METHODE ET APPAREIL DE MESURE DE LA DISPERSION MODALE DE POLARISATION DES DISPOSITIFS OPTIQUES

METHOD AND APPARATUS FOR MEASURING POLARIZATION MODE DISPERSION OF OPTICAL DEVICES

Abrégé anglais

Apparatus for measuring very low levels of polarization mode dispersion of
optical devices, that is inexpensive, robust and portable, comprises a
broadband source
and a polarizes for directing substantially completely polarized broadband
light into the
device under test with the polarization in a plane substantially perpendicular
to the
propagation direction of the light. Light leaving the device is analyzed
spectrally to
produce a spectrum of intensity in dependence upon wavelength or frequency of
such
light for each of at least two mutually orthogonal polarization axes in a
plane
perpendicular to the propagation axis of the light leaving the device. The
spectra are used
to compute Stokes parameters s 1, s 2 and ~ s 3 ~ for each of a plurality of
wavelengths
within the bandwidth of the broadband light. The polarization mode dispersion
of the
device is characterized in dependence upon the Stokes parameters using one of
several
techniques including standard Fixed Analyzer techniques and polarimetric
techniques,
especially the Poincaré sphere technique. The apparatus is particularly
suitable for
measuring PMD of components of optical telecommunications systems, including
optical
fibers, optical isolators, couplers, light amplifiers, and dispersion
compensators.

Revendications

20
CLAIMS
1. Apparatus for measuring polarization mode dispersion of an optical device
comprising:
(i) means for directing substantially completely polarized broadband light
from a broadband light source into the device with the polarization in a plane
substantially perpendicular to the propagation direction of the light;
(ii) analysis means for analyzing light leaving the device to produce one or
more spectra of intensity in dependence upon wavelength or frequency of said
light
leaving the device;
(iii) means for computing, from the at one or more spectra, a Stokes parameter
for each of a plurality of wavelengths within the bandwidth of the broadband
light; and
(iv) means for characterizing polarization mode dispersion of the device in
dependence upon the Stokes parameter.
2. Apparatus according to claim l, wherein the analysis means produces a said
spectrum for each of at least two mutually orthogonal polarization axes in a
plane
perpendicular to the propagation axis of the light leaving the device and the
computing
means uses both spectra to compute the Stokes parameter;
3. Apparatus according to claim 1, wherein the analysis means analyzes the
light
leaving the device at four different polarization axes, comprising two pairs
of said
mutually orthogonal polarization axes, the means for computing computes, from
the four
spectra, Stokes parameters s 1, s 2 and ~ s3 ~ for each of a plurality of
wavelengths within
the bandwidth of the broadband light; and the characterizing means
characterizes
polarization mode dispersion using the Stokes parameters.
4. Apparatus according to claim 1, 2 or 3, wherein the analysis means
comprises
a rotatable analyzer means rotatable to each of a plurality of angular
positions
corresponding to said polarization axes and spectrum measuring means for
scanning light
from the rotatable analyzer at each of said polarization axes to provide said
plurality of
spectra.

21
5. Apparatus according to claim 4, wherein the optical spectrum measuring
means
comprises an optical spectrum analyzer for providing said spectra
6. Apparatus according to claim 4, wherein the optical spectrum measuring
means
comprises an interferometer for providing a set of interference fringes for
each of said
mutually orthogonal polarization axes and means for performing a Fourier
transform on
each set of fringes to provide said spectra.
7. Apparatus according to claim 3, wherein the analysis means comprises means
for
generating interference fringes directly from the light leaving the device, a
real-time
Stokes analyzer for producing a corresponding set of fringes for each of said
orthogonal
polarization axes, and means for performing a Fourier transform on each set of
fringes
to provide said spectra.
8. Apparatus according to claim 4, 5 or 6, wherein the rotatable analysis
means
comprises a polarizer and a waveplate fixed rotatably relative to each other
and rotatable
together to said plurality of positions.
9. Apparatus according to claim 4, 5 or 6, wherein the rotatable analysis
means
comprises a fixed polarizer and a rotatable waveplate, the waveplate being
rotatable
relative to the polarizer to each of said plurality of positions corresponding
to said
mutually orthogonal axes.
10. Apparatus according to any of the preceding claims, wherein the means for
directing polarized light into the device is adjustable to select first and
second different
polarization states for the light directed into the device and the analysis
means provides
two spectra for said mutually orthogonal polarization axes, respectively, for
each of the
first and second input polarization states.
11. Apparatus according to any one of the preceding claims, wherein the means
for
characterizing polarization mode dispersion comprises means for performing
polarimetric
characterization.

22
12. Apparatus according to any one of claims 1 to 10, wherein the means for
characterizing polarization mode dispersion comprises means for plotting
trajectories on
a Poincaré sphere of the Stokes vectors corresponding to the Stokes
parameters.
13. Apparatus according to any one of claims 1 to 10, wherein the means for
characterizing polarization mode dispersion comprises means for performing
Fixed
Analyzer analysis upon the spectra, and means for performing polarimetric
analysis upon
the spectra, the Fixed Analyzer analysis means and the polarimetric analysis
means being
selectable alternatively.
14. Apparatus for measuring polarization mode dispersion of an optical device
comprising:
(i) means for directing substantially completely polarized broadband light
from a broadband light source into the device with the polarization in a plane
substantially perpendicular to the propagation direction of the light;
(ii) analysis means for analyzing light leaving the device to produce a
spectrum of intensity in dependence upon wavelength or frequency of output
light that
has passed through the analysis means;
(iii) means for computing
(a) from the output spectrum a corresponding spectrum for the light input
to the analysis means by measuring and summing values of the intensity at
successive
pairs of points on the input light spectrum, each pair of points being
separated from each
other by one half of a mean period of the input light spectrum;
(b) dividing the output spectrum by the input spectrum to obtain the
normalized transmission of the spectral analysis means;
(c) deriving the envelope amplitude and phase of the normalized
transmission waveform;
(d) computing, from the envelope and phase, a Stokes parameter for each
of a plurality of wavelengths within the bandwidth of the broadband light; and
(e) characterizing polarization mode dispersion of the device in dependence
upon the Stokes parameter.

23
15. Apparatus according to claim 14, wherein the Stokes parameter is computed
from
the envelope and phase according to the expressions:
<IMG>
where A is the peak amplitude of the normalized transmission waveform, and ~
is its
phase with respect to an arbitrary reference phase.
16. A method of measuring polarization mode dispersion of an optical device
comprising the steps of:
(i) directing substantially completely polarized broadband light from a
broadband light source into the device with the polarization in a plane
substantially
perpendicular to the propagation direction of the light;
(ii) analyzing light leaving the device to produce one or more spectra of
intensity in dependence upon wavelength or frequency of said light leaving the
device;
(iii) computing, from the one or more spectra, a Stokes parameter for a range
of wavelengths within the bandwidth of the broadband light; and
(iv) characterizing polarization mode dispersion of the device in dependence
upon the Stokes parameter.
17. A method according to claim 16, wherein the light leaving the device is
analyzed
to produce a said spectrum for each of at least two mutually orthogonal
polarization axes
in a plane perpendicular to the propagation axis of the light leaving the
device and the
Stokes parameter is computed using the two spectra.
18. A method according to claim 16, wherein the step of analyzing the light
leaving
the device analyzes the light for each of at least two pairs of mutually
orthogonal
polarization axes to provide two pairs of spectra, the computing step computes
Stokes
parameters s 1, s 2 and ~ s 3 ~ for each of a plurality of wavelengths within
the bandwidth

24
of the broadband light, and the polarization mode dispersion is characterized
using the
Stokes parameters.
19. A method according to claim 16, wherein the step of analyzing the light
includes
the step of passing the light through a linear analysis means, rotating the
linear analysis
means to each of a plurality of angular orientations corresponding to said
polarization
axes, and scanning light from the linear analysis means at each of said
polarization axes
to provide said plurality of spectra.
20. A method according to claim 19, wherein the step of scanning the light
from the
linear analysis means uses an optical spectrum analyzer.
21. A method according to claim 19, wherein the step of scanning the light
from the
linear analysis means to provide said spectra comprises the steps of obtaining
a set of
interference fringes for each of said mutually orthogonal polarization axes
and
performing a Fourier transform on each set of fringes to provide said spectra.
22. A method according to claim 19, 20 or 21, wherein the light from the
device is
passed through a linear analysis means comprising a polarizer and a waveplate
that are
fixed relative to each and rotated together to said plurality of orientations.
23. A method according to claim 19, 20 or 21, wherein the light from the
device is
passed through a rotatable analysis means comprising a fixed polarizer and a
waveplate,
and rotating the waveplate relative to the polarizer between the said
plurality of
orientations corresponding to said mutually orthogonal axes.
24. A method according to claim 18, wherein the analysis step comprises the
steps
of generating interference fringes directly from the light leaving the device,
using a
real-time Stokes analyzer to produce from the fringes a corresponding set of
fringes for each
of said orthogonal polarization aces, and performing a Fourier transform on
each set of
fringes to provide said spectra.

25
25. A method according to any of claims 18 to 24, further comprising the step
of
selecting first and second different polarization states, alternatively, for
the polarized
light directed into the device, said analysis step providing four spectra, two
for said
mutually orthogonal polarization axes, respectively, for each of the first and
second input
polarization states.
26. A method according to any one of claims 18 to 25, wherein the
characterizing of
the polarization mode dispersion is done by a polarimetric method.
27. A method according to any one of claims 18 to 25, wherein the
characterizing of
the polarization mode dispersion is done by plotting trajectories on a
Poincaré sphere of
Stokes vectors corresponding to the Stokes parameters.
28. A method according to any one of claims 18 to 25, wherein the
characterizing of
the polarization mode dispersion is done by either a Fixed Analyzer analysis
method or
a polarimetric analysis method in dependence upon whether or not the device
exhibits
weak polarization mode coupling, as predetermined by a user.
29. A method of measuring polarization mode dispersion of an optical device
comprising the steps of:
(i) directing substantially completely polarized broadband light from
a broadband light source into the device with the polarization in a plane
substantially
perpendicular to the propagation direction of the light;
(ii) directing light leaving the device through a fixed analysis means
to provide a spectrum of intensity in dependence upon wavelength of output
light leaving
the analysis means, the intensity varying periodically with respect to
frequency at a rate
significantly higher than a rate of variation of the state of polarization of
light leaving
the device under test;
(iii) deriving from the output light spectrum a corresponding spectrum
for the light input to the analysis means by measuring and summing values of
the
intensity at successive pairs of points on the output light spectrum, each
pair of points
being separated from each other by one half of a mean period of the output
light

26
spectrum and from respective ones of an adjacent pair by a predetermined
interval that
is significantly less than said mean half of said mean period;
(iv) dividing the output spectrum by the input spectrum to obtain the
normalized transmission waveform of the analysis means;
(v) deriving the amplitude envelope and phase of the normalized
transmission waveform;
(vi) computing, from the amplitude envelope and phase, a Stokes
parameter for each of a plurality of wavelengths within the bandwidth of the
broadband
light; and
(vii) characterizing polarization mode dispersion of the device in
dependence upon the Stokes parameters.
30. A method according to claim 29, wherein the Stokes parameters are each
computed from the envelope and phase according to the expressions:
<IMG>
where A is the peak amplitude of the normalized transmission waveform, and ~
is its
phase with respect to an arbitrary reference phase.

Description

CA 02236521 1998-OS-O1
1
METHOD AND APPARATUS FOR MEASURING POLARIZATION MODE
DISPERSION OF OPTICAL DEVICES
FIELD OF THE INVENTION
The invention relates to a method and apparatus for measuring polarization
mode
dispersion of optical devices, especially, but not exclusively, components of
optical
telecommunications systems, including optical fibers, optical isolators,
couplers, light
amplifiers, and dispersion compensators.
BACKGROUND
Polarization mode dispersion (PMD) limits the performance of optical
telecommunications systems by reducing bandwidth in digital telecommunications
systems
and contributing to distortion in analogue telecommunications systems.
Techniques have
been developed for measuring PMD so that it can be reduced or, if that is not
possible,
measures can be taken to mitigate its effects. The characterization or
measurement of
polarization mode dispersion in fiber optic telecommunications systems has
become of
great importance with the advent of high bit rate, long-haul
telecommunications links.
Optical components in such systems must be tested to verify that they do not
add
significant PMD. Measurements must be made in the laboratory environment
during
component and subsystem design, in the production environment when the
components
are being fabricated, and in the outside plant environment when the system has
been
installed.
The practical range over which PMD may need to be characterized now extends
over five orders of magnitude from about 1 femtosecond to nearly 100
picoseconds.
Moreover, in contemporary wavelength-division multiplex (WDM) systems,
measurements must frequently be made through interposed, narrow path optical
filters,
and the PMD characterized for weak, intermediate and strong mode coupling.
When the
measurements must be made in the production environment or in the field,
speed,
robustness and portability are important factors.
Generally, to characterize the PMD, it is required to determine the state of
polarization of the light at the output of the device under test. There are
several
standardized methods for measuring polarization mode dispersion, which can be
classified into two categories according to the kind of data, i.e. time-domain
or

CA 02236521 1998-OS-O1
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frequency-domain, that is collected. Thus, time-domain data is collected by
the
Interferometric method (INT). Frequency-domain data is collected by the fixed
analyzer
method (FA), also known as wavelength scanning, and by the polarimetric
method, that
is Jones Matrix Eigenanalysis (JME) method or the Poincare Sphere (PS) method.
The following ANSI standards apply:
TIA/EIA-455-124 for the Interferometric method
TIA/EIA-455-122 for the Jones Matrix Eigenanalysis method
TIA/EIA-455-113 for the Fixed Analyzer method.
The interferometric measurement methods typically pass polarized light from a
broadband light source through the device under test and to an interferometer,
for
example a Michelson interferometer or a Mach-Zehnder interferometer. For
measurements in the field, the interferometric method usually is preferred
because it
provides measurements quickly and uses comparatively light apparatus. INT also
gives
the more reliable results in the important case of long installed fibres,
owing to its
insensitivity to fast fluctuations of the output state of polarization.
Disadvantages of previously-known interference methods include limitation of
the
measurement range to PMD values larger than about 150 femtoseconds, especially
in the
strong mode-coupling regime characteristic of most optical fibre measurements.
Another
disadvantage is that the measurement is sensitive to the shape of the spectrum
transmitted
through the device under test, so results are affected whenever some kind of
filter is
present in the path. Yet another disadvantage is that measurement is virtually
impossible
in the case of optical components which have limited spectral bandwidth.
Techniques have been proposed to improve the measurement of low PMD. For
example, in US patent specification number 5,654,793 issued August 1997, A.J.
Barlow
et al. disclosed a "PMD-biasing" technique for measuring low PMD using a
birefringent
artefact with a stable PMD value in series with the fiber under test. The
interferogram
is biased away from the central autocorrelation peak and PMD is obtained by
measuring
the broadening of the peak. While lower PMD values may be measured in this
way,
ultra-low values, i.e. less than 10 femtoseconds, cannot.
What may be considered an improvement over Barlow's technique was disclosed
in an article entitled "Interferometric Polarization Mode Dispersion
Measurements with
Femto Second Sensitivity" by T. Oberson et al. , Journal of Light Wave
Technology,
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1997. Oberson et al. discussed standard techniques for PMD measurements using
the
Michelson interferometer and an envelope detector, the PMD delay being deduced
from
the width of the interferogram and concluded that such standard techniques
were not
suitable where the polarization mode delay is smaller than, or comparable to,
the
coherence time of the source. According to Oberson et al. , a PMD of 104
femtoseconds
represented the lower limit of PMD measurable using standard interferometric
techniques. To extend the measurement range, Oberson et al. proposed modifying
the
standard set-up by inserting a high birefringent (HiBi) fiber with a PMD of
about 0.5
picoseconds between the fibre under test and the analyzer. The HiBi fibre
produced two
side peaks, one each side of the central autocorrelation peak. The
differential group
delay (DGD) was determined from the extremes of separation between the side
peaks.
While Oberson et al.'s technique may measure PMD values in the range of 10
femtoseconds, it does not address the problem of measurements being sensitive
to the
shape of the spectrum transferred to the device under test or the measurement
of PMD
of optical components with limited spectral bandwidth. Other limitations
include a
lengthy measurement time, application to weak mode-coupling only, and a
requirement
for a polarization controller in the light path which can introduce residual
PMD which
randomly adds to, or subtracts from, the measured PMD.
The Fixed Analyzer method makes a plurality of measurements at different
wavelengths and analyzes the measured spectrum by counting extrema.
Measurements
at the different wavelengths may be obtained by varying the wavelength of the
input light
source, for example a tunable laser, or using a broadband source with a
monochromator.
The light from the source is polarized and passed through the device under
test to a fixed
analyzer and then to a photodetector. Alternatively, a broadband source could
be used
and the output from the polarizer/analyzer analyzed using an optical spectrum
analyzer.
The resulting spectrum exhibits a multiplicity of maxima and minima because
the state
of polarization at the output of the device under test, and hence at the input
of the
analyzer, changes with wavelength. The PMD is estimated by averaging the
number of
maxima and minima. While this might be satisfactory where the PMD is
relatively
large, it is not satisfactory for low PMD because the state of polarization
does not
change very much and there will be very few, perhaps only one or two, maxima
and
minima to average. Thus, its main disadvantage is that it can measure only PMD
values
.~,.~.rof

CA 02236521 1998-OS-O1
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which are much larger than the inverse of the source spectral width. For
example, with
one 1550 nm LED (20 THz width), the mean number of extrema is approximately 1
when PMD is equal to 25 fs.
The polarimetric methods use a laser or other narrowband light source that can
be tuned across the range of wavelengths to be measured. The Poincar~ sphere
method,
for example, then uses a polarimeter which measures state of polarization
directly but
at only one wavelength at a time. In addition to requiring an expensive
tunable laser,
this approach is time-consuming because the measurements must be repeated at
the
different wavelengths. Moreover, the scanning range of a tunable laser
typically is about
100 nm, which is very restricted compared with that provided by a broadband
source.
The Jones Matrix Eigenanalysis (JME) also uses a tunable laser, the output of
which is passed through a polarization controller and a set of linear
polarizers at
respective angles of 0°, 45° and 90°, before being passed
through the device under test.
The light from the test fibre is analyzed using a polarimeter.
Hence, current polarimetric methods use bulky and/or expensive apparatus, such
as a polarimeter and a widely tunable narrow line width laser, and the
measurement time
is long, making measurements on long installed fibres generally impractical.
Contrasting the Fixed Analyzer method with the Polarimetric methods, the Fixed
Analyzer method is quick because it uses a broadband source and inexpensive
because
it does not need a tunable laser or a polarimeter. Its spectrum analysis
approach,
however, i.e. counting extrema, loses important phase information. The
polarimetric
methods are much slower because they entail repeated measurements at the
different
wavelengths and expensive because they require a tunable source (laser) and a
polarimeter, but they have the advantage of retaining phase information and
providing
complete information about the state of polarization. It would be desirable,
therefore,
to have a PMD measurement method which, like the Fixed Analyzer method, was
quick
to use and inexpensive, yet provided more complete information about the PMD.
SUMMARY OF THE INVENTION
The present invention seeks to eliminate or mitigate some or all of the afore-
mentioned disadvantages and to provide an improved method for the measurement
of

CA 02236521 1998-OS-O1
very low levels of polarization mode dispersion and apparatus for use therein
that is
inexpensive, robust and portable.
According to one aspect of the invention, apparatus for measuring polarization
mode dispersion of an optical device comprises:
5 (i) means for directing substantially completely polarized broadband light
from a broadband light source into the device with the polarization in a plane
substantially perpendicular to the propagation direction of the light;
(ii) analysis means for analyzing light leaving the device to produce at least
one spectrum of intensity in dependence upon wavelength or frequency of said
light
leaving the device;
(iii) means for computing, from the at least one spectrum, a Stokes parameter
for each of a plurality of wavelengths within the bandwidth of the broadband
light; and
(iv) means for characterizing polarization mode dispersion of the device in
dependence upon the Stokes parameters.
According to a second aspect of the invention, a method of measuring
polarization
mode dispersion of an optical device comprises the steps of:
(i) directing substantially completely polarized broadband light from a
broadband light source into the device with the polarization in a plane
substantially
perpendicular to the propagation direction of the light;
(ii) analyzing light leaving the device to produce at least one spectrum of
intensity in dependence upon wavelength or frequency of said light leaving the
device;
(iii) computing, from the at least one spectrum, a Stokes parameter for each
of a plurality of wavelengths within the bandwidth of the broadband light; and
(iv) characterizing polarization mode dispersion of the device in dependence
upon the Stokes parameters.
The means for analyzing the light leaving the device may produce two spectra,
each for a respective one of two mutually orthogonal polarization axes in a
plane
perpendicular to the propagation axis of the light leaving the device, and the
computing
means may use both of said two spectra to compute the Stokes parameters.
The characterizing of the polarization mode dispersion may be effected by a
Fixed
Analyzer method, in which case only two spectra for a pair of mutually
orthogonal
polarization axes are used.
ap600~refi6nml.mf

CA 02236521 1998-OS-O1
6
Alternatively, the light leaving the device may be analyzed to produce at
least
four spectra, comprising two pairs of spectra for two different pairs,
respectively, of
mutually orthogonal polarization axes in a plane perpendicular to the
propagation axis
of the light leaving the device. Each pair of spectra so produced may be used
to compute
Stokes parameters s,, sz and ~ s3 ~ for each of a plurality of wavelengths
within the
bandwidth of the broadband light.
In embodiments of either aspect of the invention, a rotatable
analyzer/polarizer
for selecting different polarization components of the light from the device
may be
rotated to each of a plurality of angular positions corresponding to said
polarization axes
and, for each axis, light from the rotatable analyzer/polarizer scanned to
provide said
plurality of spectra, conveniently by means of an optical spectrum analyzer.
Alternatively, an interferometer may be used to generate, from the light
leaving the
rotatable analyzer/polarizer, a set of interference fringes for each of the
mutually
orthogonal polarization axes, and Fourier transform performed on each set of
fringes to
provide said spectra.
The rotatable analyzer may comprise a linear polarizes and a waveplate,
rotatable
together to said plurality of positions. Alternatively, the rotatable
analyzer/polarizer may
comprise a fixed linear polarizes and a waveplate, the waveplate being
rotatable relative
to the polarizes between the plurality of positions corresponding to said
mutually
orthogonal axes.
Preferably, the polarization state of the polarized light directed into the
device
may be set to first and second different polarization states, and the set of
spectra
generated for each of them.
As an alternative to using a rotatable analyzer/polarizer, the light from the
device
under test may be supplied directly to an interference fringe generating unit
for
generating interference fringes, and a real-time Stokes analyzer used to
produce a
corresponding set of fringes for each of the orthogonal polarization axes.
Fourier analysis
may then be performed on each set of fringes to provide said spectra.
According to another embodiment of the invention, the analysis means comprises
a polarizes preceded by a highly-birefringent component, such as a HiBi
waveguide, both
the polarizes and the component being fixed relative to each other and a
propagation axis
of light from the device under test so that a high transmission axis of the
polarizes
~.ro~

CA 02236521 1998-OS-O1
7
extends at an angle of 45 degrees relative to a birefringence (fast) axis of
the component
in the plane perpendicular to the propagation axis, the analyzer providing a
spectrum of
the intensity in dependence upon wavelength of output light leaving the
analyzer, the
intensity varying periodically with respect to frequency at a rate
significantly higher than
a rate of variation of the state of polarization of light leaving the device
under test, and
the means for computing:
(a) derives from the output light spectrum a corresponding spectrum for the
light input to the analysis means by measuring and summing values of the
intensity at
successive pairs of points on the output light spectrum, each pair of points
being
separated from each other by one half of a mean period of the output light
spectrum and
from an adjacent pair by a predetermined interval that is significantly less
than said mean
half of said mean period;
(b) divides the output spectrum by the input spectrum to obtain the normalized
transmission waveform of the analysis means;
(c) derives the amplitude envelope and phase of the normalized transmission
waveform;
(d) computes, from the amplitude envelope and phase, a Stokes parameter for
each of a plurality of wavelengths within the bandwidth of the broadband
light; and
(e) characterizes polarization mode dispersion of the device in dependence
upon
the Stokes parameters.
The polarization mode dispersion may be characterized by any of several
standard
methods, including the Interferometric, Fixed Analyzer and polarimetric
methods.
Preferably, the polarization mode dispersion is characterized by plotting
trajectories on
a Poincare sphere of Stokes vectors corresponding to the Stokes parameters.
The method and apparatus may provide for selecting either the Fixed Analyzer
method or the polarimetric method in dependence upon whether or not the device
exhibits weak polarization mode coupling, as predetermined by a user.
BRIEF DESCRIPTION OF THE DRAWINGS
An embodiment of the invention will now be described by way of example only
and with reference to the accompanying drawings in which:
.~.~~..~

CA 02236521 1998-OS-O1
8
Figure 1 is a block diagram of apparatus for measuring polarization mode
dispersion (PMD) of a device, such as an optical fiber;
Figure 2 illustrates one spectrum obtained by measurements taken at one
analyzer
orientation;
Figure 3 illustrates the basic sequence of operations when using the apparatus
to
measure PMD;
Figure 4 is a flowchart illustrating a data acquisition sequence of the
apparatus
of Figure 1;
Figure 5 is a flowchart illustrating interpretation of the spectra and
determination
of PMD;
Figure 6 is a detail view of a first modification which uses a Fourier-
transform
spectrometer to obtain a plurality of spectra;
Figure 7 is a detail view of a modified polarizer/analyzer of the apparatus of
Figure 1 or Figure 6;
Figure 8 is a detail view of yet another modification which uses a real time
Stokes analyzer;
Figure 9 is a block diagram similar to Figure 1 but in which the
polarizer/analyzer comprises a fixed polarizes and a fixed highly birefringent
component
in series;
Figure 10 illustrates variation in intensity of light leaving the analyzer of
Figure
9;
Figure 11 illustrates calculation of values of a curve representing variation
in
intensity of light at the output of the analyzer;
Figure 12 illustrates a normalized transmission waveform for the analyzer; and
Figure 13 is a flowchart illustrating operation of the device of Figure 9.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENT
In the drawings, corresponding components in the different Figures have the
same
reference numerals, with a prime where they are not identical.
Referring now to Figure 1, apparatus for measuring PMD comprises a low-
coherence, broadband, substantially unpolarized light source 10 which may
comprise one
or more light emitting diodes. Light emitted by the source 10 is passed
through a linear
~60V~mfifini.nf

CA 02236521 1998-OS-O1
9
input polarizes 12 and injected into the device under test 14. The polarizes
12 is
mounted in a support 16 and rotatable about the propagation axis of the light
beam by
a suitable drive unit (not shown) so that its maximum transmission axis can be
set to two
different angles, e. g. 0 ° and 45 ° . On leaving the device
under test 14, the light is
passed through a rotatable linear analyzer 18 which is mounted in a second
support 20
and rotatable about the propagation axis by means of a drive unit (not shown).
In
practice, the rotatable analyzer 18 also is a linear polarizes. Light leaving
the
polarizer/analyzer 18 is passed to an optical spectrum measurement unit 22
which
analyses the light in the frequency/wavelength domain to determine the optical
energy
(spectral density) at each wavelength.
Before it is passed through the polarizes 12, the light from the source 10 is
collimated by a first collimator 24, for example a GRIN lens or other suitable
means,
mounted on the support 16. A second collimator lens 26 carried by the support
20 and
aligned with lens 24 focuses the light leaving the polarizes 12 for injection
into the
device under test 14. The direction of propagation of the beam passing between
collimators 24 and 26 is substantially perpendicular to the maximum
transmission axis
of polarizes 12.
Light leaving the device under test 14 is collimated by a third collimating
lens 28
before passing through the rotatable analyzer 16. A fourth collimating lens 30
focuses
the light leaving the rotatable polarizer/analyzer 18 for injection into the
optical spectrum
measurement unit 22. The direction of propagation of the collimated beam
passing
between the collimators 28 and 30 is substantially perpendicular to the
maximum
transmission axis of the rotating polarizer/analyzer 18. The collimators 28
and 30 are
mounted coaxially upon the support 20.
The polarizes support 16 has a connector part 32 adjacent, and coaxial with,
the
collimator lens 26 for receiving a complementary connector part 34 coupled to
the input
of device 14 by a fiber pigtail. The connector part 32 is configured so that
the end of the
fiber pigtail abuts the adjacent end face of the collimator lens 26. The
analyzer support
20 has a similar connector part 36 to receive a connector part 38 coupled to
the output
of device 14 by a fiber pigtail so that the end of the fiber pigtail abuts the
end of the
collimator lens 28.
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CA 02236521 1998-OS-O1
Abutting the ends of the device 14's fiber pigtails directly onto the ends of
the
collimator lenses 26 and 28, respectively, avoids introducing additional fiber
pigtails,
showing PMD, into the path between the polarizes 12 and the polarizer/analyzer
18.
Although, for convenience, polarizes 12 provides linear polarization, the
state of
5 polarization is not important; it could be circular, elliptical and so on.
It is important,
however, that the degree of polarization be substantially 100 per cent. The
maximum
transmission axis of input polarizes 12 may be rotated through 45°, if
necessary, to
ensure that it is not aligned with one of the input principal states of
polarization of the
device under test 14.
10 The rotating polarizer/analyzer 18 may be rotated to set its maximum
transmission axis at each of four orientations differing by 45 ° from
each other, for
example 0 ° , 45 ° , 90 ° and 135 ° . In use,
eight measurements a sually will be made, a sing
each of the four angular positions of the maximum transmission axis of
polarizer/analyzer 18 with each of the two angular positions of the maximum
transmission axis of polarizes 12, as will be described later.
As shown in Figure 1, a retarder in the form of a wave plate 40 is attached to
the
rotatable polarizer/analyzer 18. The angle between the birefringence axis of
the
waveplate 40 and the maximum transmission axis of the rotatable
polarizer/analyzer 18
is substantially 45°, independently of the orientation of the maximum
transmission axis
of polarizer/analyzer 18. The waveplate 40 is a quarter waveplate, i.e. with a
retardance
of a/2 at the wavelength corresponding to the centre of the emission spectrum
of source
10. In order for the retardance to be substantially a/2 at any wavelength
within the
spectral bandwidth of the source 10, the waveplate 40 preferably is a zero-
order
waveplate or any substantially achromatic waveplate. The addition of the
waveplate 40
ensures that the state of polarization of the light passed to the unit 22 is
always
substantially circular, regardless of the orientation of the maximum
transmission axis of
the rotatable polarizer/analyzer 18. This virtually eliminates any adverse
effect upon the
measurement from the polarization dependent loss (PDL) of the assembly
following the
polarizer/analyzer 18 (i. e. the fourth collimator 30, and other components of
the optical
spectrum measurement unit 22).
As illustrated in Figure 2, the spectrum produced at the output of the
polarizer/analyzer 18 by a broadband source 10 comprising two LEDs having
centre
ap600'VeAfiml.ref

CA 02236521 1998-OS-O1
11
frequencies of 1300 nm and 1550 nm, respectively, comprises two similar
segments.
Each segment comprises only a limited number of maxima and minima. In Figure
2,
the bandwidth of the LED sources without any intervening device under test is
represented by a broken line curve, and the spectral density S(v) (in
watts/Hz) for one
of the four angles of the polarizer/analyzer 18 is represented by a full line
curve. The
difference between the full curve and the broken curve represents the spectrum
for the
other, orthogonal angle of the polarizer/analyzer 18 assuming the same
orientation of the
polarizes 12. The different permutations of the angles of the polarizes 12 and
polarizer/analyzer 18 will yield spectra which differ from each other.
Referring also to Figure 3, in use, the apparatus first carnes out a data
acquisition
step I which involves carrying out scans for all permutations of the different
settings of
the polarizes 12 and polarizer/analyzer 18 to obtain eight spectra. In the
specific
embodiment illustrated in Figure 1, the optical spectrum measurement unit 22
comprises
an optical spectrum analyzer (OSA) 42 which scans the output of the
polarizer/analyzer
18 over the spectral bandwidth of the broadband source 10, for each of the
eight
combinations of angles for polarizes 12 and polarizer/analyzer 18. In this
case, the
bandwidth is about 400 nm, i.e. the bandwidth of two LEDs. The spectra
produced by
the OSA 42 are stored in spectra storage means 44. When the eight spectra have
been
stored, in the second step II the Stokes parameter calculating means 46
calculates
normalized Stokes parameters s,, s2 and ~ s3 ~ , the modulus of parameter s3,
for each
wavelength and for each of the two angles of polarizes 12. In step III, the
PMD
characterizing means 48 uses the Stokes parameters to obtain PMD, using
whichever of
several methods is appropriate, as will be explained later, and displays the
results on
display 50 (step IV).
The data acquisition step I is illustrated in more detail in Figure 4. In step
4.1,
the apparatus is initialized and the source 10 turned on. With the axis of
input polarizes
12 set to 0 ° (step 4.2), and the axis of the polarizer/analyzer 18 set
to 0 ° (step 4. 3), the
optical spectrum measurement unit 22 acquires the spectrum (step 4.4) and
saves the
resulting data (step 4.5). The loop comprising decision step 4.6 and function
step 4.7
causes the sequence to repeat for analyzer angles of 45 °, 90°
and 135 ° and the
corresponding data (spectra) are stored. Steps 4.8 and 4.9 then change the
orientation
angle 9p of input polarizes 12 to 45°, and scanning steps 4.4, 4.5, 4.6
and 4.7 are
.nsomrons~.rer

CA 02236521 1998-OS-O1
12
repeated to obtain, and store, a set of spectra for an input polarizer angle
of 45 ° . Once
this has been done, step 4.10 uses the stored spectra to compute the Stokes
parameters.
Referring now to Figure 5, in step 5.1, normalized Stokes parameters are
computed for each wavelength in the scanned range. Two sets of Stokes
parameters are
computed, one for each setting of the polarizer 12, vis. for angles 6P = 0
° and AP =
45°. Stokes parameters of each set are calculated as follows:-
S(o,~) - S(90,~.)
s(o,~,) + s(9o,~)
Sa (~) = S(45, ll) -S(135, ~)
,S(45, ~.) +S(135,.~)
(si (h) + sa (~) )
where the term S (0, ~) + S (90, ~) represents the spectral den sity at the
input of
polarizer/analyzer 18. The three Stokes parameters are the coordinates of the
point
representing the state of polarization in the Poincar~ sphere representation.
The Stokes parameters are supplied to output 5.3 for display by display device
50 (Figure 1), and decision step 5.4 determines, based upon the user's
selections prior
to/during initialization, whether or not the device exhibits strong
polarization coupling.
For the case where the device 14 is NOT strongly mode-coupled, step 5.5
analyzes the
sets of Stokes parameters as a function of optical frequency v, using a known
technique
such as cosine fitting of curves S;(v), to find the PMD value. Where ~(v) is
the period
of the sinewave variations of S;(v) found by the fit, the value of PMD is 1
/w.
If the device does exhibit strong polarization mode coupling, step 5.7
analyzes
the trajectory on the Poincare sphere using known algorithms such as disclosed
by C.D.
Poole et al in "Polarization Dispersion and Principal States in a 147 km.
Undersea
Lightwave Cable", Journal of Lightwave Technology, 7, p. 1185, 1989, and
outputs that
as the PMD value. The Stokes parameters are used to determine the state of
polarization
at the input of the polarizer/analyzer 18 which is represented by the
trajectory of the
output Stokes vector on the Poincar~ sphere as a function of v (the Poincare
sphere is a
representation of SOP widely used in PMD analysis).
.~sowens~.roe

CA 02236521 1998-OS-O1
13
In certain circumstances, specifically if the device 14 exhibits weak mode-
coupling, the spectra produced by the polarizer/analyzer 18 may be analyzed,
to derive
the PMD, using a method according to the Fixed Analyzer standard TIA/EIA-455-
113.
In this case, only one Stokes parameter needs to be computed, which can be
done using
only one pair of spectra for mutually orthogonal polarization angles.
If it is apparent from the first three scans, with analyzer angles of 0
° , 45 ° and
90 ° , that two suitable scans have been obtained, the measurement at
135 ° may be
omitted. Generally, however, it is more convenient to take all four
measurements.
It should be appreciated that, at this stage, either time-domain
interferometric
analysis or frequency-domain fixed-analyzer analysis could be performed on the
data.
Analysis of the normalized spectrum allows very small PMD values of only a few
femtoseconds to be measured, providing the device is weakly mode-coupled.
Various modifications to the above-described embodiment may be made within
the scope of the present invention. Thus, in the optical spectrum measurement
unit 22
(Figure 1), the optical spectrum analyzer (OSA) 42 could be replaced by a
Fourier
transform spectrometer. Figure 6 illustrates such a Fourier-transform
spectrometer 52
comprising a modified Michelson interferometer unit 54 without the usual
envelope
detector. More specifically, instead of the output of the photodetector being
rectified and
the fringe envelope used, the interferometer has a storage unit 56 for storing
interference
fringes, a Fourier transform unit 58, and a modulus computing unit 60. For
each of the
eight permutations of the angles of the polarizer 12 and polarizer/analyzer
18, the
Michelson interferometer unit 54 stores a set of fringes in storage means 56.
Each set
of fringes is processed by the Fourier transform unit 58 which, in addition to
performing
the Fourier transform from the time domain to the frequency domain, may
provide some
scaling. The modulus computing unit 60 then deduces the modulus of the Fourier
transform of the interference fringes (time-domain data) to obtain the
spectral density
S(v) and outputs it to the spectra storage unit 44 (Figure 1).
Imbalance of chromatic dispersion between the interferometer arms, which
distorts the shape of the interferogram, manifests in the Fourier transform as
a
frequency-dependent phase term. Taking the modulus of the Fourier transform
eliminates this phase term.
ap600~rafl5naLnf

CA 02236521 1998-OS-O1
14
The eight spectra from the Fourier-transform spectrometer 52 are processed in
the same manner, described with reference to Figure 5, as those produced by
the OSA
42.
It is envisaged that a relatively inexpensive interferometer could be used and
any
detrimental effects of mirror position errors corrected by means of a
narrowband
reference, for example a laser. The reference signal would be combined with
the output
of the rotatable polarizer/analyzer 18, using a coupler, before it was
inputted to the
interferometer. The wavelength of the reference signal would lie outside the
bandwidth
of the broadband source. Discrete Fourier Transform would be performed upon
the
fringe data, and the transformed data supplied to a broadband filter and a
narrowband
filter, respectively, which would segregate broadband (LED) and narrowband
(laser
reference) components. Inverse Discrete Fourier Transform would be applied to
the
filtered data to produce, respectively, an uncorrected interferogram for the
broadband
data and a position error of the scanning minor of the interferometer. The
position error
would be used to correct the interferogram. Discrete Fourier Transform would
be
performed upon the corrected interferogram to produce the spectra.
As illustrated in Figure 7, the rotatable polarizer/analyzer 18 may be
replaced by
a rotatable quarter-waveplate 40' followed by a fixed polarizer/analyzer 18' .
An
advantage of making the quarter-wave plate 40' rotatable, instead of the
polarizer/analyzer 18' , is that it allows the state of polarization at the
output of the
polarizer/analyzer 18' to be rigorously fixed. The waveplate 40' should be
precisely
calibrated (retardance) as a function of wavelength. Calculation of the Stokes
parameters
is more complex.
Figure 8 illustrates a modification to the apparatus of Figure 6. The
modification
entails omitting the rotatable polarizer/analyzer 18 completely and modifying
the
interferometer unit 54 (Figure 6) by replacing the photodetector (not shown)
with a real-
time Stokes analyzer. Thus, referring to Figure 9, the output from the device
14 is
passed directly to interferometer 54' wherein it passes through a coupler 64
to a fixed
minor 66 and, via a lens 68, to a moving minor 70. The light from the minors
66 and
70 is returned via the coupler 64 to real-time Stokes analyzer 72 wherein it
is reflected
by a first sputter 74 to pass through a quarter wave plate 76 and a first
polarizes 78 to
a first detector 80. The polarizes 78 has a maximum transmission axis set at
45 degrees
ap60Qwefl5vt.ref

CA 02236521 1998-OS-O1
relative to a reference. Light transmitted by the first sputter 74 and
reflected a second
sputter 82 passes through a second polarizes 84 to a second detector 86. The
axis of the
second polarizes is set to 135 degrees. Light transmitted by the second
sputter 82 is split
by a polarizing beam splitter 88 into a vertically-polarized reflected
component which
5 is supplied to third detector 90 and a horizontally-polarized transmitted
component which
is supplied to fourth detector 92. The outputs of the four detectors 80, 86,
90 and 92,
respectively, are converted to digital numbers by an analog-to-digital
converter 94, the
output of which is supplied to the storage unit 56 and Fourier-transform unit
58 (Figure
6). Processing may then be carried out as described previously to obtain the
Stokes
10 parameters and characterize PMD. However, because the real-time Stokes
analyzer
provides the sign of the Stokes parameter s3, it is possible to perform Jones
Matrix
Eigenanalysis (JME).
An advantage of using the real time Stokes analyzer is that four
interferograms
are obtained in the same scan of the moving mirror. However, it should be
recognized
15 that this approach is more costly and is more sensitive to residual PMD and
PDL of the
interferometer. Moreover, it requires an airpath interferometer to be used.
The analyzers of Figures 1 and 7 measure the intensity I of the light from the
device under test at each of a plurality of angular orientations in a plane
perpendicular
to the propagation axis of the light. In the embodiment of Figure 1, both the
polarizes
18 and the quarter waveplate 40 rotate together to the different angles of
orientation. In
the embodiment of Figure 7, the polarizes 18' is fixed and is preceded by a
quarter
waveplate 40' which can be rotated to the different angles of orientation. In
both of these
embodiments, a set of measurements of polarization state at the different
frequencies or
wavelengths are made for each of the different orientation angles.
The embodiment of Figure 9 differs from those of Figures l and 7 in that
neither
of the analyzer components rotate physically. The analyzer of Figure 9
comprises a fixed
polarizes 18' preceded by a highly birefringent component 62 which also is
fixed. The
output of the device under test 14 passes through the component 62 and the
fixed
polarizes 18' . From the point of view of the state of polarization at the
input end of the
HiBi component 62, this setup is equivalent to an analyzer whose axis rotates
continuously with optical frequency. Assuming that the axis of fixed polarizes
18' is

CA 02236521 1998-OS-O1
16
along the s, coordinate (sl=1, s2=0, s3=0), the rotation of the equivalent
"analyzer"
occurs in the sls3 plane.
The component 62 may be a highly birefringent (HiBi) fiber, a highly
birefringent
crystal, or other suitable component. The maximum transmission axis of the
fixed
polarizer 18' is displaced, relative to the birefringence (fast) axis of the
component 62,
by precisely 45 degrees in the plane perpendicular to the propagation axis. In
practice,
a precision of 0.1 degrees has been found to be suitable. Such precision is
required in
order for the equivalent axis of the analyzer, i.e. its generalized high
transmission axis,
to rotate along a geodesic on the Poincare sphere.
As illustrated in Figure 10, the intensity I of the light from the output of
the
analyzer of Figure 9 varies as a function of wavelength/frequency, as if the
high
transmission axis of the analyzer (i. e. the combination of polarizer 18' and
component
62) were being rotated physically as a function of frequency. The variation is
at a much
higher rate than the variation of the state of polarization at the output of
the device under
test and, in effect, is the equivalent of sampling a signal at a rate which is
much higher
than the Nyquist rate. In the sample waveform illustrated in Figure 10, the
intensity I
varies generally sinusoidally with a mean period of about 1 TeraHertz. The
period
actually varies from cycle to cycle as the phase of the signal varies. The
amplitude of
the envelope E of the waveform also varies. The variation in the amplitude E
of the
envelope and in the phase of the intensity I represent the state of
polarization of the light
leaving the device under test.
As illustrated in Figure 11 and in the flowchart of Figure 13, in the
processor 22'
(Figure 9), measurements are taken of the intensity values A and A' at a first
pair of
points on curve I which are orthogonal, i. e. spaced apart by one half of the
mean period
1/28To of the periodic waveform for intensity I. The total intensity value
midway
between the pair of points is interpolated by adding the two measurements A
and A' .
Similar measurements are made for a second pair of points B and B' which also
are
orthogonal but each displaced by one sample interval from the corresponding
one of the
first pair of points. Typically, for a period of 1 TeraHertz, the sample
interval might be
0.1 TeraHertz. The procedure is repeated until a sufficient number of pairs of
points
have been measured and interpolated to cover the entire bandwidth of the
signal at the
output of the device under test, which will be equal to or less than the
bandwidth of the

CA 02236521 1998-OS-O1
17
broadband source. The resulting interpolated values represent the deduced
spectrum I;
at the input of the analyzer, as deduced from the values of I°"~, and
illustrated in Figure
10.
The output spectrum I~ then is divided by the deduced input spectrum I;a. The
division is effected by dividing each value of I°", by the value of Im
at the same
wavelength or frequency. The resulting curve, illustrated in Figure 12,
represents the
normalized transmission waveform of the analyzer.
An advantage of this "simulated rotation" analyzer is that it avoids moving
parts
and their associated alignment difficulties. Moreover, the state of
polarization is
rigorously fixed at the output of the analyzer, i. e. at collimator 26, and
only one scan
is needed, instead of the four scans at 0 °, 45 ° , 90 °
, 135 ° , respectively, of the
embodiments of Figures 1 and 7.
It should be appreciated that the rate of variation of the normalized
transmission
waveform of the analyzer of Figure 9 must be significantly greater than the
rate of
variation of the state of polarization at the output of the device under test;
typically, at
least by a factor of 2 times the highest value of the rate of variation of the
polarization
state of the device under test. The rate of variation of the normalized
transmission of the
analyzer is, in fact, the delay 8To of the high birefringence component 62.
The operating sequence when using the analyzer of Figure 9 is similar to that
shown in Figure 4, but minus some of the steps and with the additional step of
computing the normalized transmission waveform for use in calculating the
Stokes
parameters instead of the raw spectra. Thus, refernng to Figure 13, in step
13.1, the
equipment is initialized by turning on the sources and adjusting power levels
and gains,
and so on. In step 13.2, the orientation of the input polarizer 12 is set to
zero degrees
and, in step 13.3, the spectral data acquired as described above with
reference to the
embodiment of Figure 1. In step 13.4, the data is saved. Decision step 13.5
determines
that the polarizer 12 is set to zero and step 13.6, in the return loop, sets
it to 45 degrees.
Steps 13.3 and 13.4 are repeated to save corresponding data for the second
orientation
of polarizer 12 and, upon decision step 13.5 returning a negative result, step
13.7
devices the envelope and phase of the normalized transmission as described in
reference
apE004efl5ml.nf

CA 02236521 1998-OS-O1
18
to Figures 10 - 12, for each setting of polarizer 12. Finally, step 13.8
computes the
Stokes parameters from the saved spectra. The Stokes parameters are computed
from the
envelope and phase according to the expressions:
Sl ~~) I = 1 - (Sa (~,) + S3 t~) )
sz = A cos(~)
s3 = A sin()
where A is the peak amplitude of the normalized transmission waveform, and ~
is its
phase with respect to an arbitrary reference phase. The PMD then is
calculated, as
before, according to the flowchart of Figure 5.
This embodiment of the invention overcomes the following drawbacks of the
standard interferometric method, particularly the PMD-biasing technique
described in
patent No. 5,654,793 (which uses interferometric or WS Fourier analysis):-
(1) It is sensitive to the shape of the spectrum transmitted through the
device
under test. The width and shape of the side peaks depend strongly on the shape
of this
spectrum.
(2) The width and shape of the peak also depend strongly on the relative
orientations of the birefringence axes of the DUT and the artefact. It is only
the RMS
value of the width, averaged over a large number of relative orientations that
obeys the
difference of squares formula. The only occurrence where the ifference of
sqaures
formula is obeyed with certitude without averaging over a large number of
relative
orientations is when a large, strongly coupled PMD value is measured. As an
example,
in the case of a weakly coupled DUT whose principal state of polarization
happens to
be aligned with the birefringence axis of the PMD artefact, there is no
broadening of the
peak; only a displacement.
An advantage of embodiments of the present invention is that they allow the
use
of apparatus which is relatively inexpensive and portable to make PMD
measurements
using data analysis techniques according to the different standardized
methods. The
particular analysis method may be selected according to the type of device
under test,
range of PMD values, stability of the device under test, degree of mode
coupling, type
of results needed, and so on. Moreover, given that PMD is an inherently
fluctuating

CA 02236521 1998-OS-O1
19
quantity that is difficult to characterize with full certainty, the ability to
use different
forms of data analysis may afford a greater degree of comfort with the
measurements.
ap600~renfiul.xef

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