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A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy
Optics Communications 86 ( 1991 ) 509-512 North-Holland
OPTICS COMMUNICATIONS
A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy H.Y. Zhang, X.H. He, Y.H. Shih Department of Physics, Universityof Maryland at Baltimore County, Baltimore, MD 21228, USA
and S.H. Tang Department of Physics, National University of Singapore, Singapore 0511 Received 3 July 1991; revised manuscript received 5 September 1991
A new method for measuring electrooptic coefficientsof nonlinear crystals has been developed and used to obtain an accurate measurement of ra3 and r~3for Strontium Barium Niobate (SBN). An etectrooptic modulator was used with a Michelsoninterferometer for ac modulation (sub-Hz to MHz). By observingthe appearance and symmetrical shape of the second harmonic of the ac modulation, the electrooptic coefficients r33and r~3of SBN were measured with higher accuracy. The unclamped electrooptic coefficientsof poled ofSrxBal _xNb206singlecrystal are: r33= 237 + 3 pm/V and rl3= 37 + 1 pm/V, at 2= 632.8 nm and T= 21 °C. In addition the piezoelectriccoefficientd23 has been measured with d23= 25 + 5 pm/V.
1. Introduction The electrooptical properties of n o n l i n e a r crystals have been used for m a n y i m p o r t a n t applications [ 1,2]. The m e a s u r e m e n t of the electrooptic coefficients (Pockels coefficients) of nonlinear crystals has been an i m p o r t a n t subject. Different methods have been published [3,4] with a m e a s u r e m e n t error of 10% or more. Feinberg et al. reported an interferometric method for measuring the electrooptic coefficient r33 of SBN at low frequency with an error of about 10% in 1987 [ 4 ]. This method has been widely accepted as a standard method. However, we found it difficult to improve the accuracy because this method depends very much on the absolute value m e a s u r e m e n t of both the intensity I and the change of the intensity A / o f the interferometer. The nonlinearity of the photo detector a n d the stability of the interferometer also affect the accuracy of the measurement. The absolute value m e a s u r e m e n t s o f / a n d AI need a highly stabilized interferometer at half-intensity, i.e., the most critical point of the interference, during the measurements. It is hard to obtain
a 10% accuracy in most of the experiments (the best result we got by using this technique was about 10%). We report here a new method, which does not measure the absolute value of I a n d AJ of the interferometer, but instead, monitors the appearance a n d symmetrical shape of the second h a r m o n i c of the m o d u l a t i o n ( 2 f m o d u l a t i o n ) at extreme intensities of the interference (total constructive or total distractive interference). The observation of the 2 f m o d u l a t i o n symmetrical shape provided a higher accuracy of the measurement. The lock-in amplifier is not a necessary part for the measurement, an oscilloscope (high frequency m e a s u r e m e n t ) , a chart recorder (low frequency m e a s u r e m e n t ) or any instrum e n t which can recognize the appearance a n d symmetrical shape of the 2 f m o d u l a t i o n , can be used for the observation. This new method combines the electrooptical m o d u l a t i o n with the interferometric technique for the m e a s u r e m e n t of electrooptic coefficients. An electrooptical m o d u l a r ( E O M ) is used as a tunable compensator of the optical path a n d also as an ac modulator (sub-Hz to M H z ) to modulate the laser
0030-4018/91/$03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
5 09
Volume 86, number 6
OPTICS COMMUNICATIONS
beam of the interferometer. By observing the 2 f modulation at extreme intensities of the interference, the electrooptic coefficients can be determined. The measurement is only concerned with the monitoring of the appearance and symmetrical shape of the second harmonic of the ac modulation (not the absolute value), which can be quite sensitive and quite easy to operate. On the other hand, the observation of the appearance and symmetrical shape of the 2fmodulation does not depend on the linearity of the detector. The advantages above yield a much higher accuracy than that of previous publications.
2. Experimentand measurements The basic optical system used for the measurements of electrooptic coefficients and the piezo-electric coefficient is a Michelson interferometer as shown in fig. 1. A HeNe laser with wavelength 6328 is used as the light source. The TEMoo laser beam is expanded by a spatial filter SF. The SBN crystal is placed in one arm of the interferometer. The positive direction of the z-axis of the coordinate system is defined by the applied electric field Ez which is the same as the c-axis of the SBN crystal. The c-axis of SBN is defined as the direction of polarization fixed by the applied poling electric field direction. The laser beam propagates along the y direction, and is polarized in the z direction for r33 measurement and in the x direction for r~3 measurement. The SBN crystal is a uniaxial crystal with indices of refraction n3= n¢= 2.2953 and n~ = n2= no= 2.3116 at wavelength 6328/1, and at room temperature. The index of refraction of the crystal changes, because of M1
'~
the electrooptic effect, when an electric field E is applied across the crystal in the z direction, according to An3 = -- in3ra3Ez, I 3
( 1)
and
Anl
=
--
ln3r ~ 1 13L~z
~
ALy=d23EzLy,
(3)
which has to be considered for an accurate measurement of/'33 and r~3. An EOM is placed in another arm of the interferometer. The electric field applied to the EOM has both a dc and an ac part. V=Vdc+Vac where Va¢= Vo sin 2rift (Vo<< Vdc). The dc part is used to adjust the length of the optical path and the ac part modulates the output, as explained in the next paragraph, at twice the input frequency in extreme intensity of interference to ease detection. The main advantage of the new method is that the signal detection at twice the frequency of the input does not depend on the linearity of the detector and does not require a quantitative measurement of the intensity or the change of the intensity of the interferometer. From fig. 2, it is clear that an input Va~ of the EOM
lmax
. . . . .
--._ --_. _-- _-- _ . _
_.LL
J.fl
P L1 ' BS ~-t2- ~
(2)
•
The same applied electric field Ez can, because of the piezoelectric effect, cause a length change of the crystal along the y axis:
//~.-l-
SBN% SF
15 December 1991
I
M2 . 2 .
I _ I t
i
_
-
I
I I
i
I
I
l_ t
t
-t-t I t I
I
_ [ 2 - 1
I
I
t
2f._%,,'LL.-:~.q~. signal ,-.
_.
f signal
_
- _
_
I
.
-
', ',zf sigoal
¢
Laser
DR Recorder
Fig. I. Experimental setup.
510
,m1,
I
V.^:V^ Sin 2zrft
Fig. 2. Measurement of V~/2 by monitoring the 2fsignal.
Volume 86, number 6
OPTICS COMMUNICATIONS
at frequency fgenerates an output signal at 2fwhen the interference is fully constructive (I=/max) or fully destructive ( I = Imin)" If the intensities of the laser beam in two arms are equal, the output of the interferometer/out is a simple function of the optical path along the two arms of the interferometer,
Io,t=Iocos2(8/2) ,
(4)
where 8 = (2~r/20) (optical path length 1 minus optical path length 2). If optical path length 1 is changed due to the applied electric field across the SBN crystal (electrooptic effect and piezoelectric effect), the interference pattern is shifted. Optical path length 2 can then be changed in such a way as to restore the interference pattern to its original position or to a desired configuration. If the change of optical path length 2 is calibrated, i.e. the EOM is calibrated, then the change of optical path length 1 can be determined. The above principle can be used for measuring r33, r~3 and d23. The actual measurement of r33 and r~3 are simpler. For measuring r33 and r~3, first set Ez=0, and adjust the applied voltage Va¢ of the EOM to set the output of the interferometer to a minimum, Imin. The 2fsignal can be detected. Second, increasing E~ causes the 2 f signal to disappear and reappear, i.e. interference is changed from destructive to constructive. The voltage applied to the SBN crystal is set exactly equal to V~/2, where V,~/2 is the quarter-wave voltage (it is V,~/2instead of V, because of the Michelson interferometer). After subtracting the contribution of the piezoelectric effect, r33 and r,3 can be calculated. Fig. 3 is a chart recorded trace for these measurements with 0.5 Hz modulation. We decided
15 December 1991
to observe the 2fsignal to determine the extreme interference instead of observing the maximum or minimum intensity. The reason is the following: at extreme interference the change of the output intensity is not sensitive to the change of the optical path difference between the two arms of the interferometer, i.e., d / / d (nL) = 0. However, the observation of the appearance and symmetrical shape of the 2f signal is very sensitive to the change of the optical path difference. The accuracy of the determination of the extreme interference can be increased by at least one order of magnitude by observing the symmetrical shape of the 2 f signal. The experimental set up for measuring d23 is almost the same as the one for r33 and r13 except that the front surface of the SBN crystal is used as the reflection mirror of the Michelson interferometer. The back surface of the crystal is clamped so that the change in optical path length 1 is now due to the change in the length of the crystal only. The corresponding quarter-wave voltage is much higher than that required for the measurement of r33 and r~3. Applying the required strong electric field to the SBN caused damage to the crystal in our experiment. The following method is used for the d23 measurement. First, measure the quarter-wave voltage of EOM. Second, set Ez=0, and adjust the applied Va¢ of the OEM to a value Vl in order to observe the 2fsignal. Then, adjust the voltage V~across the SBN crystal to about 100 V where the 2f signal disappears and change the applied Vdc of EOM to V2 until the 2fsignal reappears. The value of V,/2(EOM) can be determined
Vn/2(d23)
Vz
(5)
V,~/2(EOM) - V2 - 1:2 "
3. Experimental results and discussion The measured values of r33, rt3 and d23 of SBN Ce 60 are: r33 = 237 + 3 p m / V , r13=37+ 1 p m / V , Fig. 3. Chart recorder trace for r33 measurement (0.5 Hz modulation ).
d23 = 2 5 + 5 p m / V , at 2=6328 A and T=21 °C (room temperature). 511
Volume 86, number 6
OPTICS COMMUNICATIONS
Because changes o f tenths o f a volt in Vz (voltage across SBN) can be observed easily a r o u n d Imi. or /max using 2 f signal detection, the above measurements were rather accurate. The high accuracy and sensitivity o f this technique suggests m a n y potential applications, for e x a m p l e the electrooptical effect study o f thin film nonlinear optical materials. A series m e a s u r e m e n t s o f optical polymers are under taken in our laboratory using this technique.
Acknowledgements This research was partially s u p p o r t e d by Martin
512
15 December 1991
M a r i t t a Aero & N a v a l Systems and M a r y l a n d Industrial Partnerships.
References [ 1] I.P. Kaminow, An introduction of electrooptic devices (Academic Press, New York, 1974). [2] P. Gunter, Phys. Rep. 93 (1982) 199. [ 3 ] D.V. Lenzo, E.G. Spencer and A.A. Ballmon, Appt. Phys. Lett. II (1967)23. [4] S. Ducharme, J. Feinberg and R.R. Neurgaonkar, IEEE J. Quantum Electron. QE-23 (1987) 21 t6.
OPTICS COMMUNICATIONS
A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy H.Y. Zhang, X.H. He, Y.H. Shih Department of Physics, Universityof Maryland at Baltimore County, Baltimore, MD 21228, USA
and S.H. Tang Department of Physics, National University of Singapore, Singapore 0511 Received 3 July 1991; revised manuscript received 5 September 1991
A new method for measuring electrooptic coefficientsof nonlinear crystals has been developed and used to obtain an accurate measurement of ra3 and r~3for Strontium Barium Niobate (SBN). An etectrooptic modulator was used with a Michelsoninterferometer for ac modulation (sub-Hz to MHz). By observingthe appearance and symmetrical shape of the second harmonic of the ac modulation, the electrooptic coefficients r33and r~3of SBN were measured with higher accuracy. The unclamped electrooptic coefficientsof poled ofSrxBal _xNb206singlecrystal are: r33= 237 + 3 pm/V and rl3= 37 + 1 pm/V, at 2= 632.8 nm and T= 21 °C. In addition the piezoelectriccoefficientd23 has been measured with d23= 25 + 5 pm/V.
1. Introduction The electrooptical properties of n o n l i n e a r crystals have been used for m a n y i m p o r t a n t applications [ 1,2]. The m e a s u r e m e n t of the electrooptic coefficients (Pockels coefficients) of nonlinear crystals has been an i m p o r t a n t subject. Different methods have been published [3,4] with a m e a s u r e m e n t error of 10% or more. Feinberg et al. reported an interferometric method for measuring the electrooptic coefficient r33 of SBN at low frequency with an error of about 10% in 1987 [ 4 ]. This method has been widely accepted as a standard method. However, we found it difficult to improve the accuracy because this method depends very much on the absolute value m e a s u r e m e n t of both the intensity I and the change of the intensity A / o f the interferometer. The nonlinearity of the photo detector a n d the stability of the interferometer also affect the accuracy of the measurement. The absolute value m e a s u r e m e n t s o f / a n d AI need a highly stabilized interferometer at half-intensity, i.e., the most critical point of the interference, during the measurements. It is hard to obtain
a 10% accuracy in most of the experiments (the best result we got by using this technique was about 10%). We report here a new method, which does not measure the absolute value of I a n d AJ of the interferometer, but instead, monitors the appearance a n d symmetrical shape of the second h a r m o n i c of the m o d u l a t i o n ( 2 f m o d u l a t i o n ) at extreme intensities of the interference (total constructive or total distractive interference). The observation of the 2 f m o d u l a t i o n symmetrical shape provided a higher accuracy of the measurement. The lock-in amplifier is not a necessary part for the measurement, an oscilloscope (high frequency m e a s u r e m e n t ) , a chart recorder (low frequency m e a s u r e m e n t ) or any instrum e n t which can recognize the appearance a n d symmetrical shape of the 2 f m o d u l a t i o n , can be used for the observation. This new method combines the electrooptical m o d u l a t i o n with the interferometric technique for the m e a s u r e m e n t of electrooptic coefficients. An electrooptical m o d u l a r ( E O M ) is used as a tunable compensator of the optical path a n d also as an ac modulator (sub-Hz to M H z ) to modulate the laser
0030-4018/91/$03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
5 09
Volume 86, number 6
OPTICS COMMUNICATIONS
beam of the interferometer. By observing the 2 f modulation at extreme intensities of the interference, the electrooptic coefficients can be determined. The measurement is only concerned with the monitoring of the appearance and symmetrical shape of the second harmonic of the ac modulation (not the absolute value), which can be quite sensitive and quite easy to operate. On the other hand, the observation of the appearance and symmetrical shape of the 2fmodulation does not depend on the linearity of the detector. The advantages above yield a much higher accuracy than that of previous publications.
2. Experimentand measurements The basic optical system used for the measurements of electrooptic coefficients and the piezo-electric coefficient is a Michelson interferometer as shown in fig. 1. A HeNe laser with wavelength 6328 is used as the light source. The TEMoo laser beam is expanded by a spatial filter SF. The SBN crystal is placed in one arm of the interferometer. The positive direction of the z-axis of the coordinate system is defined by the applied electric field Ez which is the same as the c-axis of the SBN crystal. The c-axis of SBN is defined as the direction of polarization fixed by the applied poling electric field direction. The laser beam propagates along the y direction, and is polarized in the z direction for r33 measurement and in the x direction for r~3 measurement. The SBN crystal is a uniaxial crystal with indices of refraction n3= n¢= 2.2953 and n~ = n2= no= 2.3116 at wavelength 6328/1, and at room temperature. The index of refraction of the crystal changes, because of M1
'~
the electrooptic effect, when an electric field E is applied across the crystal in the z direction, according to An3 = -- in3ra3Ez, I 3
( 1)
and
Anl
=
--
ln3r ~ 1 13L~z
~
ALy=d23EzLy,
(3)
which has to be considered for an accurate measurement of/'33 and r~3. An EOM is placed in another arm of the interferometer. The electric field applied to the EOM has both a dc and an ac part. V=Vdc+Vac where Va¢= Vo sin 2rift (Vo<< Vdc). The dc part is used to adjust the length of the optical path and the ac part modulates the output, as explained in the next paragraph, at twice the input frequency in extreme intensity of interference to ease detection. The main advantage of the new method is that the signal detection at twice the frequency of the input does not depend on the linearity of the detector and does not require a quantitative measurement of the intensity or the change of the intensity of the interferometer. From fig. 2, it is clear that an input Va~ of the EOM
lmax
. . . . .
--._ --_. _-- _-- _ . _
_.LL
J.fl
P L1 ' BS ~-t2- ~
(2)
•
The same applied electric field Ez can, because of the piezoelectric effect, cause a length change of the crystal along the y axis:
//~.-l-
SBN% SF
15 December 1991
I
M2 . 2 .
I _ I t
i
_
-
I
I I
i
I
I
l_ t
t
-t-t I t I
I
_ [ 2 - 1
I
I
t
2f._%,,'LL.-:~.q~. signal ,-.
_.
f signal
_
- _
_
I
.
-
', ',zf sigoal
¢
Laser
DR Recorder
Fig. I. Experimental setup.
510
,m1,
I
V.^:V^ Sin 2zrft
Fig. 2. Measurement of V~/2 by monitoring the 2fsignal.
Volume 86, number 6
OPTICS COMMUNICATIONS
at frequency fgenerates an output signal at 2fwhen the interference is fully constructive (I=/max) or fully destructive ( I = Imin)" If the intensities of the laser beam in two arms are equal, the output of the interferometer/out is a simple function of the optical path along the two arms of the interferometer,
Io,t=Iocos2(8/2) ,
(4)
where 8 = (2~r/20) (optical path length 1 minus optical path length 2). If optical path length 1 is changed due to the applied electric field across the SBN crystal (electrooptic effect and piezoelectric effect), the interference pattern is shifted. Optical path length 2 can then be changed in such a way as to restore the interference pattern to its original position or to a desired configuration. If the change of optical path length 2 is calibrated, i.e. the EOM is calibrated, then the change of optical path length 1 can be determined. The above principle can be used for measuring r33, r~3 and d23. The actual measurement of r33 and r~3 are simpler. For measuring r33 and r~3, first set Ez=0, and adjust the applied voltage Va¢ of the EOM to set the output of the interferometer to a minimum, Imin. The 2fsignal can be detected. Second, increasing E~ causes the 2 f signal to disappear and reappear, i.e. interference is changed from destructive to constructive. The voltage applied to the SBN crystal is set exactly equal to V~/2, where V,~/2 is the quarter-wave voltage (it is V,~/2instead of V, because of the Michelson interferometer). After subtracting the contribution of the piezoelectric effect, r33 and r,3 can be calculated. Fig. 3 is a chart recorded trace for these measurements with 0.5 Hz modulation. We decided
15 December 1991
to observe the 2fsignal to determine the extreme interference instead of observing the maximum or minimum intensity. The reason is the following: at extreme interference the change of the output intensity is not sensitive to the change of the optical path difference between the two arms of the interferometer, i.e., d / / d (nL) = 0. However, the observation of the appearance and symmetrical shape of the 2f signal is very sensitive to the change of the optical path difference. The accuracy of the determination of the extreme interference can be increased by at least one order of magnitude by observing the symmetrical shape of the 2 f signal. The experimental set up for measuring d23 is almost the same as the one for r33 and r13 except that the front surface of the SBN crystal is used as the reflection mirror of the Michelson interferometer. The back surface of the crystal is clamped so that the change in optical path length 1 is now due to the change in the length of the crystal only. The corresponding quarter-wave voltage is much higher than that required for the measurement of r33 and r~3. Applying the required strong electric field to the SBN caused damage to the crystal in our experiment. The following method is used for the d23 measurement. First, measure the quarter-wave voltage of EOM. Second, set Ez=0, and adjust the applied Va¢ of the OEM to a value Vl in order to observe the 2fsignal. Then, adjust the voltage V~across the SBN crystal to about 100 V where the 2f signal disappears and change the applied Vdc of EOM to V2 until the 2fsignal reappears. The value of V,/2(EOM) can be determined
Vn/2(d23)
Vz
(5)
V,~/2(EOM) - V2 - 1:2 "
3. Experimental results and discussion The measured values of r33, rt3 and d23 of SBN Ce 60 are: r33 = 237 + 3 p m / V , r13=37+ 1 p m / V , Fig. 3. Chart recorder trace for r33 measurement (0.5 Hz modulation ).
d23 = 2 5 + 5 p m / V , at 2=6328 A and T=21 °C (room temperature). 511
Volume 86, number 6
OPTICS COMMUNICATIONS
Because changes o f tenths o f a volt in Vz (voltage across SBN) can be observed easily a r o u n d Imi. or /max using 2 f signal detection, the above measurements were rather accurate. The high accuracy and sensitivity o f this technique suggests m a n y potential applications, for e x a m p l e the electrooptical effect study o f thin film nonlinear optical materials. A series m e a s u r e m e n t s o f optical polymers are under taken in our laboratory using this technique.
Acknowledgements This research was partially s u p p o r t e d by Martin
512
15 December 1991
M a r i t t a Aero & N a v a l Systems and M a r y l a n d Industrial Partnerships.
References [ 1] I.P. Kaminow, An introduction of electrooptic devices (Academic Press, New York, 1974). [2] P. Gunter, Phys. Rep. 93 (1982) 199. [ 3 ] D.V. Lenzo, E.G. Spencer and A.A. Ballmon, Appt. Phys. Lett. II (1967)23. [4] S. Ducharme, J. Feinberg and R.R. Neurgaonkar, IEEE J. Quantum Electron. QE-23 (1987) 21 t6.