A measurement of electrooptic coefficients using a Lissajous figure

Volume 34, number 3

OPTICS COMMUNICATIONS

September 1980

A MEASUREMENT OF ELECTROOPTIC COEFFIC|ENTSUSING A LISSAJOUS FIGURE Kuniharu TAKIZAWA NHK - Japan Broadcasting Corporation, Broadcasting Science Research Laboratories, 1.10-11, Kinuta, Setagaya, Tokyo 157, Japan

Received 14 April 1980 A new method for measuring the electrcoptic coefficients is proposed. The method allows us to determine the electrooptic coefficients of crystal by detecting a small relative phase retardation between optical signals emerging from two electrooptic polarization modulators using a Lissajous figure. It is shown that the electrooptic coefficients ~" -'.be measured by applying a very small static or alternating voltage, less than 1.2% of half-wave voRage, to a crystal to be measuied.

I. Introduction

p

The electrooptic (EO) effect has been utilized in various optical devices such as optical modulator, deflector, switch and filter. The precise determination of EO coefficients is important not only for designs of optical devices, but also for investigations of the physics of EO effect in crystals. Although EO coefficients of many crystals have been measured by various methods [ 1 - 5 ], it has been required to measure more precisely EO coefficients with smaller applied voltage. in this paper a method for measuring the EO coefficients with a very s~nall applied voltage, either static or alternating, is described. This method enables us to determine the magnitude of EO coefficients by detecting the phase difference through a Lissajous figure. A Lissajous figure is produced by phase difference between two optical signals emerging from two EO polarization modulators, one of which contains a sample crystal to be measured and the other corresponds ........... rli ,,, quartz and r c of LiTaO3 and LiNbO 3 crystals at 633 nm, where r c is the combined EO coefficient given by r33 and r13, by applying static and low frequency voltages. The experimental results are in good agreement with the values reported previously [ 6 - 8 ] . l,v

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i i i ~i,i~ i,~ l,llli ~

ib,ll,

~ o ~ i

t&l, ell,~lltO

2. Method

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.............

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f~'~. l r',.~

"-I',,~r

TIL, ~

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D OSC! I_ L_C,SCOPE

Fig. 1. Schematic arrangement for measuring the EO coefficients of crystal. The incident light beam is split into two beams in order to trace a Lissajous figure on an oscilloscope. ficients of crystals is shown in fig. 1. A modulator crystal M is a reference crystal with a low half-wave voltage and is used to drive the horizontal axis of a Lissajous figure on an oscilloscope, while a sample crystal S is located in series with the crystal M between the crossed polarizer.and analyzer. The light beam transitted through the crystal M is divided into two beams by a beam splitter. One beam transmitted through only the crystal M and the other through both crystals are analyzed and the detected signals are supplied to the horizontal and vertical terminals of the oscilloscope, respectively. When two voltages Vs(t} and Vm (t) are applied to the crystals S and M, respectively, alternating components of the detected signals I x and ly are given by

Our schematic arrangement for measuring EO coef413

\,,b~mc 34, number 3 t~

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X" c,~s

7

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) < , , , - , ~. t m l"~ )

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()Plies ('OMMUNI( ATIONS

(I)

,uttl + I'~.~,, +1"~ + a I , ,.I. t. .) I n , ,

~2~

v, hme A aud l," are anlplit titles of detected signals, ,'!'ml,r! is ~hc phase retardation induced in the modut : ~ c:xstal M. I"x. and !"v are static phase retardations .rod I is at hal!f-xv.ive voltage for the sample crystal S. l h c ~hird ~erms m parelltheses of cq. (2) is the phase :ciardaliorl introduced b \ the sample crystal S. When a ~im.e dependent volta<,e~, l;n (t) is applied, a I.issajous t 1 i11e pha~;c dilfcrcnce ,'71 ~,iI rr between I x a ~ d / : . The xalue o ( / v ;.It I x = O , where al" m (t) + I x > - ' ,,: ;7, _." i.,, ,_,ix0n b\. }]~ = )" sii~ (rr I ~'I~r I. ] h u s . i~\ ~ca>t~', i~>..z' }. lhc maxiillili~l vdlue o f / v ,ztlitl }0 in tl'.c elliptic l_issajous figtire, the half-wave voltage is obtained as

(3)

I.. -a-,l, sin l i}'0'YI.

I.z ,. ~oted ~haI the amplitude ~I" l~n Ill should be ia~,_: ,r r!~,~T),~nc-xxavc voltage fl,r the ll~odtllalc~r crysz.~] \1 in ~,rdcr to ,hake the elliptic h~l> closed and t~ !'~oa
September 1980

I v versus I x show~ the complicated Lissajous figure and the vahies of Y and Y0 are not weh defined in the case that both frequencies are comparable. Fig. 2 shows a process for measuring the EO coefficients with a static voltage Vs. if r x 4= r v , a Lissajous figure is in general an ellipse even at Vs " O, as shown in fig. 2 (M. By adjusting an optical c o m p e n s a t o r so as to I x = Fv, the kissajous figure b e c o m e s linear, as shown in fig. 2 ( b ) . Wllen the static voltage Vs is ap. plied to the sample crystal under the condition e l l " x = I"v, the figure becomes again an ellipse, as shown in fig. 2(c). By measuring I Y o / Y [ in the figure and ttsing eq. (3), we can ~btain the half-wave voltage of the sample crystal. Fig. 3 shows a l,issajous figure obtained by applying alternating voltages l:~n (t) = Vm sin corot and 1~(1) = I~ sin cost to the crystals M and S, respectively, after cquali/ing l'v 1o !-"v. Bolh frequencies arc chosen Io be cos > c°m t~r m s <~ corn to discrimilmlc the phase shift induced in the salnplc crystal S. In tilts case, we can also obtain the half-wave w~ltage of tim crystal S by measuring the values Y ;tnd Y0 in tile cnvel¢~pe of l,issajous figure, as shown ill fig. 3. A modified mctllod Itir tlmasuring tile I:()cocfl'icicllts witl~ an altcrimlill,,,.'7 w~ltagc l •,,; tt ) is nl,~wn. Wllell alternating voltages I' mlt) and l"~(t~ arc applied I~ two crystals M and S, respectively, :,l i'x. :~,~ I v, llle l.issaj~us figure Ii:ls all illncr space, its sllt)wu in fig. 41d ) We lind four verl ical values of mweiope, A, B, (' and I), at I x = 0 where a V m l t ) + l'x = -+ rr/2, which arc given by

t i:. 2. A pr~,cess for measuring the 1!O coefficients of crystal with a static voltage I's. (a) The oscilloscope trace of l.is~tious figure .,r I ,, tt
~

i v --: l'y.

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~

,

•

Volume 34, number 3

OPTICS COM MUN ICATION S

Ivl

September 1980

= Ysin(2,'!"/V),

(5)

/v4 = - Y sin(2nVs/l/~r)" By measuring the vertical values Y and YO, in the same way as mentioned pceviously, we obtain the half-wave voltage of the sample crystal S as

V. = 2nVs/sin- J I Y o / Y I .

Fig. 3. The oscilloscope trace of Lissajous figure obtained oy applying altt mating voltages I m sin COint and I's sin cost, to the crystals M and S, respectively, under the conditions of 1"x I' I, a l i d cos *,. toll 1.

/vl - Y siillAl'

-t 'i'rl~ll'~)

1,.: = 1" sili(~l"

n'l~tl'.!. t4)

1,,.~ Iv4

-

)" sililAl" Yyi,l(-~l

(6)

Comparing eq. (6) with eq. (3), we see that the applied voltage needed in the modified method is reduced to half of the voltage in the method explained in fig. 3. It is well k n o w n that the Lissajous figure may detect sensitively a phase difference between two signals. Therefore, our method using the l_issajous figure is considered to be sensible for measuring the halfwave voltage with a low applied voltage, while a large voltage is, in gene~ al, required to measure a phase shift induced by EO effect. The lower limit of the applied voltage is detennined by the detectability in the kissajous figure, which is limited by the line width on an oscilloscope t~ace.

nl',,tl~. 1. ~ nI~,/17,1.

~llcie AI' --- I'~ I'~. Wllen ~,~e elilninale tile i[inur space, as slu~wn m fig. 4{b), by adjusting AI" or ls to he ,AI" = nl~,/l',, iv ~ and !v3 vanish and ly I and Iv4 ale given by

3. Experimental results We measured the t':O coefficients of kl l'aO 3. LiNbO~ and quartz crystals to examine experimentaliy our methods. A LiTaO 3 crystal with a half-wave voltage of 30V was used as a reference crystal, which

I i~. 4. A process of modified method for measuring tile !'O coefficients of crystal with an alternating voltage I"slt). (a) The oscilh~scope trace of general l.is~tlOUS figure obtained by application of l"s(t) to the sample crystal in the case of I"x ~- 1"v. (b) The It;ice o b l a i n c d I)y adiusting i" v l'x. or I s to be !"v I"x = rrl's/V~, where points B and C in fig. 4Ca) coincide with each other. 415;

V,qumc 34, tmmber 3

OPTICS COMMUNICATIONS

lablc I IO ,,x~cl'l"i~terttsof l.iTaO3, kiNbO3 and quartz crystals, measurL,xtat ,X= 632.8 nm by our method. r { 10 -12 l i t / V ) _

_

l_ffa03

r c = 21.8

LiNbO3

""C =

Quartz

rtl = 0.478

17.7

~as driven by a voltage with all amplitude of 60V and a frequency of 50Hz. A Babinet Soleil compensator was used to adjust static phase retardations r x and Fy. !!O coefficients r c of LiTaO 3 and LiNbO 3 crystals and ril of quartz were measured at 633 nm by applymga static or alternating voltage with the frequency of 70 kltz. r c is the combined EO coefficient given by r33 - ( n o / h e )3 r13 where n o and n e are the ordinary and extraordinary refractive indices, respectively ¢ We could measure the EO coefficients by a voltage with at, amplitude less than ! .2% of the half-wave voltage of sample crystals. Measured EO coefficients, listed in table 1, are in good agreement with the values reported pre'dously [6 - 8 ] . We can also find no significant difference between values obtained by applying a siatic and alternathag voltages.

l he retractive indices of these crystals are quoted from ref. [81.

416

September 1980

4. Conclusions We have described a method using a Lissajous analysis for the measurement of EO coefficients. Although this method needs an appropriate EO modulator crystal with a low half-wave voltage as a reference in addition to a sample crystal, it has the advantage that the half-wave voltage may be easily measured with a very low applied voltage, even in the cases of small EO coefficients and the infrared region. The lowest applied voltage is only limited by the line width on an osciloscope trace. The author wishes to express his apprecation to Dr. M. Okada for his discussions of an interest in the problem.

References

[1] R. O.B. Carpenter, J. Opt. Soc. Am. 40 (1950) 225. [2] S.J. Williamson, J.M. Weingart and R.D. Andrews, J. Opt. Soc. Am. 54 (1964) 337. [31 I.P. Kaminow, Appl Phys. Letters 7 (1965) 123. [41 I.P. Kaminow, IEI';E J. Quantum Electron. QE-4 (1968) 23. [51 K. Onuki, N. Uchida and T. Saku, J. Opt. Soc. Am. 62 (1972) 1030. 16l l'.V. Lenzo, E.II. Turner, 1:,.(;. Spencer and A.A. Ballman. Appl. Phys. Letters 8 11966) 81. [71 P.V. Lenzo, E.(;. Spencer and K. Nas~lu, J. Opt. Soc. Am 56 (1966) 633. [81 Landolt-Bornstein, new series (;roup i!i, Vol. 11, editor in chief: K.-tt. llellwege (Springer-Verlag, Berlin, lleidelberg, New York, 1979).