Polarization mode dispersion measuring instrument and method

A polarization mode dispersion measuring apparatus includes a variable wavelength light source for providing light of a variety of wavelengths; a light intensity modulator optically connected to the light source to provide light of modulated intensity; a polarization controller optically connected to the light intensity modulator to provide light of controlled polarization; a beam splitter optically connected to the polarization controller to provide beams of p and s polarization components; an O/E conversion unit optically connected to the beam splitter to provide electrical signals with respect to the beams of the p and s polarization components; and an analyzing unit for controlling the light intensity modulator to provide a sine wave of a predetermined frequency and a predetermined intensity, and the light source and the polarization controller to determine parameters of Jones matrix from the electrical signals and a polarization mode dispersion defined by the parameters, thereby measuring a polarization mode dispersion of an object placed between the polarization controller and the beam splitter.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to methods of and apparatus for measuring the 
polarization mode dispersion of optical fibers for use in optical 
communications. 
2. Description of the Related Art 
In optical communications, polarization planes are used to provide multiple 
values for increasing information amounts or contents of optical signals. 
Consequently, it is necessary to use optical fibers having identical 
polarization modes and, therefore, to measure the polarization mode 
dispersion for each guide wave frequency. 
The polarization mode dispersion defined by Stokes parameters has been used 
for such measurement. The Stokes parameters include four parameters for 
expressing the polarization conditions including the polarization degree. 
If orthogonal x and y components of elliptically polarized light are 
EQU Ex=Ax cos (.omega.t-.DELTA.x) 
EQU Ey=Ay cos (.omega.t-.DELTA.y) 
EQU .DELTA.y-.DELTA.x=.DELTA. 
then respective parameters S.sub.0, S.sub.1, S.sub.2, and S.sub.3 are 
expressed as 
EQU S.sub.0 =Ax.sup.2 +Ay.sup.2 
EQU S.sub.1 =Ax.sup.2 -Ay.sup.2 
EQU S.sub.2 =2AxAy cos .DELTA. 
EQU S.sub.3 -2AxAy sin .DELTA. 
For perfectly polarized light, S.sub.0.sup.2 =S.sub.1.sup.2 +S.sub.2.sup.2 
+S.sub.3.sup.2. Since S.sub.0 is a parameter for expressing the light 
intensity, the polarization mode dispersion is given by the following 
expressions: 
##EQU1## 
FIG. 2 shows a conventional polarization measuring instrument for measuring 
the polarization mode dispersion by the Stokes parameters. 
The measuring instrument consists of a variable wavelength light source 
201, an optical coupler 202, a fiber-type polarizer 203, an optical fiber 
204 to be measured, a Stokes analyzer 205, an A/D converter 206, a 
wavelength meter 207, and a control unit 208. 
The variable wavelength light source 201 adjusts the wavelength of output 
light in response to a control signal from the control unit 208. The 
optical coupler 202 divides the light from the light source 201 into two; 
one being directed to the fiber-type polarizer 203 and the other to the 
wavelength meter 207. The light linearly polarized in the polarizer 203 
enters the Stokes analyzer 205 via the optical fiber 204. The Stokes 
analyzer 205 incorporates optical measurement elements, such as light 
detectors and receivers, to determine the Stokes parameters S.sub.0 
-S.sub.3. The Stokes parameters S.sub.0 -S.sub.3 are then digitized in the 
A/D converter 206 and fed to the control unit 208. A signal indicative of 
the wavelength of the measurement light is also fed to the control unit 
208 from the wavelength meter 207 to determine the polarization mode 
dispersion for the wavelength of the light from the variable wavelength 
light source 201 through the above expressions (1)-(3) and the inputted 
Stokes parameters S.sub.1 -S.sub.3. Then, the control unit 208 changes the 
wavelength of the light from the light source 201 for repeating the above 
operations. 
In the above conventional polarization mode dispersion measuring method, 
the Stokes parameters S.sub.1 -S.sub.3 are used to define the polarization 
mode dispersion by the expressions (1)-(3). If the Stokes parameter 
S.sub.1 approaches .+-.1, .beta..sub.1 diverges so that it is impossible 
to determine the polarization mode disperion for the object to be measured 
whose Stokes parameter S.sub.1 is near .+-.1. 
SUMMARY OF THE INVENTION 
Accordingly, it is an object of the invention to provide a polarization 
mode dispersion measuring apparatus and a method capable of measuring a 
wide variety of objects. 
According to the invention there is provided a polarization mode dispersion 
measuring apparatus which includes a variable wavelength light source for 
providing light of a variety of wavelengths; a light intensity modulator 
optically connected to the light source to provide light of modulated 
intensity; a polarization controller optically connected to the light 
intensity modulator to provide light of controlled polarization; a beam 
splitter optically connected to the polarization controller to provide 
beams of p and s polarization components; an O/E conversion unit optically 
connected to beam splitter to provide electrical signals with respect to 
beams of the p and s polarization components; and an analyzing unit for 
controlling the light intensity modulator to provide a sine wave of a 
predetermined frequency and a predetermined intensity, and the light 
source and the polarization controller to determine parameters of Jones 
matrix from the electrical signals and a polarization mode dispersion 
defined by the parameters, thereby measuring a polarization mode 
dispersion of an object placed between the polarization controller and the 
beam splitter. 
The analyzing unit includes a network analyzer for controlling the light 
intensity modulator to modulate intensity of light from the light source 
and determining parameters of Jones matrix from the electrical signals 
from the O/E conversion unit and a control unit for controlling the light 
source and the polarization controller to determine the polarization mode 
diepserion defined by parameters. 
The control unit scans the variety of wavelengths of light from the light 
source for measurement and permits for each of the scanned wavelengths a 
linearly polarized wave of the light from the polarization controller 
aligned with a p direction of the beam splitter to enter the object and 
then rotates the light from the polarization controller by 90.degree. and 
permits a linearly polarized wave aligned with an s direction of the beam 
splitter to enter the object. 
The analyzing unit corrects measurements of the object placed between the 
polarization controller and the polarized beam splitter based on initial 
measurements made in advance with no object placed between the 
polarization controller and the polarized beam splitter. 
According to another aspect of the invention there is provided a method of 
measuring a polarization mode dispersion by directing a linearly polarized 
light sine wave of a predetermined light intensity and frequency to a 
polarized beam splitter via an object to measure a polarization mode 
dispersion of the object from p and s polarization components from the 
polarized beam splitter, which includes the step of scanning wavelengths 
to determine parameters of Jones matrix and a polarization mode dispersion 
defined by the parameters. 
The method further includes a step of determining initial measurements 
without any object to correct measurements with an object based on the 
initial measurements. 
According to the invention Jones matrix for expressing characteristics of 
polarization elements is used to define polarization mode dispersion so as 
to avoid the fact that the use of Stokes parameters for defining 
polarization mode dispersion makes it impossible to measure polarization 
mode dispersion. 
The frequency dependency of phase change and amplitude of matrix elements 
of a transfer function matrix T! of an optical fiber is defined by Jones 
matrix as follows: 
##EQU2## 
wherein .vertline.T.sub.ij .vertline. and .phi..sub.ij are the amplitude 
and the phase change of each matrix element, respectively, and functions 
of light frequency .omega.. 
The polarization mode dispersion .tau..sub.PMD is defined as follows: 
##EQU3## 
wherein .theta. is the polarization angle, .phi..sub.1 the phase change in 
a direction in a plane perpendicular to the direction of light 
propagation, and .phi..sub.2 the phase change in a direction perpendicular 
to .phi..sub.1. 
Each parameter of the expression (5) is determined through the expression 
(4) as follows: 
EQU .theta.(.omega.)=a COS (.vertline.T.sub.11 .vertline..sup.2 
-.vertline.T.sub.21 .vertline..sup.2) (6) 
EQU .phi..sub.1 (.omega.)=(.phi..sub.11 -.phi..sub.22)/2,.phi..sub.2 
(.omega.)=(.phi..sub.21 -.phi..sub.12 +.pi.)/2 (7) 
Accordingly, by measuring each component of the expression (4), it is 
possible to determined the polarization mode dispersion .tau..sub.PMD 
through the expression (5). 
According to the invention, out-of-phase and in-phase components of two 
orthogonal components of phase change in the expression (7) are defined as 
follows: 
EQU .phi.(.omega.)=(.phi..sub.1 (.omega.)-.phi..sub.2 (.phi.))/2(8) 
EQU .phi.(.omega.)=(.phi..sub.1 (.omega.)-.phi..sub.2 (.omega.))/2(9) 
Taylor expansions about .theta.(.omega.), .phi.(.omega.), and 
.phi.(.omega.) are given as follows: 
EQU .theta.(.omega.)=.theta..sub.0 +.alpha..sub.1 
(.omega.-.omega..sub.0)+1/2.alpha..sub.2 (.omega.-.omega..sub.0).sup.2( 
10) 
EQU .phi.(.omega.)=.phi..sub.0 +.beta..sub.1 
(.omega.-.omega..sub.0)+1/2.beta..sub.1 (.omega.-.omega..sub.0).sup.2( 11) 
EQU .psi.(.omega.)=.psi..sub.0 +.gamma..sub.2 
(.omega.-.omega..sub.0)+1/2.gamma..sub.2 (.omega.-.omega..sub.0).sup.2( 
12) 
The polarization mode dispersion .tau..sub.PMD given by the expression (5) 
is modified through the expressions (10), (11) and (12) as follows: 
##EQU4## 
Thus, the polarization mode dispersion .tau..sub.PMD defined in the 
invention has three parameters {.theta., .phi., .phi.}. 
The polarization mode dispersion defined by Stokes parameter according to 
the prior art is expressed as follows: 
##EQU5## 
and has only two parameters {.theta., .phi.}. Since there is no in-phase 
component .phi., it diverges when Stokes parameter S.sub.1 is near .+-.1. 
By contrast three parameters {.theta., .phi., .phi.} are measured to 
determine polarization mode dispersion in the invention so that it is 
possible to avoid the inability to measure polarization mode dispersion 
.tau..sub.PMD as in the prior art and to broaden the range of objects to 
be measures.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In FIG. 1, the polarization condition or mode measuring apparatus includes 
a variable wavelength light source 101, a light intensity modulator 102, a 
polarization controller 103, an optical fiber 104 to be measured, a 
polarized beam splitter 105, an O/E converter 106.sub.1 and 106.sub.2, a 
network analyzer 107, an amplifier 108, and a control unit 109 for 
cooperating with the network analyzer 107 to form an analyzing unit. 
The light intensity modulator 102 modulates the intensity of light from the 
light source 101 so that the light has a sine wave having an intensity of 
approx. a few GHz and a fixed frequency of fm and feeds it to the 
polarization controller 103. The polarization controller 103 controls the 
polarization of the input light, and the output light enters the polarized 
beam splitter 105 via the optical fiber 104. The s and p polarization 
components from the beam splitter 105 are converted into electrical 
signals in the O/E converter 106.sub.1 and 106.sub.2, respectively, and 
fed to the network analyzer 107. The network analyzer 107 determines the 
polarization mode dispersion .tau..sub.PMD from the input values and 
controls the intensity modulation ratio in the intensity modulator 102 via 
the amplifier 108. The control unit 109 responds to the operation 
conditions of the network analyzer 107 to control the output wavelength of 
the light source 101 and the polarization conditions in the polarization 
control 103. 
In order to determine the accurate polarization mode dispersion 
.tau..sub.PMD, the network analyzer 107 stores values of the s and p 
polarization components for respective wavelengths of the light from the 
light source 101 which does not go through the optical fiber 104. Based on 
these stored values, it corrects the output values of the O/E converters 
106.sub.1 and 106.sub.2 to increase the accuracy of measurements of the 
polarization mode dispersion .tau..sub.PMD. 
In operation, upon measurement, the control unit 109 makes the output light 
of the polarization controller 103 of the linear polarization aligned with 
the p direction of the polarized beam splitter 105 and permits it to enter 
the optical fiber 104. The output light of the optical fiber 104 is given 
by the following expression. 
##EQU6## 
The output light is divided by the beam splitter 105 into the s and p 
polarization components and fed to the O/E converters 106.sub.1 and 
106.sub.2 to determine 
EQU .vertline.T.sub.11 .vertline.e.sup.-j.phi..sbsp.11, .vertline.T.sub.21 
.vertline.e.sup.-j.phi..sbsp.21 
Then, the control unit 109 rotates the output light of the polarization 
controller 103 by 90.degree. to provide a linearly polarized wave aligned 
with the s direction of the beam splitter 105 and permits it to enter the 
optical fiber 104. The output light of the optical fiber 104 is given by 
the following expression. 
##EQU7## 
The above output beams are separated into the s and p polarization 
components, respectively, by the beam splitter 105 and fed to the O/E 
converters 106.sub.1 and 106.sub.2 to determine 
EQU .vertline.T.sub.12 .vertline.e.sup.-j.phi..sbsp.12, .vertline.T.sub.22 
.vertline.e.sup.-j.phi..sbsp.22 
The network analyzer 107 determines .theta., .phi..sub.1, .phi..sub.2 
through the measured parameters and the expressions (6) and (7). 
The measurement is repeated by scanning the output wavelength of the light 
source 101 to determine .theta.(.omega.), .phi..sub.1 (.omega.), and 
.phi..sub.2 (.omega.) from the respective measurements, and the control 
unit 109 determines the polarization mode dispersion .tau..sub.PMD through 
the expression (5). 
Alternatively, the O/E converters provided for the p and s polarization 
components may be replaced by a single O/E converter to which the 
respective polarization components are directed. 
According to the invention it is possible to measure all parameter values 
and broaden the range of objects to be measured and increase the accuracy 
of measurements.