Electrooptic voltage sensor: birefringence effects and compensation methods. Kyung Shik Lee. Crystals of Bi4Ge3O1 2 from two different sources exhibited ...
Electrooptic voltage sensor: birefringence effects and compensation methods Kyung Shik Lee
Crystals of Bi 4 Ge3O1 2 from two different sources exhibited linear birefringences of 1.7 X 10-5-5.4 X 10-5 (or, phase retardations of 1.3-4.10 /cm) at a wavelength of 830 nm. These birefringences, however, are sensitive to temperature. The temperature variation of the birefringence dB/(BodT) normalized by the room temperature birefringence Bo was-1 to-7X 10-3/0C. The effects of the temperature dependent birefringence and the birefringence induced by pressure on an electrooptic voltage sensor were measured and quantitatively compared to the predictions. To remove the temperature dependent birefringences, the crystals were annealed over two days. The birefringences were reduced to about half of their original values after a first annealing process, but the values remained unchanged after a second annealing process. To eliminate the effects of the birefringences, a compensation method was used. After applying this compensation method to an electrooptic voltage sensor, the temperature stability of the sensor was improved to +0.75% from +7.0% in the temperature range between -2 and 651C, and the pressure stability was improved to 10.2% from +2% under pressure as high as 1 X 105 N/M2 .
1. Introduction
Bismuth germanate (Bi 4Ge 3 0 2 ) has been used for an electrooptic (EO) voltage sensor,",2 because it does not possess natural birefringence, which is usually temperature dependent. However, other types of birefringence in Bi 4Ge 3012 have been discussed by many investigators. 3 -5 The purposes of this work are: (1) to quantify the amount of the linear birefringences in the crystals; (2) to measure the temperature dependences of the birefringences; (3) to examine the effects of the birefringences on an electrooptic voltage sensor; (4) to remove the birefringences from the crystals by annealing; and (5) to show experimentally that a compensation method 3 previously proposed by the author can eliminate the effects of the birefringences on the voltage sensor. In this work, we also examine optical properties such as
The author is with Sung Kyun Kwan University, Electronics Engineering Department, Chunchun-Dong, Suwon, Kyuggi, South Korea. Received 28 November 1989. 0003-6935/90/304453-09$02.00/0. © 1990 Optical Society of America.
birefringence, the depolarization level, and the extinction ratio of Bi 4Ge 3012 (BGO). In Sec. II.A, the optical properties of the EO crystals are compared. The temperature dependences of the birefringences are discussed in Sec. II.B. The effects of the temperature dependent birefringences and pressure-induced birefringences on an optical voltage sensor are examined and compared to the predictions in Sec. II.C. Annealing effects are considered in Sec. III.A, and the effects of a compensation method on a voltage sensor 2 are discussed in Sec. III.B. 11. Birefringences inBGO Crystals and the Effects on a Voltage Sensor A. Optical Properties of Bismuth Germanate for Electrooptic Voltage Sensors Horowitz and Kramer 4 mention that typical BGO crystals exhibit two main types of imperfection: yellow color and precipitates. Both types of imperfection reduce the crystal performance considerably. 6 Unruh7 reports three types of precipitate: spheroidal bubbles, irregular shaped precipitates, and sheets of much smaller particles. These precipitates are associated with impurities such as Si, Ca, Al, Zn, Mg, Cu, K, Na, S, and Cl, and the last two types are birefringent.4 In addition to the birefringence due to the precipitates in BGO crystals, BGO crystals often have some degree of strain birefringence 5 as the result of thermal-gradients developed by the sudden heating or cooling of materials.8 20 October 1990 / Vol. 29, No. 30 / APPLIED OPTICS
4453
In the presence of birefringences the polarization state of incident light becomes perturbed, and linearly polarized incident light becomes depolarized to some degree due to scattering caused by the impurities as the light propagates along the crystal. Thus the birefringences and depolarization will reduce the precision of polarimetric EO voltage sensors and degrade the performance of the sensors. Because the precipitates and strains in crystals are randomly distributed over the crystals and may vary with time, the birefringences (induced by the precipitates and strains) may also be randomly distributed throughout the crystals and vary with time. For this reason the birefringence, degree of depolarization, and extinction ratio should be averaged over certain time intervals and certain spatial distances to evaluate the optical properties of an EO crystal. When only an xpolarization mode is excited at the crystal input, the average extinction ratio is defined by n(dB) = -10 log((P)/(P,)),
(1)
and the degree of the average depolarization, in other words, the linear polarization defect, is defined by (PY)
(P") + (PY)(2
77 s Axis, 0 a B
Crystal Technology
Crismatec
(32-34) dB (4.6-5.4) X 10-4 Varied (2.3-4.1) deg/cm (3.0-5.4) X 10-5
(50-53) dB (4.5-9.5) X 10-6 0 or 900 (1.3-2.2) deg/cm (1.7-2.9) X 10-5
crystal length and the (fast or slow) axis of the birefringence are listed in Table I. Similarly, the degree of the depolarization s in these crystals at every rotation of the input polarizer is obtained from Eq. (2). The degree of the depolarization s listed in Table I is the value measured at the maximum extinction ratio. After the (fast or slow) axis was determined, the input polarizer was rotated 450 from that axis, and subsequently the ensemble average powers (Pr) and (Py) were measured. From the measured ensemble average powers the phase retardation 5 = cosl[((P,) - (Py))/((P.) + (Py))]} and the average birefringence given by B = (no- no) = Xb/(27rL)
(3)
~~~~~~~~~~~~~~(2) were determined.
Here (P.) and (Py are the ensemble average powers in the x- and y-polarization modes, respectively, at the crystal output. Among four samples used in this measurement, two were obtained from Crystal Technology and the other two from Crismatec. All the samples were parallelepiped. The front and back surfaces of these crystals were optically polished so that a polarized beam was not depolarized at the surfaces. A LED beam (peak wavelength, 830 nm) collimated by a microscope objective propagated through input polarizer, crystal sample, output polarizer, and photodetector. A chopper was placed between the LED and the input polarizer. The synchronized signal from the chopper and the signal from the photodetector were sampled by a lockin amplifier (EG&E 4207). The sample was placed between two high quality polarizers (extinction ratio 60 dB). We always assumed that the input polarizer was oriented so that only the x-polarization mode was excited at the crystal input. Then we read the ensemble average powers (P.) and (Py) from the output of the lock-in amplifier by setting the output polarizer parallel to the input polarizer for (P.) and perpendicular for (Py). Here the lock-in amplifier was set at a long time constant (>1 s). The input polarizer was rotated from 0 to 900 iteratively along the direction of the light propagation. At every rotation of the input polarizer (P.) and (Py) were measured, and from Eq. (1) one extinction ratio was computed. Then the maximum value among these extinction ratios, defined here as the maximum extinction ratio, was determined. The orientation of the input polarizer at the maximum extinction ratio indicates the (fast or slow) axis of the birefringence.
The maximum extinction ratio measured over a 1-cm 4454
Table 1. Optical Properties In BI4Ge3012 at 830 nm
APPLIED OPTICS / Vol. 29, No. 30 / 20 October 1990
The measured phase retardations and the average birefringences are listed in Table I. The axes of the average birefringences existing in the crystals from Crystal Technology vary randomly with location in crystals. However, the axes in the crystals from Crismatec were 0 or 90° regardless of the location. This may indicate that the majority of the birefringences observed in the crystals from Crystal Technology are the birefringences related to the precipitates, while the birefringences in the crystals from Crismatec are the birefringences induced by the pressure (or stress) given parallel or perpendicular to the crystal surface. None of the crystals tested shows any circular birefringences. B. Temperature Dependent Linear Birefringence Crystals with symmetry lower than cubic usually have temperature dependent natural birefringence. Therefore, temperature compensation schemes have been investigated to eliminate the effect of the natural birefringence in lithium tantalate light modulators 9 and lithium niobate modulators. Crystals with cubic symmetry generally have no natural birefringence. However, in some ionic cubic crystals, natural birefringences induced by the spatial dispersion have been reported 0 l 1 near the fundamental absorption edge. Although there are not generally any natural birefringences in cubic crystals far from their absorption edges, we have observed birefringences of other types in Bi 4Ge 3 012 as discussed in Sec. II.A. When these birefringences are temperature dependent, the electrooptic sensor with the birefringences becomes unstable. To measure the temperature dependence of the birefringence, a BGO crystal was inserted in the tempera-
ture controllable oven consisting of a heating element,
1.00-
10
w U
2
a~~~~~~~~~~ \
.989-i
110 001
M
0
M N
Beam
X.
