Automatic polarization controller having broadband, reset-free operation

Wide optical bandwidth and broad wavelength tuning range are achieved in a reset-free, optical, automatic polarization controller by combining three controllable fractional wave elements in cascade and further by controlling the orientations of both outermost fractional wave elements to differ by a prescribed angular amount which is maintained substantially constant. The prescribed angular amount is defined to be between 0 and 2.pi., inclusively. Synchronous control of both outermost fractional wave elements maintains the prescribed angular difference to be maintained constant during operation of the polarization controller. The three fractional wave elements are described as an endlessly rotatable half-wave element and two synchronously rotatable quarter-wave elements wherein the half-wave element is placed between the quarter-wave elements. Each fractional wave element varies the orientation of linear birefringence along its optical wavepath and introduces a specified phase retardation. Embodiments of the polarization controller are realized using either distributed bulk optic devices or integrated electrooptic waveguide devices. Rotation of the elements is afforded by a feedback control circuit which monitors the output optical polarization and derives appropriate electrical drive signals to achieve the proper rotation of the elements.

TECHNICAL FIELD 
This invention relates to devices for controlling polarization of incident 
optical signals and, more particularly, to devices which permit endless or 
reset-free operation. 
BACKGROUND OF THE INVENTION 
Optical fiber communication systems based on fiber other than polarization 
preserving fiber cause lightwave signals in the fiber to experience random 
changes in polarization state from one end of the fiber to the other. 
Fiber birefringence is the cause of the random polarization changes. 
Random polarization changes are evidenced as fading or loss of the 
lightwave signal at the receiver because the polarization of the received 
signal differs from a prescribed or expected polarization. 
In order to correct the polarization state of lightwave signals emerging 
from the optical fiber and, thereby, avoid polarization fading, 
polarization transformers have been developed to transform the fiber 
output polarization into the prescribed polarization state for 
applications such as heterodyne detection and interferometric signal 
processing. Conventional polarization transformers provide a limited range 
of birefringence compensation and require a reset cycle when the range is 
exceeded. Reset cycles give rise to periods of unacceptable data loss. 
Endless polarization transformers provide continuous control of the 
polarization state over a virtually infinite range of birefringence 
compensation. 
Endless polarization transformers have been developed using cascaded 
polarization transformers having a limited transformation range such as 
fiber squeezers and electrooptic devices using lithium niobate. Fiber 
squeezers mechanically induce birefringence in the fiber axes to cause 
retardation between the two orthogonal modes perpendicular and parallel to 
the direction of pressure. While these cascaded devices permit truly 
endless (reset free) operation, individual elements within the devices 
still require occasional reset cycles. Although the reset cycles can be 
performed without affecting the overall polarization transformation 
(quasi-endless polarization control), these devices generally fail to 
permit polarization fluctuations during reset cycles. Moreover, they 
require sophisticated and even computer controlled drive algorithms for 
proper operation which, undoubtedly, results in a slow response. 
Recently, a reset-free, endless polarization transformer was demonstrated 
performing general polarization transformations from any arbitrarily 
varying optical input polarization into any arbitrarily varying optical 
output polarization by producing adjustable elliptical birefringence of 
constant total phase retardation in a single-mode waveguide. See U.S. Pat. 
No. 4,966,431 issued to Heismann on Oct. 30, 1990. A particular 
transformation is obtained by adjusting the azimuth of linear 
birefringence and the ratio of linear to circular birefringence. In its 
integrated-optic realization, the endless polarization transformer 
includes at least one cascadable transformer section comprising cascaded 
first and second TE TM mode converters. Phase shifting (TE/TM) is 
performed in a section between the mode converters, in a section following 
the mode converters, or both between and following the mode converters. 
All sections are formed over a birefringent waveguide capable of 
supporting propagation of TE and TM optical signal modes. While the recent 
endless, reset-free polarization transformer is cascadable and affords 
simplicity of design and operation over prior art devices, it cannot be 
overlooked that this polarization transformer has a relatively narrow 
optical bandwidth at wavelengths of interest--less than 1 nm at 1.55 
.mu.m--and permits only limited tunability over a small wavelength 
range--approximately 10 nm. 
SUMMARY OF THE INVENTION 
Wide optical bandwidth and broad wavelength tuning range are achieved in a 
reset-free, optical, automatic polarization controller by combining three 
controllable fractional wave elements in cascade and further by 
controlling the orientations of both outermost fractional wave elements to 
differ by a prescribed angular amount which is maintained substantially 
constant. Synchronous control of both outermost fractional wave elements 
maintains the prescribed angular difference to be maintained constant 
during operation of the polarization controller. 
In the embodiments described herein, the three fractional wave elements are 
an endlessly rotatable half-wave element and two synchronously rotatable 
quarter-wave elements wherein the half-wave element is placed between the 
quarter-wave elements. Each fractional wave element varies the orientation 
of linear birefringence along its optical wavepath and introduces a 
specified phase retardation. 
Embodiments of the polarization controller are realized using either 
distributed bulk optic devices or integrated electrooptic waveguide 
devices. Rotation of the elements is afforded by a feedback control 
circuit which monitors the output optical polarization and derives 
appropriate electrical drive signals to achieve the proper rotation of the 
elements.

DETAILED DESCRIPTION 
Endless polarization controllers are ideally suited for applications in 
fiber optic coherent communication systems, where polarization controllers 
of essentially unlimited (endless) transformation ranges are needed to 
match the optical polarization states of the local oscillator laser and 
the received optical signal. The preferred embodiment of the polarization 
controller utilizes the electrooptic effect and is realized with 
integrated-optic strip waveguides. It allows general polarization 
transformations from arbitrarily varying input optical polarization states 
into any arbitrary output optical polarization state, requiring from the 
control circuit six drive voltages of limited range depending on two 
independent variables. Both analog and digital control circuits have been 
utilized to generate the independent electrical drive signals. The digital 
control circuit offers the advantage of higher speed operation over the 
analog control circuit. 
An analysis of the operation of a reset-free polarization controller is 
based on three cascaded endlessly rotatable fractional wave elements: a 
first quarter-wave plate 10 followed by a half-wave plate 11 and a second 
quarter-wave plate 12 that is rotated synchronously with the first 
quarter-wave plate 10. Synchronous operation of the quarter-wave plates 10 
and 12 is indicated by dashed line 13. It is shown that, for any arbitrary 
angular offset between the outermost elements, quarter-wave plates 10 and 
12, the controller allows continuous and reset-free transformations from 
any varying general input state of polarization into any general output 
state of polarization. It is understood by persons skilled in the art that 
orientation of the fractional wave elements refers to the angular 
orientation of the same selected principal axis, either ordinary or 
extraordinary, with respect to a selected reference direction. The 
principal axes are contained in a plane which, for each fractional wave 
element, is perpendicular to the propagation axis of the optical beam 
through the controller. Dots on each wave plate depict the point at which 
the propagation axis passes through each wave plate. 
The arrangement shown in FIG. 1 allows general polarization transformations 
of unlimited range from the varying polarization state of input optical 
beam 1 to the desired polarization state of output optical beam 2, if all 
three wave plates 10, 11, and 12 are independently rotatable. In FIG. 1, 
however, the second quarter-wave plate is rotated synchronously with the 
first quarter-wave plate, such that their relative orientation is always 
constant. Hence, the polarization controller permits adjustment of only 
two independent parameters, namely, the angular orientation of 
quarter-wave plate 10 indicated as .alpha./2 and the angular orientation 
of center half-wave plate 11 indicated as .gamma./2. The angular offset of 
second quarter-wave plate 12 relative to first quarter-wave plate 12 is 
indicated as .epsilon./2 and can be arbitrary in the range between 0 and 
2.pi.. In particular, quarter-wave plate 12 can be angularly oriented 
parallel to the first quarter-wave plate (.epsilon.=0). In this case, the 
entire controller acts like an endlessly rotatable wave plate with 
endlessly adjustable linear phase retardation. When .epsilon.=.pi. 
(crossed quarter-wave plates), the controller acts like a generalized 
half-wave plate, producing endlessly adjustable elliptical birefringence 
of constant phase retardation .pi.. 
The arrangement in FIG. 1 is realizable by using bulk optics which are 
commercially available and are well known to persons skilled in the art. 
Transducers or electromechanically controlled rotation stages (not shown) 
for the wave plates are available for varying the angular orientation of 
each wave plate. A control circuit similiar to the one shown in FIG. 3 can 
be adapted for use with the wave plates and rotation stages in order to 
generate control signals for causing rotation of the wave plates and for 
insuring synchronous rotation of quarter-wave plates 10 and 12. 
An integrated-optic realization of the arrangement in FIG. 1 is shown in 
FIG. 2. The polarization controller is fabricated on a low birefringence, 
x-cut, z-propagation LiNbO.sub.3 substrate 20 and operates with a standard 
titanium-indiffused, single-mode waveguide 21. It employs three cascaded 
electrode sections corresponding to the three rotatable fractional wave 
plates. Each section induces an adjustable combination of TE TM mode 
conversion and relative TE-TM phase shifting, that is, linear 
birefringence of variable orientation but constant phase retardation. TE 
TM mode conversion is accomplished via the r.sub.61 electrooptic 
coefficient by applying common drive voltage component V.sub.Ci, where 
i=1, 2, or 3, to the section electrode pairs on either side of electrode 
25 on top of waveguide 21, namely, electrodes 22--22', electrodes 23--23', 
and electrodes 24--24', while TE-TM phase shifting is accomplished via the 
r.sub.22 and r.sub.12 electrooptic coefficients by applying opposite drive 
voltage components V.sub.Si /2 and -V.sub.Si /2 to the section electrode 
pairs on either side of electrode 25. Center electrode 25 over waveguide 
21 is shown connected to ground. It is understood that the drive voltage 
components and the ground potential may be applied in different 
combinations to the three electrodes (e.g., electrodes 22, 22', and 25) in 
a particular section without departing from the spirit and scope of the 
invention. 
The first electrode section comprising electrodes 22 and 22' and grounded 
electrode 25 is driven by voltages 
EQU V.sub.C1 =(V.sub.0 /2) sin .alpha. 
EQU V.sub.S1 =V.sub.T +(V.sub..pi. /2) cos .alpha.. 
When driven by these voltages, the section of the integrated-optic device 
acts like a quarter-wave plate oriented at a variable angle .alpha./2. 
The second electrode section comprising electrodes 23 and 23' and grounded 
electrode 25 is driven by voltages 
EQU V.sub.C2 =V.sub.0 sin .gamma. 
EQU V.sub.S2 =V.sub.T +V.sub..pi. cos .gamma.. 
When driven by these voltages, the section of the integrated-optic device 
acts like a half-wave plate oriented at a variable angle .gamma./2. 
The third electrode section comprising electrodes 24 and 24' together with 
grounded electrode 25 is driven by voltages 
EQU V.sub.C3 =(V.sub.0 /2) sin (.alpha.+.epsilon.) 
EQU V.sub.S3 =V.sub.T +(V.sub..pi. /2) cos (.alpha.+.epsilon.). 
When driven by these voltages, this section of the integrated-optic device 
acts like a quarter-wave plate oriented at a variable angle 
(.alpha.+.epsilon.)/2. 
In the equations defining the drive voltages to all three electrode 
sections described above, V.sub.0 denotes the voltage required for 
complete TE TM mode conversion and V.sub..pi. denoted the voltage for 
inducing a TE-TM phase shift of .pi.. Additional bias voltage V.sub.T is 
applied to compensate for any residual birefringence in the waveguide. In 
an illustrative example of the polarization controller in operation, the 
bias voltages were determined as follows V.sub.0 .apprxeq.19 V, V.sub..pi. 
.apprxeq.26 V, and V.sub.T .apprxeq.54 V where the polarization controller 
had a length of approximately 5.2 cm. 
For practical applications, two special cases .epsilon.=0 and 
.epsilon.=.pi. are of particular interest. In the first case, both 
quarter-wave plate sections are driven by the same voltages, 
EQU V.sub.C3 =V.sub.C1 
EQU V.sub.S3 =V.sub.S1 
whereas in the second case, the two quarter-wave plate sections are 
essentially driven by voltages of opposite polarities, 
EQU V.sub.C3 =-V.sub.C1 
EQU V.sub.S3 =-V.sub.S1 +2V.sub.T. 
The following is a more detailed description of the electrooptic operation 
within the polarization controller. In the crystal orientation of FIG. 2, 
TE-TM phase shifting is accomplished via the r.sub.22 and r.sub.12 
electrooptic coefficients (r.sub.12 =-r.sub.22 
.apprxeq.3.4.times.10.sup.-12 m/V) by applying a voltage V.sub.Si, for 
i=1, 2, or 3, across the two outer electrodes, which induces an electric 
field E.sub.y in the waveguide 21. The relative TE-TM phase shift 
2.zeta..sub.i induced in an electrode section of length L.sub.i is given 
by 
##EQU1## 
where .GAMMA..sub.y is the spatial overlap of the applied electric field 
E.sub.y with the optic fields (0.ltoreq..GAMMA..sub.y .ltoreq.1), 
.lambda.o the wavelength in free space, n.sub.o the ordinary index of 
refraction, W is the width of the center electrode, and G the width of the 
gaps between the center and the outer electrodes. 
TE TM mode conversion is accomplished via the r.sub.61 electrooptic 
coefficient (r.sub.61 =-r.sub.22) by applying a voltage V.sub.Ci across 
the center and the side electrodes, which induces a field E.sub.x in the 
waveguide. The phase retardation 2.eta..sub.i for mode conversion induced 
in an electrode section of length L.sub.i is 
##EQU2## 
where .GAMMA..sub.x is the spatial overlap of the applied electric field 
E.sub.x with the optic fields (0.ltoreq..GAMMA..sub.x .ltoreq.1). The 
voltage amplitudes V.sub.0 and V.sub..pi. are adjusted such that at the 
wavelength of operation -.pi./4.ltoreq..zeta..sub.i, .eta..sub.i 
.ltoreq..pi./4 in the two sections of quarter-wave plates, i=1,3, and 
-.pi./2.ltoreq..zeta..sub.2, .eta..sub.2 .ltoreq..pi./2 in the half-wave 
plate section where i=2. 
It follows that the polarization controller can easily be tuned in 
wavelength over the entire range of single-mode operation by adjusting 
V.sub.0 and V.sub..pi. to the new wavelength of operation. However, 
complete mode conversion (.eta..sub.i =.pi./2) requires identical 
propagation constants for the TE and TM polarized modes. That is, there is 
no static birefringence in the waveguide. This can be achieved by 
propagating the light slightly off the z-axis (.apprxeq.1.degree. in the 
yz-plane), such that the positive waveguide birefringence is largely 
compensated for by the negative crystal birefringence. Any remaining small 
birefringence .DELTA.n can be reduced further by applying a bias voltage 
V.sub.T to the phase shifter electrodes to induce a differential index 
change of exactly opposite sign, i.e., -.DELTA.n=.GAMMA..sub.y 
n.sub.o.sup.3 r.sub.22 V.sub.T /(2G+W). 
In spite of the fact that the r.sub.61 coefficient for mode conversion in 
z-propagation LiNbO.sub.3 is only about 12% of the corresponding r.sub.51 
coefficient in y-propagation LiNbO.sub.3, it turns out that the voltages 
required for complete mode conversion are comparable because the overlap 
parameter .GAMMA..sub.x in the z propagation device is substantially 
larger than the corresponding parameter in a y-propagation device. The 
voltages for TE-TM phase shifting are also comparable because the 
effective electrooptic coefficient in z-propagation LiNbO.sub.3 is about 
30% of that in y-propagation LiNbO.sub.3. Typical voltages for a 20 mm 
(length) electrode section at .lambda..sub.0 =1.5 .mu.m are V.sub..pi. 
.apprxeq.25 V and V.sub.0 .apprxeq.20 V. 
In practical realizations, slight misalignment of the electrodes may cause 
cross modulation between the two voltages, i.e., the voltage V.sub.Ci not 
only induces the desired TE TM mode conversion but also a small amount of 
TE-TM phase shifting, and likewise, the voltage V.sub.Si may also induce a 
small amount of undesired TE TM mode conversion. This effect causes a 
deviation from the ideal transfer function and hence leads to increased 
polarization crosstalk in the output of the transformer. This non-ideal 
behavior may be compensated for by pre-distorting (mixing) the drive 
voltages V.sub.Ci and V.sub.Si. But such pre-distortion has not yet proved 
necessary in operation of the polarization controller. 
In the following paragraphs, the transfer function of the polarization 
controller is derived and it is shown to describe general polarization 
transformations of unlimited range. For this analysis, it is assumed that 
the waveguide is lossless and that it supports only the fundamental TE- 
and TM-polarized modes. By neglecting the lateral mode distributions as 
well as the common time and space dependent factors, the relative 
amplitudes and phases of the TE- and TM polarized modes are described by 
complex numbers a.sub.1 and a.sub.2, with .vertline.a.sub.1 
.vertline..sup.2 +.vertline.a.sub.2 .vertline..sup.2 =1. A general state 
of polarization (state of optical polarization) is then represented by a 
normalized Jones vector, 
##EQU3## 
where .theta. and .phi. characterize the relative amplitudes and phases of 
the left and right circular polarization states, with 
0.ltoreq..theta..ltoreq..pi./2 and 0.ltoreq..phi..ltoreq.2.pi.. The 
transfer function of a quarter-wave plate oriented at an azimuth .alpha./2 
is described by a Jones matrix, 
##EQU4## 
and that of a rotatable half-wave plate oriented at an azimuth .gamma./2 
by, 
##EQU5## 
The overall transfer matrix of the entire cascade of elements for the 
controller shown in FIGS. 1 and 2 is then given by 
T=Q.sub..alpha.+.epsilon. .multidot.H.sub..gamma. .multidot.Q.sub..alpha. 
and calculated as, 
##EQU6## 
The matrix T describes general elliptical birefringence, where 2 arc sin B 
is the total amount of induced linear phase retardation at 0.degree. 
(TE-TM phase shifting), 2 arc sin D the amount of induced linear phase 
retardation at 45.degree. (TE TM mode conversion), and 2 arc sin C the 
amount of circular phase retardation. The total amount of induced 
elliptical phase retardation .psi. is given by cos .psi.=2A.sup.2 -1. 
It can be shown with the latter equations that T describes general 
transformations from any arbitrary input into any arbitrary output state 
of optical polarization. Moreover, for any arbitrary offset .epsilon., it 
is found that the transformation range of T is unlimited if .alpha. and 
.gamma. are endlessly adjustable. By applying T to a general input state 
of optical polarization of the form shown above with .theta..sub.in and 
.phi..sub.in arbitrary, .theta..sub.out and .phi..sub.out of the output 
optical state of optical polarization are given as follows, 
##EQU7## 
where .alpha.'=.alpha.+.epsilon. and, 
EQU X.sub.in =sin 2.theta..sub.in cos (.phi..sub.in -.epsilon.) 
EQU Y.sub.in =cos 2.theta..sub.in 
EQU Z.sub.in =sin 2.theta..sub.in sin (.phi..sub.in -.epsilon.). 
It follows from the equations immediately above that for any given input 
state of optical polarization, there exists at least one transformation T 
that yields the desired output state of optical polarization. The desired 
transformation is obtained when .alpha.' and .gamma.' satisfy the 
conditions, 
##EQU8## 
Since these equations describe all possible input and output polarization 
states, it follows from the latter set of equations immediately above that 
for any general input state of optical polarization, there exist at least 
four combinations of .alpha.' and .gamma.' in the range 0.ltoreq..alpha.', 
.gamma..ltoreq.2.pi. that yield the desired general output state of 
optical polarization. If {.alpha.',.gamma.'} is one such combination, then 
it is possible to find the other three at {.alpha.'.+-..pi.,-.gamma.'}, 
{.alpha.',.gamma.'.+-..pi.}, and {.alpha.'.+-..pi.,-.gamma.'.+-..pi.}. 
This is demonstrated when the optical power transfer from a general input 
state of optical polarization into a general output state of optical 
polarization is mapped as a function of .alpha. and .gamma.. Such a 
mapping clearly displays four absolute maxima where all output power is in 
the desired output state of optical polarization as well as four absolute 
minima where all output power is in the undesired cross polarization 
state. There are no secondary maxima or minima in such a mapping. When the 
input and/or output state of optical polarization is varied, the four 
maxima (and minima) change their positions in the parameter space but they 
always remain absolute maxima (or minima). This unique feature allows 
automatic polarization stabilization via a simple electronic feedback 
circuit that searches for maximum output power in the desired output state 
of optical polarization. 
From the equations above it is reasonable to conclude that the 
transformation range of T is unlimited if .alpha. and .gamma. are 
endlessly adjustable. It then follows that the polarization controller 
allows continuous and reset-free transformations between any two endlessly 
varying general polarization states. 
The transformer of FIG. 2 allows general polarization transformations of 
infinite range. Moreover, automatic polarization control does not require 
a sophisticated polarization analyzer. As evident from FIG. 3, the desired 
values for .alpha. and .gamma. can be found by simply monitoring the power 
in the selected output state of optical polarization. Furthermore, the 
simple drive voltage generation circuitry allows automatic polarization 
stabilization via an entirely analog or digital electronic feedback 
circuit. The error signals are derived by dithering .alpha. and .gamma. 
independently. The resulting dither in the output state of optical 
polarization of the polarization controller converts into intensity 
modulation after the polarization dependent element (or a simple 
polarizer) and is then detected via phase-sensitive detectors. It is then 
possible either to maximize or to minimize the output power in the 
selected output state of optical polarization, depending on the settings 
of the outputs from the comparators in the phase-sensitive detectors. 
This automatic control loop is capable of maintaining the desired output 
state of optical polarization even in the degenerated cases where the 
values for .alpha. and .gamma. are not uniquely determined and hence may 
fluctuate randomly. For transformations close to the degenerated cases, it 
has been found that small changes in the input state of optical 
polarization require large changes in the drive voltages. This is easily 
verified on the Poincare sphere. If in the case of .epsilon.=.pi., for 
example, the input state of optical polarization traces a small circle 
centered at the antipode of the output state of optical polarization, then 
maintenance of the output state of optical polarization requires large 
changes in .alpha. or .gamma. independent of how small the radius of the 
circle is. In the case of .epsilon.=0, the same variations in the input 
state of optical polarization require only small changes in .alpha. and 
.gamma.. Likewise, if the input state of optical polarization traces a 
circle around a point having the same longitude as the output state of 
optical polarization but opposite latitude, then maintaining the output 
state of optical polarization requires large changes in .alpha. or .gamma. 
for a transformer with .epsilon.=0, but only small changes in .alpha. and 
.gamma. for .epsilon.=.tau.. 
From the above considerations, it is reasonable to conclude that any 
polarization transformer with only two independent variables may face 
situations, in which small changes in the input state of optical 
polarization require large changes in the control variables. These large 
changes, which are undesired because they may limit the control speed of 
the device, could be avoided by employing a third independent control 
variable, such as .epsilon. in the present arrangement, as well as a 
complicated drive algorithm that constantly analyzes the input state of 
optical polarization. The substantially simpler drive algorithm for 
schemes with only two independently adjustable parameters allows much 
faster polarization control and is therefore preferable. 
In an illustrative embodiment of the polarization controller, a digital 
control circuit as shown in FIG. 3 is employed to monitor the output 
optical power in the desired output polarization and to generate the 
proper drive voltages to achieve polarization control of the polarization 
of the input optical beam. Moreover, the drive signals generated for both 
outermost fractional wave elements are generated in a manner to maintain a 
constant angular offset between the orientations with respect to the same 
principal axis of both elements. That is, both fractional wave elements 
are controlled to rotate synchronously so that an offset angle .epsilon. 
is maintained constant between these two elements. 
The feedback circuit of FIG. 3 continuously monitors the power in the 
desired output polarization state using a slow-speed photo-diode and a 
conventional polarization beam splitter cube as the discriminator. It 
searches for maximum power in the desired polarization state by dithering 
the output polarization via .alpha. and .gamma.. This small dither is 
converted into intensity modulation by the polarization splitter and then 
analyzed by two phase sensitive detectors, which adjust the drive voltages 
to minimize the modulation component at the fundamental dither frequency. 
Polarization beam splitter 31 is used here to allow simultaneous detection 
of the optical power in the orthogonal cross polarization state. In 
practical application, splitter 31 may be replaced by a simple polarizer. 
As shown in FIG. 3, the digital control circuit includes optical receiver 
37, phase sensitive detector 33, clock gating circuit 34, digital sine 
generator 35 and amplifier 36. Conventions used for the symbols in FIG. 3 
are given as follows: S/H stands for sample and hold, T/4 and T/2 stand 
for time delay elements introducing delays of T/4 time units and T/2 time 
units, respectively. Drive voltages V.sub.1 through V.sub.4 are generated 
by two digital sine-wave synthesizers 351 and 353 in digital sine 
generator 35 and an array of fast, high-voltage operational amplifiers 361 
through 368 in amplifier circuit 36. The synthesizers are arranged to 
produce pairs of sinusoids (sine and cosine, each of .alpha. and .gamma.) 
and allow endless adjustment of .alpha. and .gamma. with a step resolution 
of 5.6.degree. in this exemplary embodiment. Each pair of sinusoids is 
generated by a synthesizer (elements 351 or 353) composed of a 64-step 
digital up-down counter controlled by the outputs of clock gating circuit 
34, two read-only memories addressed by the respective counter outputs 
with look-up tables for the sine and cosine functions, and two 
digital-to-analog converters to convert the digital amplitude read from 
the memory into an analog value supplied to amplifiers 36. The size of the 
look-up table in each synthesizer controls the step resolution of the 
generated sinusoids. Counters in synthesizers 351 and 353 dither .alpha. 
and .gamma. in phase quadrature at a common frequency of 88 kHz (output 
from the divide-by-4 circuit in clock gating circuit 24) with a peak 
deviation of 5.6.degree.. Time delay 352 causes voltage adjustments 
affecting .alpha. (drive voltages V.sub.1, V.sub.2, V.sub.5 and V.sub.6) 
to be out of phase with corresponding adjustments affecting .gamma. (drive 
voltages V.sub.3 and V.sub.4). 
Phase-sensitive detector circuit 33 employs four sample-and-hold amplifiers 
330-333 followed by analog-to-digital converters (included in the output 
stage of each sample-and-hold) and digital magnitude comparators 338 and 
339. Each portion of the phase sensitive detector circuit 33 re-adjusts 
.alpha. and .gamma. in every second dither cycle by one step increment up 
to a rate of 4300 rad/sec, which is much faster than an analog 
implementation. Timing element 334 divides the clock from clock generator 
347 by an appropriate amount, for example, by 8. Element 334 then reduces 
the duty cycle of the supplied, divided-down, clock pulses. Clock pulses 
delivered to the upper phase comparator cause sample and hold 330 to be 
activated approximately one-half a dither period (T/2, where T is dither 
period) after sample and hold 331. Comparator 338 compares both sample and 
hold outputs to determine whether the latest sample is less than, greater 
than, or equal to, the prior sample. A similar set of operations occurs in 
the lower portion of the phase sensitive detector. It should be noted that 
time delay 336 causes sampling in the upper portion of detector 33 to 
alternate with sampling in the lower portion of detector 33. The sample 
and hold elements are activated in any given clock period T in the 
following order: element 331, element 333, element 330, and then element 
332. In this manner, the entire digital control circuit corrects .alpha. 
substantially mutually exclusive of corrections to .gamma.. 
Clock gating circuit 34 provides the basic clock signals used in the 
control circuit as well as gating logic to select the proper correction 
for .alpha. and .gamma.. Clock gating circuit 34 receives each decision 
from comparators 338 and 339. Time delays 344, 345, and 346 delay the 
clock signal from timing circuit 334 so that each NAND gate 340-343 is 
triggered in a different exclusive time interval. The signal (high speed 
clock) from clock circuit 347 triggers AND gates 348 and 349 to deliver 
clock pulses and, if necessary, a correction pulse to the counters in 
synthesizers 351 and 353, respectively. 
Divide-by-4 logic 360 divides the output clock signal from clock circuit 
347. Its output is connected to the counters in the synthesizers to define 
the direction of the count, i.e., up or down. This permits the functions 
sin .alpha., cos .alpha., sin .gamma. and cos .gamma. to be dithered back 
and forth within a given dither period. 
As the drive voltages to the polarization controller are varied, the 
controller outputs are received, detected, and compared. But when it is 
necessary to adjust the drive voltages so that they are dithered about an 
operating point different from the current operating point, the clock 
gating circuit causes an additional clock pulse to appear from either gate 
348 or 349 or both, depending upon the correction desired. This additional 
clock pulse causes the corresponding counter to increment or decrement by 
one. The phase of the signal from element 360 controls incrementing or 
decrementing of a counter in response to the additional clock pulse. 
At the output of amplifier circuit 36, drive voltages V.sub.1 through 
V.sub.4 are shown. While not shown, it should be understood by those 
persons skilled in the art that the additional drive voltages V.sub.5 and 
V.sub.6 are easily derived via an amplifier circuit combining V.sub.1 with 
V.sub.T and combining V.sub.2 with V.sub.T for a value of .epsilon.=.pi. 
resulting in the two outermost sections of the polarization controller 
being in a crossed position relative to each other. Drive voltages are 
applied to the electrodes in the following manner: V.sub.1 =V.sub.C1 
+V.sub.S1 /2 applied to electrode 22, V.sub.2 =V.sub.C1 -V.sub.S1 /2 
applied to electrode 22'. V.sub.3 =V.sub.C2 +V.sub.S2 /2 applied to 
electrode 23, V.sub.4 =V.sub.C2 -V.sub.S2 /2 applied to electrode 23', 
V.sub.5 =V.sub.C3 +V.sub.S3 /2 applied to electrode 24, and V.sub.6 
=V.sub.C3 -V.sub.S3 /2 applied to electrode 24'. For the crossed 
orientation of the outermost sections, V.sub.5 =-V.sub.1 +V.sub.T and 
V.sub.6 =-V.sub.2 -V.sub.T. Clearly, this maintains a constant angular 
offset .epsilon.=.pi. between the first and third sections of the 
polarization controller. 
For the value of .epsilon.=0, the voltages applied to electrodes 22 and 22' 
are applied to electrodes 24 and 24', respectively. As such, no additional 
circuitry is required for generating drive voltages V.sub.5 and V.sub.6. 
When the value of .epsilon. is an arbitrary value, an additional read only 
memory is required wherein the memory is loaded with an appropriate 
look-up table for generating the sine and cosine functions for the angle 
(.alpha.+.epsilon.). The output from such a memory is supplied to an 
amplifier circuit similar to the ones shown in amplifier 36 for generating 
drive voltage V.sub.5 and V.sub.6. 
To measure the response time of the entire control system, the feedback 
circuit is turned off and the input polarization of the controller is 
adjusted such that all output light is in the undesired cross polarization 
state. When the feedback circuit is turned on, it takes the polarization 
controller with its control circuit less than 500 .mu.sec to induce the 
.pi. phase retardation required to transform the output optical beam into 
the desired polarization state. It is noted that the induced phase 
retardation changes linearly with time at a rate of 6300 rad/sec, which is 
more than 100 times faster than any previously reported speed. As a result 
of the polarization dither, about 2.5% of the output light remains in the 
undesired orthogonal cross polarization state. This level can thus be 
reduced at the expense of control speed by decreasing the step increments 
in the sine-wave synthesizers. 
An example of automatic continuous stabilization (control) of a rapidly 
fluctuating optical polarization state is shown in FIG. 4. Here, the 
feedback circuit is initially turned off, as shown in FIG. 4 under the 
heading labelled "OFF" to demonstrate the large and fast changes in the 
input polarization state of the controller, which are generated by a 
second LiNbO.sub.3 polarization transformer and which fluctuate 
periodically at rates of up to 4900 rad/sec. With the feedback circuit 
turned on, the controller automatically stabilizes the output polarization 
state and maximizes the optical power in the desired polarization state 
40, as shown in FIG. 4 under the heading labelled "ON." About 4% of the 
output light is in the orthogonal cross polarization state 41, which is 
slightly higher than for a slowly varying input polarization state because 
the feedback circuit operates close to its speed limit. The corresponding 
drive voltages V.sub.1 through V.sub.4 are shown as curves 42 through 45, 
respectively, in FIG. 4. Curves 42 to 45 clearly show the periodic 
variations in the voltages under automatic control. The periodic dither in 
the voltages with the exemplary dither period of 11 .mu.sec is too fast 
and too small to be resolved in curves 42 to 45. 
For the exemplary controller shown in FIG. 2 in combination with the 
feedback control circuit shown in FIG. 3, the measured optical bandwidth 
was estimated at approximately 50 mm with a wavelength tuning range 
greater than 100 nm. Optical bandwidth and wavelength tuning range are 
effected by adjustments to the drive voltage components V.sub.0 and 
V.sub..pi.. 
In the description above, the illustrative embodiment were depicted using 
zero-order fractional wave elements. It should now be understood by those 
persons skilled in the art that higher order fractional wave elements may 
be substituted for the zero-order fractional wave elements. Higher order 
quarter-wave elements provide phase retardation proportional to 
(2n+1).pi./2 while higher order half-wave elements provide phase 
retardation proportional to (2m+1).pi./2, where m and n are positive 
integers greater than zero. Any combination of zero order and higher order 
elements is contemplated. With respect to the nominal operational 
wavelength for the polarization controller, it is understood by persons 
skilled in the art how to design the waveguide in the controller for 
guiding optical beams at wavelengths other than the exemplary wavelength 
described above. It is further understood by persons skilled in the art 
that, while a titanium-indiffused waveguide structure for a lithium 
niobate controller is the preferred design, other waveguide formations are 
contemplated and other substrates are contemplated including but not 
limited to semiconductor materials and lithium tantalate, for example.