lk

D

(7)

Then we measure the curve of I and V. The electrooptic constants can then be obtained by a fitting procedure.

3. Discussion

n~ rys.kV+d'ikV(nj--l).) 2 Lk Lk '

The advantages of this method are: (i) The stability of the method is very good. (ii) The precision of the method is high. (iii) The constants can be obtained independently. For the Michelson interferometer method one must use a constant of a reference crystal as a pa-

(5)

where d[ik is the converse piezoelectric constant. In principle, to1, r12 will also be changed by a voltage on the crystal. But the changes are so small that we can neglect them. From eqs. ( 1 ) - ( 5 ), we can see that I is a periodic function of the voltage. The electrooptic constants can be obtained by the following methods. (i) By measuring the half-wave voltage. Because I is a periodic function of the voltage, we can measure the half period of the curve, from which we derive the half-wave voltage V~. I f we have measured the converse piezoelectric constant, we can calculate the electrooptie constants by the following equation 348

(6) "

(4)

where T i n , R , ~ i are the amplitude transmission and reflection coefficients of the semi-mirror, respectively. Io is the primary intensity of the HeNe laser beam. I f a voltage is applied on the crystal along ek, fl will change to

fl=----A--- nj

Lk

"

The intensity received by the diode is 2

d~ikV~(nj-1)) d-

(ii) By fitting an experimental I - V curve with a theoretical curve. Since we measure the relative intensities by a lock-in amplifier, we must fit the derivative curve in order to obtain the correct electrooptic constants. Figure 2 shows a measured curve of I and V. V is the peak value voltage. The correspondent derivative curve can be obtained by this curve. It should be emphasized that we can obtain a linear electrooptic constant, and a converse piezoelectric constant simultaneously using this method. (iii) First we measure the half-wave voltage so that we can obtain an equation

with

I = I o T ~2 m i R 2~ i R

n}r~kV~ 2L~

2rtL,- (

=T

In the case of multi-reflection, we have the total amplitude reflective coefficient

R = to1 +r12 e x p ( - i 2 f l ) l -I-rol r!2 e x p ( - i 2 f l )

1 September 1993

,~ ~'~'0"0-0. ~ 4 /

c~'"

"o

/

S s 8

¢'

~3

o

¢' ,/

b

/

¢' /

6

1 6

1000

2000 Voltage [ V ]

Fig. 2. A measured curve of l a n d V.

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Volume 101, number 5,6

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rameter which contribute to the total error. (iv) The path difference is twice that used in the Michelson interferometer method and in the halfwave-voltage method [ 1,2 ]. ( v ) A linear electrooptic constant and a converse piezoelectric constant can be obtained simultaneously. The weak points o f this method are (i) The method is not suited for measurement o f crystals with small electro0ptic effects. (ii) It is difficult to measure small samples with this method. (iii) The parallelism between the front and back surfaces must be much better than that used in the Michelson interferometer method and in the halfwave-voltage method. Crystals suited for electrooptic applications must have large electrooptic constants, a high quality and a large crystal size. Therefore the m e t h o d under discussion is a primary alternative for such crystals. The largest and most important electrooptic constant o f crystals o f the K T P family is r333. On Ko.TRbo.3TP this constant has been measured by the method (i) mentioned above. Measured r333 is 30.2 p m / V . Equations ( 1 ) - ( 5 ) have been obtained assuming an ideal situation. I f we consider the absorption o f crystals, we can use the following formula to measure the electrooptic constants:

1 September 1993

R -- rol -t- tot tl2rl2 exp [ - (20tL~ +i2fl) ] -1-tOl tl2(rol r12) 2 exp [ - (4olLi +i4fl) ] + ... ---- rol -brl2 exp[ -- (2otL~ +i2fl) ] 1 -I- rol r12 exp [ - (2otLi + i2p) ] '

(8)

where c~ is the absorption coefficient o f the crystal. In this case the intensity I is an oscillatory periodic function o f the voltage.

Acknowledgements The authors are indebted to prof. Haussiihl for discussions.

References [1] L. Bohaty, Z. Kxistalogr. 158 (1982) 233. [2]M.H. Jiang, Crystal physics (Science Press of Shandon, China, 1980) p. 345. [3] P.J. Pordjman, R. Masse and J.C. Guitel, Z. Kristallogr. 139 (1974) 103. [4] F.C. Zumsteg, J.D. Bierlein and T.E. Gier, J. Appl. Phys. 47 (1976) 448. [ 5 ] J.D. Bierlein and C.B. Arweiler, Appl. Phys. Len. 49 (1986) 9. [ 6 ] J.D. Bierlein, A. Ferretti, L.H. Brixner and W.Y. Hsu, Appl. Phys. Lett. 50 (1987) 1126. [7]S. Haussfihl, Kristallphysik, 2 (Verlag Chemie-Physik GmbH, Weinheim, Germany, 1983).

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