The state of polarization of an input light beam is tested by determining four components of a Stokes vector of the light. These correspond to components of the light in three polarization states, S.sub.1 : linear horizontal, S.sub.2 : linear at 45 degrees, S.sub.3 : right circularly polarized, and S.sub.0 the total power. It is not necessary to filter out these components directly and measure their powers. In accordance with this invention it is more convenient to measure the powers in three arbitrary polarization states that have known relationships to each other, and, also measure the total power. The actual Stokes vector components is calculated from this information. Conveniently, a device having three polarization beam splitting surfaces and a prism provides a novel way in which to obtain the necessary information from an input beam so that a set of equations can be solved to determine the state of polarization the input beam.

FIELD OF THE INVENTION 
This invention relates to an optical circuit and method for measuring the 
state of polarization (SOP) of an input beam of light. The acronyms SOP 
and S.o.P. have been used interchangeably through this specification. 
BACKGROUND OF THE INVENTION 
As the demand for longer transmission distances and higher information 
transfer rates for optical fibre communication increases, so does the 
importance of measuring the state of polarization of light within an 
optical fibre. The transfer properties of some optical devices such as 
polarization dependent isolators, couplers and optical amplifiers depend 
on the polarization state of light launched into them. To completely 
characterize these devices, the relationship of the input and output 
states of polarization (SOP) of the optical system must be known. 
One known way of measuring the SOP of a light beam is to align a waveplate 
and a linear polarizer in the optical path of the beam. The waveplate is 
rotatable about the optical axis and typically is a quarter-wave plate. An 
optical sensor, a photodetector, is positioned to measure the intensity of 
light transmitted by the waveplate and polarizer. In operation the 
waveplate is sequentially rotated to a minimum of four angular positions 
about the optical axis relative to the linear polarizer and the 
transmitted light intensity is measured at each position by the 
photodetector. A disadvantage of this method is the mechanical movement of 
the waveplate and the resulting slow speed of measurement. Additionally, 
since every optical element has to align in free space, miniaturization of 
such a device in not possible. 
Several polarimeters are described in U.S. Pat. No. 5,815,270 in the name 
of Lee, entitled IN-LINE FIBER-OPTIC POLARIMETER USING A FUSED 1.times.5 
STAR COUPLER. Lee's polarimeter shown in prior art FIG. 1, and other prior 
art polarimeters as well, depend on splitting a beam of light through a 
splitter and passing the sub-beams into three polarizing fibres. In FIG. 1 
a single beam launched into a 1.times.5 star coupler provides sub-beams to 
three polarizers 22, 38, and 40. In Lee's disclosure, polarizing fibres 
are utilized. Although Lee's device performs its intended function, this 
and other devices based on using a plurality of polarizers are not 
particularly efficient since only a fraction of the light in each of three 
beams being launched into respective polarizers 22, 38, and 40 in Lee's 
device is utilized. Stated differently, each detector at the output of a 
polarizer is only detecting a fraction of the light launched into a 
polarizer, and hence, a considerable amount of energy is wasted. 
It is an object of this invention to provide an optical circuit and method 
for determining the SOP which conserves energy, wherein most of the input 
light is directed to the detectors. 
In contrast to the prior art devices, the method and circuit does not 
"spill or reject" much of the light launched into the polarimeter. Most of 
the light under test in accordance with this invention is utilized, and 
advantageously, less light is required. 
SUMMARY OF THE INVENTION 
In accordance with the invention, a method is provided of determining a 
state of polarization of a beam of light comprising the steps of: 
providing a first beam; 
providing an optical system for splitting the beam of light in a 
polarization dependent manner and for polarizing at least a split portion 
of the beam and for retarding a split portion of the beam; 
dividing the first beam into two sub-beams; 
dividing each of the two sub-beams into two further sub-beams to obtain 
four sub-beams of light, wherein at least the dividing of the first beam 
or the dividing of the two sub-beams is performed in a polarization 
dependent manner; 
passing a first of the four sub-beams of light through a polarizing element 
to obtain a first polarized beam of light; 
passing a second of the four sub-beams of light to a phase retarding 
element for altering relative phase between orthogonal components of the 
second of the four sub-beams of light and subsequently passing said beam 
through a polarizing element to obtain a second polarized beam of light; 
detecting the intensity of the first polarized beam, the second polarized 
beam, and the two remaining sub-beams of; and, 
in dependence upon the detected intensities and properties of the optical 
system determining the state of polarization of the input beam. 
In accordance with the invention there is further provided, a method of 
determining a state of polarization of a beam of light comprising the 
steps of: 
providing a first beam; 
providing an optical system for splitting the first beam of light and for 
polarizing at least a split portion of the beam and for phase retarding a 
split portion of the beam; 
dividing the first beam into two sub-beams; 
dividing each of the two sub-beams into two further sub-beams to obtain 
four sub-beams of light dividing the first beam into two sub-beams; 
dividing each of the two sub-beams into two further sub-beams to obtain 
four sub-beams of light, wherein at least the dividing of the first beam 
or the dividing of the two sub-beams is performed in a polarization 
dependent manner; 
causing a phase retardation in at least one of the sub-beams; 
detecting the intensity of the each of the four sub-beams; and, 
in dependence upon the detected intensities solving a system of equations 
that characterize the optical system to determine the state of 
polarization of the input beam. 
In accordance with another aspect of the invention there is provided a 
device for measuring the state of polarization of a first beam of light 
comprising an optical system including: 
a) a first beam splitter for dividing the first beam into two sub-beams; 
b) a second beam splitter for dividing each of the two sub-beams into two 
further sub-beams to obtain four sub-beams of light, wherein at least the 
first or the second beam splitter is for splitting a beam into two beams 
in a polarization dependent manner; 
c) a phase retarding interface for phase retarding at least one of the 
sub-beams of light, and the device comprising 
d) detectors for detecting the intensity of the sub-beams of light; and, 
e) electronic processing means coupled with the detectors for solving a 
system of equations that characterize an aspect of the optical system to 
determine the state of polarization of the input beam in dependence upon 
the detected intensities. 
Yet still further in accordance with said other aspect of the invention a 
device is provided for measuring the state of polarization of an input 
beam of light comprising: 
a) a beam splitting interface for dividing the first beam into two 
sub-beams .alpha..sub.1 and .alpha..sub.2 in a polarization dependent 
manner; 
b) a beam splitting interface for dividing the sub-beam .alpha..sub.1 into 
two further sub-beams .beta..sub.1 and .beta..sub.2 in a polarization 
dependent manner; 
c) a beam splitting interface for dividing the sub-beam .alpha..sub.2 into 
two further sub-beams .gamma..sub.1 and .gamma..sub.2 in a polarization 
dependent manner; 
d) a phase retarding interface for phase retarding the sub-beam 
.alpha..sub.2 ; 
e) detectors for detecting the intensity of the sub-beams of light 
.beta..sub.1, .beta..sub.2, .gamma..sub.1, .gamma..sub.2 ; and, 
f) electronic processing means coupled with the detectors for solving a 
system of equations that characterize an aspect of the input light to 
determine the state of polarization of the input beam in dependence upon 
the detected intensities. 
Advantageously, the device in accordance with the invention comprises three 
beam splitting cubes directly coupled to one another absent any air gaps.

DETAILED DESCRIPTION 
Referring now to FIG. 2, a device 100 is shown in the form of a beam 
splitting cube having a polarizer 110a at a first output port and having a 
waveplate 112 and polarizer 110b at another output port. Adjacent the beam 
splitting cube's four output ports are photodetectors D1 to D4 for 
detecting the intensity of light incident upon them. The beam splitting 
cube is comprised of three triangular sections forming three interfaces 
.alpha., .beta., and .gamma.. 
A measure of the SOP and the degree of polarization (DOP) for light 
propagating through the device 100 is calculated by using a Mueller matrix 
formalism. The DOP of a light wave is defined as the ratio of polarized 
power to total power contained in a light beam and a mathematical 
expression is give below. 
First, the Jones matrix representation of the polarization-affecting 
element is provided and subsequently, this matrix is transformed into the 
Mueller realm following the procedure given in "Introduction to Matrix 
Method in Optics" by A. Gerrard and J. M. Burch, Dover Publications, Inc.; 
the procedure is summarized below. 
##EQU1## 
conjugate of the transpose of J. 
##EQU2## 
The approach utilized considers reflection and transmission at the .alpha., 
.beta., and .gamma. interfaces. Let r.sub.p, r.sub.s, t.sub.p and t.sub.s 
be the Fresnel reflection and transmission coefficients at those 
interfaces for p- and s-polarized lightwaves respectively. 
##EQU3## 
transmission matrix, (matrices defined a s in "Introduction to Modem 
Optics" 2.sup.nd Ed., Grant R. Fowles, Dover Publications Inc.). By 
following the prescription above we obtain their Mueller equivalent: 
##EQU4## 
Now considering the device 100 of FIG. 2: 
The Mueller matrices relating the state of polarization (SOP) at detector 
D.sub.i to the input SOP, with no polarizer or waveplate present would be: 
##EQU5## 
If we now consider the general SOP (S.sub.0 S.sub.1 S.sub.2 S.sub.3).sup.1 
and multiply it by the above four matrices we obtain the SOP at each 
output, assuming no polarizers or waveplate. 
##EQU6## 
The symbols are defined as 
##EQU7## 
Consequently, the powers measured at the detectors in the absence of a 
polarizer or waveplate are functions solely of S.sub.0 and S.sub.1 which 
implies that the DOP of the lightwave 
##EQU8## 
The Mueller matrix representation of a linear polarizer oriented at 
45.degree. is 
##EQU9## 
Consequently, adding the polarizer 110a just before D.sub.1 yields 
##EQU10## 
If we add the quarter waveplate 112 at the output near detector 4 we have a 
new SOP given by: 
##EQU11## 
Finally, including a linear polarizer 100b at 45.degree. at the output of 
the waveplate 112 yields 
##EQU12## 
To summarize, the beamsplitter having interfaces .alpha., .beta., and 
.gamma. with polarizers 110a, 110b and waveplate 112 depicted above allows 
the detectors to measure 
##EQU13## 
Of course, the system of four equations and four unknowns can now be solved 
and SOP and the DOP can be calculated. 
For the arrangement of the beam splitting interface shown in the exemplary 
embodiment of FIG. 2, the following conditions should be met. 
R.sub.p =r.sub.p.sup.2, R.sub.s =r.sub.s.sup.2 for all interfaces. 
If R.sub.p .noteq.R.sub.s for all beamsplitting interfaces and R.sub.pors 
.noteq.0 for all interfaces the set of four equations above can be solved. 
Let R.sub.p.sup.a =R.sub.s.sup.a i.e. the first interface splits light in a 
polarization independent manner. This implies that R.sub.-.sup.a 
=T.sub.-.sup.a =0. In order to be able to solve our set of four equations 
above, it is required that C.noteq.0 and L.noteq.0 which translates into 
neither p- nor s-reflectivities being zero for both beta and gamma 
interfaces. 
Furthermore, it is required that B, or E, or H, or K be different from 
zero. This implies that we must have R.sub.p.sup..beta. 
.noteq.R.sub.s.sup..beta. or R.sub.p.sup..gamma. 
.noteq.R.sub.s.sup..gamma.. 
Let R.sub.p.sup..beta. =R.sub.s.sup..beta. i.e. the beta interface splits 
light in a polarization independent manner. This implies that 
R.sub.-.sup..beta. =T.sub.-.sup..beta. =0. In order to be able to solve 
our set of four equations we require that C.noteq.0 and L.noteq.0 which 
translates into neither p- nor s- reflectivities being zero for both alpha 
and gamma interfaces. 
Furthermore, it is required that B, or E, or H, or K be different from 
zero. This implies that we must have R.sub.p.sup..alpha. 
=R.sub.s.sup..alpha. or R.sub.-.sup..gamma. R.sub.+.sup..alpha. 
+R.sub.+.sup..gamma. R.sub.-.sup..alpha. .noteq.0. 
Let R.sub.p.sup..gamma. =R.sub.s.sup..gamma. i.e. the gamma interface 
splits light in a polarization independent manner. This implies that 
R.sub.-.sup..gamma. =T.sub.-.sup..gamma. =0. In order to be able to solve 
our set of four equations we require that C.noteq.0 and L.noteq.0 which 
translates into neither p- nor s- reflectivities being zero for both alpha 
and beta interfaces. 
Furthermore, it is required that B, or E, or H, or K be different from 
zero. This implies that we must have R.sub.-.sup..beta. 
T.sub.+.sup..alpha. +R.sub.+.sup..beta. T.sub.-.sup..alpha. .noteq.0 or 
R.sub.p.sup..alpha. .noteq.R.sub.s.sup..alpha.. 
Of course there are numerous other exemplary configurations that can be 
envisaged within the scope of this invention which have not been shown for 
which a different set of conditions apply. 
Referring now to FIGS. 3a and 3b, an alternative embodiment of the 
invention is shown, which obviates the requirement for the inclusion of 
the polarizers 110a, 110b, and the waveplate 112. Prior to considering the 
embodiment of FIG. 3a and 3b, FIG. 4 is provided as simplified schematic 
diagram to illustrate some of the functional requirements of the device 
shown in FIGS. 3a and 3b which achieves this end. 
FIG. 4 includes three polarization beam splitting interfaces, denoted by 
.alpha., .beta., and .gamma.. Further included is a reflecting surface 210 
that reflects the beam propagating from the interface .alpha. in state b 
in such a way that the plane of incidence of surface 210 with the beam is 
not coplanr with the plane of incidence of the reflection at the interface 
.alpha.. Preferably the reflection at surface 210 defines parallel (p) and 
perpendicular (s) components of polarization that are at an angle of 45 
degrees to the components p and s defined by the reflection at the surface 
210. Rotation of the principle components of polarization between 
reflections is required in order for the equation to be solvable. In the 
embodiment shown if FIG. 2, phase retardation is achieved by passing a 
sub-beam through a quarter waveplate, however the embodiment of FIG. 3a 
and 3b achieves sufficient phase retardation by reflecting the beam off 
two prism faces via total internal reflection. 
Turning now to FIG. 3a, a device is shown having three beam splitting cubes 
310, 320, and 330, having beam splitting interfaces .alpha., .beta., 
.gamma., respectfully. The interfaces are selected such that light 
impinging upon any interface .alpha., .beta., .gamma. is not split into 
beams having exactly the same polarization components; Contacting the beam 
splitting cubes 310 and 330 is a prism 340 disposed at an angle of 
approximately 45 degrees to the beam splitting cubes. This rotation of, 
for example 45 degrees is necessary in order to have enough information to 
solve the set of equations. In operation, an input beam is input into an 
end of the polarization beam splitting cube (BSC) 310. The input beam is 
split in a polarization dependent manner into sub-beams .alpha..sub.1 and 
.alpha..sub.2. Sub-beam .alpha..sub.1 propagates along a straight through 
path end enters the BSC 320 wherein it splits in a polarization dependent 
manner into sub-beams .beta..sub.1 and .beta..sub.2. Sub-beam 
.alpha..sub.2 enters the prism 340 and is reflected two time. The prism is 
oriented in such a manner as to cause the sub-beam .alpha..sub.2 
propagating therein, to be reflected in two different planes of incidence. 
The prism is tilted, in this instance by 45 degrees to ensure that the 
beam reflects in two different planes of incidence from a first face 340a 
in a first plane incidence and subsequently a second face 340b in a second 
plane of incidence of the prism 340 and enters the beam splitting cube 330 
where it is separated into two sub-beams .gamma..sub.1 and .gamma..sub.2 
(.gamma..sub.1 .noteq..gamma..sub.2) corresponding to S3 and S4 
respectively. FIG. 5 shows a more complete detailed diagram of the device 
shown in FIGS. 3a and 3b in accordance with the invention. Of course the 
detectors indicated by symbols D1 through D4 must be coupled to a suitably 
programmed processor or computer to solver required system of equations. 
The matrices linking the SOP at the various detectors to that at the input 
are given by 
##EQU14## 
of the rotation matrix whose representation in Jones formalism is 
##EQU15## 
The matrix representing a total internal reflection is expressed as 
##EQU16## 
which when multiplied by itself yields 
##EQU17## 
Expressed in Mueller formalism, the last matrix becomes 
##EQU18## 
Below is a set of generalized equations for measuring polarization by 
interface reflections. 
An unknown Stokes vector S.sup.o is passed through four optical elements 
with known polarisation transformations M to generate four new optical 
beams with Stokes vectors S.sup.i 
##EQU19## 
The four power measurements D.sup.i are proportional to the first elements 
of the four Stokes vectors S.sup.i.sub.0 
The elements S.sup.i.sub.1 are calculated from the top rows of the four 
Mueller matrices that correspond to the four polarization transformations 
leading to the four measurements D.sup.i 
##EQU20## 
where k is a proportionality constant 
This is a linear system of four equations that can be solved for the 
components of the unknown stokes vector S.sup.o. Rewrite the equations as 
##EQU21## 
The matrix .GAMMA. is a established by calibrating the device. The input 
Stokes polarisation vector is then determined by the matrix operation. 
##EQU22## 
Of course, numerous other embodiments of the invention may be envisaged, 
without departing from the spirit and scope of the invention. For example, 
FIG. 6 illustrates another embodiment wherein three beam splitting cubes 
62a, 62b, and 62c are oriented in a predetermined manner and optically 
coupled to a prism 68.