Note: Descriptions are shown in the official language in which they were submitted.
I L~L~:lyllJ
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FIXER OPTIC ROTATION SENSOR UTILIZING
HIGH BIREFRINGENCE FIBER
Background of the Invention
The present invention relates to rotation sensors for
use in, e.g., gyroscopes, and particularly to fiber optic
rotation sensors.
Fiber optic rotation sensors typically comprise a loop
of single-mode optical fiber to which a pair of light waves
are coupled for propagation in opposite directions around
a loop. If the loop is rotated, the counter-propagating
waves will undergo a phase shift, due to the well-known
Sagnac effect, yielding a phase difference between the
waves after traverse of the loop. By detecting this phase
difference, a direct indication of the rotation rate of
the loop may be obtained.
If the optical path lengths about the loop for the
counter-propagating waves are equal when the loop is at
rest, the interferometer is said to be "reciprocal In
practice, however, fiber interferometer loops are
ordinarily not reciprocal, due to the fact that present,
commercially available optical fibers are not optically
perfect, but are birefringent (i.e., doubly refractive),
resulting in two orthogonal polarization modes, each of
which propagates light at a different velocity. One of
the polarization modes, therefore, provides a "fast
channel", while the other provides a "slow channel." In
addition, the fiber birefringence is sensitive to
environmental factors, such as temperature, pressure,
magnetic fields, etc., so that, at any given point along
the fiber, the birefringence can vary over time in an
unpredictable manner. Birefringence affects the counter-
propagating waves in a complex way, however, the effect
may be viewed as causing a portion of the waves to be
coupled from one of the polarization modes to the other,
i.e., from the "fast channel" to the "slow channel or vice
versa. The result of such coupling between modes is that
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each of the counter-propagating waves may travel different
optical paths around the loop, and thus, require different
time periods to traverse the fiber loop, so that there is
a phase difference between the waves when the loop is at
rest, thereby making the interferometer non-reciprocal.
The foregoing may be more fully understood through a
rather simplistic, extreme example in which it is assumed
that there is birefringence only at one point in the fiber
loop, and that this point is located near one end of the
loop. It is also assumed that such birefringence is
sufficient to cause light energy to be entirely coupled
from one polarization mode to the other, and that there is
no coupling between modes anywhere else in the fiber
loop. If -the counter-propagating waves are introduced
into the loop in the fast channel, one of the waves will
immediately be coupled to the slow channel while the other
wave will traverse most of the loop before being coupled
to the slow channel. Thus, one of the waves will traverse
most of the loop in the fast channel, while the other will
traverse most of the loop in the slow channel, yielding a
phase difference between the waves when the loop is at
rest. If this birefringence-induced phase difference were
constant, there would, of course, be no problem, since the
rotational induced Sagnac phase difference could be
measured as a deviation from this constant birefringence-
induced phase difference. Unfortunately, however, such
birefringence-induced phase differences vary with time in
an unpredictable manner, and thus, these birefringence-
induced phase differences are indistinguishable from
rotationally-induced, Sagnac phase differences. Thus,
time varying changes in birefringence are a major source
of error in fiber optic rotation sensors.
The prior art has addressed the problem of non-
reciprocal, birefringence-induced phase differences in a
variety of ways. In one approach, described by R. A.
Burgh, H. C. Lefevre, and H. J. Skew in Optics Letters,
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Volume 6, No. 10 (October 1981), a fiber optical polarizer
is utilized to block light in one of the tow orthogonal
polarization modes while passing light in the other. This
insures that only a single optical path is utilized,
thereby providing reciprocity. This approaches also
described in International Patent Application No. PCT/US
8~/00400 published October 14, 19~2, as Publication No. WOW
82/03456, entitled "Fiber Optic Rotation Sensor," and also
in U.S. Patent No 4,410,275, entitled "Fiber Optic
Rotation Sensor". Another approach involves utilizing
unpolarized light, which has been found to result in
cancellation of birefringence-induced phase differences
upon combining the counter-propagating waves after
traverse of the loop. The degree of cancellation is
proportional to the degree to which the light waves are
unpolarized. This approach is described in detail in
International Patent Application No. PCT/US ~2/00985,
published February 17, 1983 as Publication No. 83/00552,
and also in corresponding U.S. Patent No. 4,528,312,
entitled "Fiber Optic Rotation Sensor ~tilizin8
Unpolarized Light".
It is also known in the art to utilize polarization-
conserving fibers to reduce coupling between the modes.
Polarization-conserving fibers are essentially high
birefringence fibers, in which the fiber is mechanically
stressed during manufacture to increase the difference in
the refractive indices of the two polarization modes.
This reduces coupling between the modes, since the high
birefringence tends to preserve the polarization of the
light waves. In effect, changes in birefringence due to
environmental factors are overwhelmed by the stress-
induced birefringence created during manufacture of the
fiber.
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Summary of the Invention
The present invention comprises a fiber optic Sagnac
interferometer employing high birefringerlce fiber, e.g.,
of the type described in Electronics Letters Volume 18,
Number 24 November 25, 1982), pages 1306 to 1308 This
high birefringence fiber reduces the average optical power
transferred from one polarization mode to the other to
about one percent or less over 1 km of fiber. As an
approximation, the maximum phase error due to coupling
between modes is equal to the fraction of power
transferred between the modes. Thus, for a l-km fiber
loop having a power transfer rate of 1% per km, the
maximum phase error would be .01 or 10-2 radians.
In a preferred embodiment, the present invention
substantially reduces the maximum phase error by utilizing
a wide band, short coherence length laser source in
combination with the high birefringence fiber. The amount
of reduction is dependent upon the "giber coherence
length", which is a newly coined term that should be
distinguished from the coherence length of the source us
used herein, the term "fiber coherence length" is defined
as the length of fiber required for the optical path
length difference between the two polarization modes to
equal one coherence length of the light source. It is
approximately equal to the coherence length of the source
divided by the difference in refractive index between the
polarization modes. In general, the shorter the fiber
coherence length, the greater the reduction in phase
error. More specifically, use of a short fiber coherence
length results in a phase error reduction which is
proportional to lo , where N is the loop length divided
by the fiber coherence length.
The fiber loop may thus be considered as being divided
into N segments, each having a length of one fiber
coherence length. Light coupled from one polarization
mode to another over one segment (fiber coherence length)
I
will add coherently over that segment but not
thereafter. Further, after the waves have traversed the
fiber loop, and are recombined, the only portions of the
coupled light which will interfere with each other will be
those which were coupled at symmetric segments of the
fiber loop. Consequently, interference between light wave
components coupled between polarization modes is reduced
dramatically, thereby reducing the birefringence-induced
phase error. Through use of present, state of the art
components, such reduction in interference provides, e.g.,
an additional factor of 100 improvement, so that the
maximum phase error, assuming a 1 km, high birefringence
fiber having a power transfer rate of 1%, decreases from
10 2 radians to 10 4 radians.
Further improvement in phase error reduction may be
obtained by launching each of the orthogonal polarization
modes with light that is of substantially equal intensity,
and preferably uncorrelated so that the light is
unpolarized. This may be accomplished, for example, by
using an unpolarized light source. However, if the source
is not unpolarized, such equalized intensity can be
obtained by orienting the source so that its major axis of
polarization is at 45 relative to the principal axes of
birefringence of the fiber. To the extent that the
intensities are equal and the phases are uncorrelated,
phase differences between interfering cross-coupled light
wave components will cancel, yielding a net non-
rotationally-induced phase difference of zero. Assuming
that the intensities are equalized to within I of each
other, use of unpolarized light in combination with the
high birefringence fiber and short coherence length source
provides a further improvement of a factor of about 100 in
the maximum phase error, reducing it to, e.g., 10 6
radians.
thus, the present invention substantially eliminates
the effects of bireEringence-induced phase differences,
d
permitting detection of the rotationally induced Sagnac
phase difference with a high degree of accuracy.
In a preferred embodiment of this Sagnac rotation
sensor, a coupler is utilized to couple an input light wave
to the fiber inter~erometer loop. This coupler splits the
input light wave into first and second light waves which
propagate around the loop in opposite directions, and
combines these first and second light waves to form an
optical output signal which is detected at a detector.
The detected optical output signal provides an indication
of the rotation rate of the loop. The plural fiber
coherence lengths in the loop reduce phase errors in the
optical output signal caused by coupling of light from one
mode to the other. In another embodiment of the
invention, a polarizer is inserted between the light
source and the coupler to pass light of a selected
polarization, while rejecting light of the orthogonal
polarization. The polarizer is positioned relative to the
fiber so that the selected polarization pass by the
polarizer is aligned with the principal axis of
bire~rinyence of the fiber which corresponds to a
polarization mode in which the input light wave
propagates. By way of example, the coupler may comprise
two portions of the birefringent fiber, juxtaposed for
coupling there between, such that the principal axes of
birefringence of one of the juxtaposed fiber portions are
parallel to the corresponding principal axes of the other
of the fiber portions
In addition to reducing phase error, the present
invention advantageously improves the stability of the
detected output signal. Those skilled in the art will
recognize that even though an interferometer is perfectly
reciprocal and generates no phase errors, the output
signal may nevertheless vary in intensity. Such
variations, in effect, change the "scale factor" or
"proportionality factor" between the detected intensity
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and the rotation rate. In unpolarized light rotation
sensors these variations are caused, e.g., by interference
between light wave components which are coupled between
polarization modes. Since the present invention reduces
interference between such coupled light wave components,
these "scale factor" variations are reduced, thereby
further improving performance of the rotation sensor.
These and other advantages of the present invention
are best understood through reference to the drawings.
Description of the Drawings
Figure 1 is a schematic drawing of the rotation sensor
of the present invention, showing a single, continuous
strand of optical fiber, to which light from a light
source is coupled, and showing the multimedia sensing loop,
formed from such single, continuous strand; in addition,
Figure 1 shows a detection system for detecting the phase
difference between waves counter propagating through the
fiber loop;
Figure 2 is a schematic drawing illustrating a
conceptual model of the fiber loop, showing, for an
exemplar pair of polarization modes, the electric yield
components of the counter propagating waves as they
traverse the fiber loop;
Figure 3 is a schematic drawing of the conceptual
model of Figure 2, showing the electric field components
of the counter propagating waves after they have traversed
the fiber loop;
Figure 4 is a vector diagram of the optical output
signal, showing a vector directed along the real axis,
which represents the vector sum of the "do" terms
resulting from the electric field components shown in
Figure 3, and another vector, rotating in the manner of a
fuzzier, which represents the vector sum of the
interference terms resulting from the electric field
components shown in Figure 3, and further illustrating the
response of the vector representing the interference terms
icky
to l) the rotationally-induced Sagnac phase difference,
and 2) phase errors caused by non-rotationally induced
phase differences;
Figure 5 is a graph, corresponding to the vector
diagram of Figure 4, of the optical intensity, as measured
by the detector, versus the Sagnac phase difference,
illustrating the effect of non-rotationa].ly induced phase
errors;
Figure is a vector diagram of the interference terms
resulting from Group III electric field components;
Figure 7 is a vector diagram showing a resultant
vector which represents the vector sum of the two vectors
of Figure 6, and illustrating the phase error associated
with such resultant vector sum;
Figure 8 is a vector diagram showing the vectors of
Figure 6 equalized in magnitude;
Figure 9 is a vector diagram of a resultant vector,
which represents the vector sum of the vectors of Figure
8, illustrating that phase errors may be eliminated by
equalizing the magnitudes of the vectors;
Figure lo is a graph of the optical intensity, as
measured by the detector, versus the Sagnac phase
difference, illustrating the effect of changes in the
magnitude of the interference factor of Figure 4, assuming
a phase error of zero;
Figure if is a schematic drawing illustrating the
fiber loop divided into two segments, each having a length
of one fiber coherent length;
Figures 12 and 13 are schematic drawings illustrating
conceptual models of the fiber loop, showing, for an
exemplary pair of polarization modes, the cross coupled
electric field components of the counter propagating waves
as they traverse the plural segment loop of Figure if;
Figure 14 is a vector diagram of the interference term
resulting from group III electric field components in the
two segment fiber loop of Figures if, 12, and 13, and
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I
illustrating that the vector in addition of such
components yield resultant vectors which are reduced in
magnitude;
Figure 15 is a vector diagram similar to that of
Figure 14, illustrating Group III interference components
for a 10 segment loop victrola adding to yield result
injectors which are further reduced in magnitude;
Figure 16 is a vector diagram of the optical output
signal at the detector, showing the interference vectors
for Group I, Group II, and Group III components
victrola adding to form the overall interference
vector, which represents the vector sum of all the
interference terms, and further illustrating the effect of
the magnitude and phase of Group III interference terms on
the phase of the overall interference vector;
Figure aye and (b) are vector diagrams at times if
and to, respectively, illustrating how variations in the
phases of Group III interference components for the two
polarization modes can cause scale factor problems through
variations in Group III vector magnitude.
Figure 18 is a sectional view of one embodiment of the
fiber optical directional coupler for use in the rotation
sensor of Figure l; and
Figure 19 is a sectional view of a fiber optic
polarizer which may be utilized in the rotation sensor of
Figure 1.
Detailed Description of the Preferred Embodiment
In the preferred embodiment, shown in Figure 1, the
rotation sensor of the present invention comprises a light
source 10 for introducing a ow light wave into a single,
continuous length or strand of single mode optical fiber
11. As used herein, "single mode fiber" means that the
fiber supports only one fundamental mode for the
particular source light used, as opposed to multimedia
fiber which supports more than one fundamental mode.
However, it will be recognized that a single mode fiber
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includes two orthogonal polarization modes, each of which
propagates light at a different velocity.
The fiber 11 passes through ports, labeled A and C, ox
a first directional coupler 12, and through ports, labeled
A and C of a second directional coupler 14. Thus, the
fiber 11 extends from the light source 10 to port A of the
coupler 12 and extends from port C of the coupler 12 to
port A of the coupler 14 Jo form a line portion lo of
fiber between the source 10 and coupler 14. The portion
of the fiber 11 extending from port C of the coupler 14 is
wound into a loop 16. By way of specific example, the
loop 16 may comprise about 1400 turns, each bounding an
area of about 150 so, cm for a total loop length of 600
meters. The end of the fiber 11, from the loop 16, is
passed through ports, labeled D and B, of the coupler 14,
with port D adjacent to the loop I A small portion 17
of the fiber 11 extends from port B of the coupler 14 and
terminates non reflectively, without connection
A second length of fiber 19 is passed through the
ports labeled D and B of the coupler 12. The portion of
the fiber 19 projecting from port D terminates
non reflectively, without connection, However, the portion
ox the fiber 19 projecting from port B of the coupler 12
is optically coupled to a photodetector 20, which produces
an output signal proportional to the intensity of the
light impressed thereon.
The present invention also includes detection
electronics 22, comprising a lock-in amplifier 24, a
signal generator 26, and a phase modulator 28. my way of
specific example, the phase modulator 28 may comprise a
PUT cylinder, having a diameter of ego, about 1 to 2
inches, about which a portion of the fiber loop 16 is
wrapped, erg., 4 to 10 times. The fiber is bonded to the
PUT cylinder 28 by a suitable adhesive, so that the fiber
35 11 will be stretched upon radial expansion of the cylinder
28. In this regard, the phase modulator 28 is driven by
an AC modulating signal, having a frequency in the range
erg._
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of, e.g., Lucas, which is provided on a line 30 from
the signal generator 26. For proper operation ox the
detection electronics 22, it is important that the phase
modulator I be located on one side of the loop lo, e.g.,
adjacent to the port D of the coupler 14, rather than at
the center of the sensing loop 16.
The AC modulation signal from the generator 26 is also
supplied on a line 32 to the lock-in amplifier 24. A line
34 connects the lock-in amplifier 24 to receive the
detector 20 output signal. The amplifier utilizes the
modulation signal from the generator 26 as a reference for
enabling the amplifier 24 to synchronously detect the
detector output signal at the modulation frequency. Thus,
the amplifier 24 effectively provides a band pass jilter
at the fundamental frequency (i.e., the frequency of
modulation) of the phase modulator 28, blocking all other
harmonics of this frequency. It will be understood by
those skilled in the art that the magnitude of this
harmonic component of the detector output signal is
proportional, through an operating range, Jo the rotation
rate of the loop 16. The amplifier 24 outputs a signal
which is proportional to this first harmonic component,
and thus, provides a direct indication of the rotation
rate.
Additional details of the detection electronics 22 are
described in international patent application No. PCT/US
82/00400 published October 14, 1982, as publication No. WOW
82/03456, and entitled "Fiber Optic Rotation Sensor", and
in U.S. Patent No. 4,410,275. This detection Sistine is
also described in Optics Letters, Vol. 6, No. 10, (October
1981) pp. 502-50~.
In the embodiment shown, the fiber 11 comprises a
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highly birefringent single mode fiber, e.g., of the type
described in the article entitled "Fabrication of
Polarization Maintaining Fires Using Gas-Phase Etching",
Electronics Letters, Vol. 18, No. 24, p.1306 (November 25,
1982).
The light source 10 should provide light which has a
short coherence length. A preferred light source for use
as the source 10 is a super radiance diode, e.g., of the
type described in the article entitled "High Power Low
Divergence Super radiance Diode", Physics Letters,
Vol. 41, No. 7 (October 1, 1982).
The photodetector 20 is a standard pin or avalanche-
type photo diode, which has a sufficiently large surface
area to intercept substantially all of the light exiting
the fiber lo, when positioned normal to the fiber axis.
The diameter of the photodector 20 is typically in the
range of about l millimeter, the exact size depending upon
the diameter of the fiber 19, the numerical aperture of
the fiber lo (which defines the divergence of the light as
it exits the fiber lo) an the distance between the end of
the fiber lo and the photodetector 20~
In operation, a light wave Wit is input from the light
source 10 for propagation through the fiber if. As the
wave Wit passes through the coupler 12, a portion of the
I light (e.g. 50 per cent) is lost through port D. The
remaining light propagates from port C of the coupler 12
to the coupler 14, where the light is split evenly into
two waves We, We, which propagate in opposite directions
about the loop 16. After traverse of the loop 16, the
I waves We, We are recombined by the coupler 14 to form an
optical output signal We. A portion of the recombined
wave We may be lost through the port B of the coupler 14,
while the remaining portion travels from port A of the
coupler 14 to port C of the coupler 12, where it is again
split, with a portion thereof (e.g., 50~) transferred to
the fiber 19. Upon exiting the end of the fiber 19, the
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wave We is impressed upon the photodetector 20, which
outputs an electrical signal that is proportional to the
optical intensity of the wave We.
The intensity of this optical output signal will vary
in proportion to the type (i.e., constructive or
destructive) and amount of interference between the waves
We, We, and thus, will be a function of the phase
difference between the waves We, We. Assuming, for the
moment, that the fiber 11 is "ideal" (i.e., that the fiber
has no birefringence, or that the birefringence does not
change with time), measurement of the optical output
signal intensity will provide an accurate indication of
the rotationally induced Sagnac phase difference, and
thus, the rotation rate of the fiber loop 16.
As indicated above, present state-of-the-art, fibers
are far from "ideal", in that 1) they are birefringent,
and 2) the birefringence is environmentally sensitive and
tends to vary, thus, yielding non rotationally induced
phase differences Leo phase errors), which are
indistinguishable from the rotationally induced Sagnac
phase difference. The present invention utilizes three
different techniques to reduce or eliminate these phase
errors, namely, 1) the use of a high birefringence giber
to reduce coupling between the polarization modes; 2) the
use of a sideband, highly incoherent light source in
combination with the high birefringence fiber to reduce
interference between light wave components which have been
coupled between polarization modes; and 3) equalizing the
light wave intensity in each of the two polarization modes
to cause the phase differences between interfering
components of light which has been coupled between
polarization modes to cancel.
Phase Error Analysis:
Such reduction or elimination of phase errors may be
more fully understood through reference to Figure 2, which
depicts a conceptual model of the two orthogonal
I
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polarization modes of a single mode fiber. Each
polarization mode has a prorogation velocity different
from that of the other polarization mode. Further, it is
assumed that there is coupling of light energy between
modes, which may be caused e.g. by variations or
perturbations in the principal axes of birefringence of
the fiber. Such coupling of energy will be referred to
herein as "cross coupling."
The conceptual fiber model of Figure 2 will be
utilized to represent the sensing loop 16 (Figure 1). Tune
counter propagating waves We, We, are schematically
represented as being coupled, by the coupler 14, to the
loop 16, by the dashed arrows. The two polarization modes
of the single mode optical fiber are schematically
represented in Figure 2 by a first line, connecting a pair
of terminals C' and D', and a second line, parallel to the
first liner connecting a second pair of terminals C'' and
D". The terminals C' and C'' on the left side of Figure
2 correspond the port C of the coupler 14, while the
terminals Do and Do on the right side of Figure 2
correspond to the port D of the coupler 14. The above
mentioned first and second lines connecting the terminals
will be used to represent arbitrary modes i and j,
respectively, of the fiber loop 16.
Cross coupling between the modes i and j is
represented by a pair of lines, labeled "Branch 1" and
"ranch 2", respectively. Branch 1 represents cross
coupling between the terminals C'' and D' while branch 2
represents cross coupling between terminals C' and D''.
The intersection of branch 1 with branch 2, designated by
the referenced numeral 50, will be referred to as the
"coupling center". It will be understood that no coupling
exist between the two branches 1 and 2. The coupling
center 50 is shown as being offset from the center of the
fiber loop 16 to illustrate that the coupling between the
polarization modes is not uniform along its length.
:~2~:~76~
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Therefore, cross coupled light will travel a longer path
in one of the modes than the other, yielding a
non rotationally induced phase difference there between.
Moreover, it will be understood that, in reality, the
fiber birefringence, being environmentally sensitive,
varies with time, thus making the optical paths traveled
by the cross coupled light also time varying.
As shown in Figure 2, the wave of We is coupled to the
fiber loop 16 so that the modes i and j are launched with
electric field amplitudes Hi and En respectively.
Similarity, the wave We is coupled to launch each of the
modes i and j with electric field amplitudes El and En
respectively. The plus (+) and minus (-) superscripts
designate the direction of propagation, the -clockwise
direction about the loop 16 being designated by the plus
(+) sign, and the counterclockwise direction around the
loop 16 being designated by the minus (-) sign.
As light in each of the modes i and j traverses the
fiber loop 16, energy is coupled between the modes, so
that each electric field is divided into two components,
namely, a "straight through" component, designated by the
subscript "s", and a "cross coupled" component, designated
by the subscript "c". Thus, El is divided into a
straight through component His which remains in mode i
during traverse of the loop 16, and a cross coupled
component Ejc which is cross coupled to mode j during
traverse of the loop 16. Similarity, Hi is divided into
components Ens and Eke; E]
is divided into components Epic and Ens; and E
is divided into components Ens and Elm
After the light waves have traversed the fiber loop
16, the light at terminal C' will comprise
E- d E- ; the light at terminal C'' will
comprise component Ens and Eke ; the light at terminal D'
will comprise components His and Epic ; and the light at
terminal D' ' will comprise components Ens and Ejc as
~2~766~
-16-
shown in Figure 3. These 8 electric field components are
combined by the coupler 14 to form the optical output
signal We. It will be recognized by those skilled in the
art that, in general, superposition of any two electric
field components, e.g., Ens and Eke will yield a
resultant intensity (I), as measured by the detector 20,
which may be defined as follows:
I E+ 1 2 + I E+ 1 2 + 2 I ENS I I Epic I ( 1 )
where, in this particular example, is the phase
difference between field components E+ and Eke .
The first two terms of equation (1), namely
ESSAY and EKE are steady-state or do terms, while
the last term is an "interference" term having a magnitude
depending upon the phase difference between the fields
E US and Epic .
In general, all 8 of the above fields
is' Epic, Ens, EKE ENS, EKE r ENS and E+ ,
will interfere with each other to provide an optical
intensity at the detector 2Q (Figure 1) comprised of 8
"do" terms, which are not phase-dependent, and 28
"interference" terms which are phase-dependant~ The
number of combinations of phase-dependant terms is
actually n(n-1) or 56 phase-dependent terms. However,
one-half ox these terms are simply the reordered forms of
the other half, yielding 28 non-redundant terms.
I
The 8 do terms are shown in Figure 4 as a single
vector sum, labeled Id, while the 28 interference terms
are shown in Figure 4 as a single vector, labeled Ii
These vectors Id and Ii are plotted in a complex plane.
Upon rotation of the fiber loop 16 (Figure 1) the phase-
dependent vector Ii rotates, in the manner of a fuzzier,
through an angle equal to the rotationally reduced phase
difference us due to the Sagnac effect. The projection of
the interference vector Ii upon the real axis, when added
to the vector Id, yields the total optical intensity IDES
of the optical output signal We, as measured by the
276~
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detector 20 (Figure 1). In Figure 5, this optical
intensity IDES is plotted as function of the Sagrlac phase
difference so as illustrated by the curve 52.
As indicated above in reference to Figure 2, cross
coupling between the modes i and j can cause the fiber
loop 16 to be nonreciprocal, resulting in a
nonrotationa]ly induced phase difference between the above
described electric field components, and yielding an
accumulated phase error eye which is indistinguishable
JO from the rotationally induced Sagnac phase difference
us The phase error ye causes the fuzzier Ii to be
rotated, e.g., from the position shown in solid lines to
the position shown in dotted lines in Figure 4. This
results in the curve 52 of Figure 5 being translated by
an amount ye e.g., from the position shown in solid lines
to the position shown in dotted lines in Figure 5.
Elimination or reduction of the accumulated phase
error ye requires an analysis of the 28 interference terms
resulting from superposition of the 8 electric field
components discussed in reference to Figure 2. At the
outset, it will be recognized that interference between
electric field components Ens with Eye, and Ens with Ens
result in no phase error contribution, since the light
represented by these components is not cross coupled, and
traverses the loop in a single one of the modes. However,
the remaining 26 interference terms can contribute to the
accumulated phase error ye. These 26 interference terms
correspond to 26 pairs of electric field components which
may be classified into 3 groups, namely, Group I, Group
I II, and Group III, as follows:
7 6 6 I r
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Group I Group II
Ens and Eke His and Eke
essay and Elm Ens and Ens
Ens and Eke Ens and Eke
Ens and Elm His and Ens
Lucy and Eke Epic and Ens
Ens and Eke Epic and Ens
us and Eke Epic and Eke
Ens and Eke Epic and Ens
Epic and Eke
Epic and Ens
Elm and Eke
E. and E+
I lo US
Group III Ens and EJc
Elm and Epic Ens and Ens
Eke and Eke Ens and Eke
Ens and Ens
US
~2';~66C)
--19--
though only the interfering electric field components
are listed above, and not the interference terms
themselves, it will be understood that the interference
term for each of the above listed pairs of components may
be readily calculated in accordance with the example
provided in reference to equation (1).
Elimination of Grow errors-
Group I includes those pairs of field components which
originated in different modes, but which are in the same
mode upon reaching the coupler 14, after traversing the
loop 16. For example, the first of Group I pair of
components comprises a straight-through component Ens
which originated in mode i and remained in mode i during
traverse of the loop 16, and a cross coupled
component Eke which originated in mode j but was cross
coupled to mode i during traverse of the loop 16.
Ordinarily, these components would interfere with each
other, as described in reference to equation I
However, if the phase difference between these light
wave components is random, interference between the light
wave components will be averaged to zero in the detector
20. Accordingly, Group I interference terms can be
eliminated by insuring that, upon reaching the coupler 14,
and thus the loop 16, the light in each mode is
incoherent, i.e., random in phase with respect to the
light in the other mode. Thus, for example, if the light
in mode i is incoherent with respect to light in mode j,
the interference between, e.g., the components
Ens and Eke , will be averaged to Nero in the detector
30 20. Similarly, the interference between the remaining
components, e.g., Ens and Epic; His and Epic; etc., will be
averaged to zero.
Such incoherence between Group I components is
achieved in the present invention by using the high
birefringence fiber 11 in combination with the short
coherence length light source 10. Specifically, the
I
20-
birefringence of the fiber 11 and the coherence length of
the source 10 should be selected such that there is at
least one "fiber coherence length" between the source 10
and the coupler 14. As used herein, "fiber coherence
length" is defined as the length of fiber required con the
optical path length difference between the two
polarization modes to equal one coherence length of the
light source 10. As a good approximation, the fiber
coherence length is equal to the coherence length of the
source 10 divided by the difference in refractive index
between polarization modes. Accordingly, by utilizing a
sufficiently short coherence length source 10, in
combination with a sufficiently high birefringence fiber
11, interference between the components listed in Group I
and thus, phase errors caused by such interference, may be
eliminated.
It will be understood by those skilled in the art that
the optical path lengths of the fiber modes may be
measured or calculated, using modal dispersion data
provided by the manufacturer of the fiber.
Elimination of Group II Errors:
Group II includes -those pairs of electric field
components which are in different modes, after traverse of
the loop 16, regardless of the mode in which they
originated. Thus, for example, field component Ens in
mode i is paired with component Eke in mode j. Since
the modes, i and j are orthogonal, and since the electric
fields of orthogonal modes do not interfere, there will be
no interference between the terms in Group II. It is
important to recognize, however, that the field patterns
of the paired electric fields in Group II are only
orthogonal in a "global" sense. That is, the entire field
patterns must be spatially averaged over a plane normal to
the fiber axis to eliminate interference. If such spatial
averaging is accomplished for only a portion of the field
patterns, orthogonality may not exist. To ensure that
foe
-21-
substantially the entire field patterns of the
polarization modes i and j are spatially averaged, the
present invention utilizes a detector 20 which has a
surface area sufficiently large to capture substantially
all of the light exiting the end of the fiber 19, as
discussed above.
Elimination of Group III Errors Through Use Of Unpolarized
Light:
Only two interference terms result from the pairs of
electric field components listed in Group III, namely, an
interference term resulting from superposition of the
component Eke with Epic , and another interference term
resulting from superposition of the
components Ejc with Eke . Thus, each interference term
results from a pair of components, one of which originated
in a first mode and, during traverse of the loop 16 was
cross coupled to a second mode, while the other originated
in that same first mode and was cross coupled to the same
second mode, but traversing the loop 16 in the opposite
direction. These interference terms, while being only two
in number, are highly sensitive to the environment and can
result in a phase error which may be orders of magnitude
larger than the Sagnac phase difference.
The interference between Epic and Epic yields a phase
dependent term:
Al edgy¦ coy (us+ up I (5)
Similarly, the interference between Ejc and Eke yields
a phase dependent term:
Al eye¦ coy so Pi I (6)
Where is the fraction of the optical power that is
coupled between the i and j modes per unit of fiber length
(e.g. km); L is the length of the fiber loop 16 (e.g. in
I km); I is the rotationally induced, Sagnac phase
difference between the two components; up is the total
t~fiGO
-22-
accumulated phase for light that is cross coupled from one
mode to another between the terminals C'' and D'; I is
the total accumulated phase for light that is cross
coupled from one mode to the other between terminals C'
and D"
The vectors corresponding to these interference terms
(5) and I are plotted in a complex plane in Figure 6, as
the vectors 56 and 58, respectively. The vector 56
represents light which has been coupled from the j mode to
the i mode and the vector 58 represents light which has
been coupled from the i mode to the j mode. It will be
understood that the interference terms (5) and (6) are
merely the projections of the vectors 56 and 58
respectively, upon the real axis. The i mode vector 56
and j mode vector 58 may be victrola added to yield a
resultant vector 60, shown in Figure 7. Note that, for
clarity of illustration, the Sagnac phase difference us is
assumed to be zero in Figures 6 and 7. Further, although
the phase angle up - I for the vectors 56, 68 is
necessarily shown in the drawings as being constant, it
will be recognized that this angle is environmentally
sensitive and can vary with time between zero and 360.
As shown in Figure 7, the vector 60 is inclined from
the real axis by a phase angle eye which represents
the non-rotationally induced phase error contribution to
the total phase error ye (Fig. 4) that is due to
interference between the components of Group III. The
projection of the vector 60 upon the real axis is simply
the algebraic sum of the two interference terms (5) and
Al {edgy¦ COY So Pi I + Neil coy I pi I (7)
Since the detector 20 measures that component of the
vector 60 which is along the real axis, the detector 20
output will be a function of the algebraic sum (7). Thus,
it may be seen that the Group III phase error eye
I I
-23-
(Figure 7) will cause a corresponding error in the
detector 20 output.
The algebraic sum (7) of the interference terms may be
rewritten as follows:
L [(eye -I ¦ En ¦ 2) coy (up- I coy so (eye
- IEj I sin (up- I sin so (8)
Note that, if eye¦ and IEj ¦ are equal, this aloe-
brain sum (8) reduces to:
2L YE¦ COY (UP- I COY US (9)
In this form, the effect of variations in the quantity
up - I can be distinguished from the rotationally induced
Sagnac phase difference so as may be more fully
understood through reference to Figures 8 and 9, which
show the effect, upon the resultant vector 60, of making
the vectors 56 and 58 equal in magnitude. It will be seen
that, regardless of the value of the quantity up - I the
resultant vector 60 will always be directed along the real
axis, and thus, the direction of the vector 60 is
independent of variations in the quantity up - I
However, such variations in pi will cause the Group III
resultant vector 60 to fluctuate in magnitude, which will
cause the signal measured by the detector 20 to
concomitantly fluctuate. That is, variations in pi
will still cause the magnitude of the output waveform 52
to increase or decrease, e.g., from the position shown in
solid lines in Figure 10 to the position shown in dotted
lines, but so long as the vectors 56 and 58 are equal in
magnitude, the output waveform 52 will not shift laterally
along the X axis, as did the waveform 52 in Figure 5.
Thus, so far as Group III errors are concerned, equalizing
the light intensity in each of the two polarization modes
will eliminate phase errors, but not scale factor
problems. Further, in practice, it is difficult to make
3LZ2~76~0
-24-
the light intensity for the modes precisely equal, so
there may be at least a small phase error due to Group III
components.
Preferably, the light in both polarization modes
should be substantially equalized with respect to
intensity so that the light is substantially unpolarized
by the time it reaches the coupler 14 and is split into
the counter propagating waves. This insures that the Group
III interference terms have the proper magnitudes for
substantial cancellation of the phase error at the
detector 20. As used herein, the terms "substantially
equalized" or "substantially unpolarized" means that the
respective intensities ox light in the modes are within
10~ of each other. It will be understood that presently
available light sources typically have both polarized and
unpolarized components, so that the source light may have
a degree of polarization. To equalize the light intensity
when the wide band source 10 is not completely
unpolarized, the source 10 should preferably be oriented
such that its major axis of polarization is 45 relative
- to the principal axis of birefringence.
Elimination Of Group III Errors Through Use Of A High
Birefrin~ence Fiber/Short Coherence Length Source:
The present invention provides a novel technique for
reducing the phase error contribution of Group III
components, which, advantageously, may be used in
combination with the above-discussed method relating to
unpolarized light, or it may be used independently.
The technique comprises utilizing the high
birefringence fiber 11 in combination with the short
coherence length source 10 to reduce the magnitude of the
vectors 56, 58 (Figure 6) and concomitantly reduce the
magnitude of the Group III resultant vector 60 (Figure
7). Although such reduction in vector magnitude will not
change the phase angle eye) (Figure 7) of the Group III
resultant vector 60, such decrease does reduce the
~766~3
-25-
fraction of the total interference Ii (Fig. 4) contributed
by the vector 60, thus reducing the overall significance
of the Group III interference terms and their effect on
the total phase error ye (Fig. 4). Further, such
reduction in vector 60 magnitude reduces scale factor
problems, since its contribution to the detected intensity
or the output waveform 52 (Fig. lo is reduced, thereby
resulting in improved stability.
Reduction in the magnitude of the vector 60 is
accomplished in two ways. First, the high birefringence
fiber if tends to conserve polarization and reduce cross
coupling between the polarization modes. This reduces the
value of Al in expression 7, thus, reducing the magnitude
of the vector 60. To a good approximation, the total
~15 phase error ye (Fig. 4) may be expressed as follows:
I En 1 2 I E ill
Sal sin (up I YE 12 + EYE¦ (10)
As an indication of the phase error magnitude with the
high birefringence fiber, it will be noted that the
maximum phase error Max will occur when (l) the
quantity pi of expression lo is 90, and (2) only one
of the modes is launched with light so that either Hi or
En is zero. Assuming that the total phase error ye (Fig.
4) is due entirely to Group III components, the maximum
phase error may be approximated as:
Max (if)
For presently available high birefringence fibers, the
value of a is typically on the order of Oily per km.
Thus, use of a high birefringence fiber such as the fiber
if, results in a total phase error ye on the order of 10-2
radians, assuming a loop length of l km.
~L2~66~)
-26-
The magnitude of the vector 60 (Fig. 7) may be further
reduced by using the wide band, short coherence length
source 10 in combination with the high birefringence fiber
11. Specifically, the source 10 and the fiber 11 should
be selected to provide a combination of sufficiently short
source coherence length and sufficiently high giber
birefringence so that the loop 16 is comprised of plural
fiber coherence lengths. It will be recalled that the
"fiber coherence length" is defined as the length of fiber
required for the optical path length difference between
the two polarization modes to equal one coherence length
of the source 10. As a good approximation, the fiber
coherence length may be expressed as:
lo Jo
1 (12)
where: to is the fiber coherence length; lo is the
coherence length of the source and on is the difference in
refractive index between the two polarization modes of the
fiber.
By making the fiber coherence length sufficiently
: short, such that the fiber loop 16 is comprised of plural
fiber coherence lengths, the coherence between portions of
: the waves which are coupled from one mode to the other
during traverse of the loop, is reduced, thereby reducing
the interference.
The foregoing may be understood more fully through
reference to Figure 11 which schematically illustrates the
fiber loop 16 of Figure 1. As shown therein, the loop 16
is divided into plural segments, each of which has a
length equal to one fiber coherence length tic). It will
be understood that while only two segments are shown in
Figure 11 for illustrative purposes, a greater number of
segments is preferable. The number of segments (N) is
determined by the fiber coherence length to and the loop
length L, such that:
6~1D
1 (13)
c
The fiber coherence length, in turn, is determined by
the birefringence of the fiber 11 and coherence length of
the source 10, in accordance with equation 12. Thus, for
example, if the giber 11 and source 10 are chosen such
that the fiber coherence length is 100 meters, there will
be 10 segments within a 1,000 meter fiber loop.
Figures 12 and 13 depict a conceptual model of the two
segments of the fiber loop 16 of Figure 11. For clarity
of illustration, Figure 12 shows only the clockwise wave
We, while Figure 13 shows only the counter-clockwise wave
We. However, it will be understood that Figures 12 and 13
represent one and the same fiber, namely the fiber 16 of
Figure 11. The fiber models of Figures 12 and 13 are
identical, in all respects, to the fiber model discussed
in reference to Figures 2 and 3, except that the models of
Figures 12 and 13 include two pairs of cross-coupling
branches, which correspond to the two segments of the
fiber loop 16 (Figure 11). Branches 1 and 2 depict a
scattering center 80 at the mid point of segment 1 of the
1OGP 16 (Figure 11). Similarly, branches 3 and depict a
scattering center 82 at the mid point of segment 2 of the
loop 16 (Figure 11). wince the segments 1,2 are each one
fiber coherence length (to) in length, the scattering
centers 80,82 are also separated by one fiber coherence
length. Because the present discussion concerns only
Group III components, only the cross-coupled components
Epic, Ejc~ are shown in the drawings. The cross-coupled
components in segment 1 of the fiber 16 are denoted by a
subscript 1, while the cross-coupled components in segment
2 of the fiber 16 are denoted by a subscript 2. A plus
(~) superscript is used to denote the clockwise direction
of the wave W, while a minus (-) superscript is used to
denote the counterclockwise direction of the wave We.
~'~Z~6~0
-28-
For the purposes of this discussion it will be assumed
that both polarization modes i and j are launched with
light having equal intensities, although it will be
understood that this is not necessary for operation or use
of the present invention. Referring to Figure 12, the
wave We will include a cross-coupled
component Elm which is coupled from mode j to mode i in
branch 1, and a cross-coupled component EjC(l) which is
coupled from mode i to mode j in branch 2. In addition,
the wave We includes a cross-coupled component Eke
which is coupled from mode j to mode i in branch 3, and a
cross-coupled component EKE which is coupled from mode
i to mode j in branch 4. Thus, when the wave We reaches
the end of the fiber 16, the components Eke
and fig will be in mode i, while the
components EKE and Eke will be in the j mode.
However, since the scattering centers 80,82 are separated
from each other by one fiber coherence length, the segment
1 cross-coupled components will be incoherent with the
segment 2 cross-coupled components, and thus, will not
interfere. In other words, component EKE will be
incoherent with component fig and component EjC(l)
will be incoherent with component EjC(2) Note alto that
there will be no interference between mode i light and
mode j light, since the two modes are orthogonal.
The same analysis may be applied to the counter
propagating wave We as shown in Figure 13. In segment 2,
a component EKE is coupled from mode j to mode i in
branch 4, while a component Eke is coupled from mode i
to mode j in branch 3. In segment 1, the
component Epic is coupled from mode j to mode i in
branch 2, while a component Eke is coupled from mode i
to mode j in branch 1. The segment 1 cross-coupled light
in mode i, Epic will not interfere with the segment 2
cross-coupled light in mode i, Epic and the segment 2
cross-coupled light in mode j, EjC(2) will not interfere
AL Z~2 7~i60
--29-
with the segment 1 cross-coupled light in mode j,
EKE . Nor will there be any interference between mode
i light and mode j light, since these modes are
orthogonal.
When the counter propagating waves We, We are
recombined at the coupler 14 (Figure 1), the only cross-
coupled components of wave We that will interfere with the
cross-coupled components of the wave We are those
components which were coupled on symmetrical sides of the
loop 16. That is, wave We light which is cross coupled in
segment 1 will interfere with wave We light which is
coupled in segment 2, and wave We light which is coupled
in segment 2, will interfere with wave We light which is
cross coupled in segment 1. Thus, for example, Elm
will interfere with Eta; Eta will interfere
with Elk Equal will interfere
with Eke and Ejc(2) will interfere with Eke-
Thus, upon recombination of the waves, We, We at the
coupler 14, the Group III resultant vector 60 (Figure 7)
will be comprised of four vectors, two representing i mode
cross-coupled light, and two representing j mode cross-
coupled light components.
The foregoing may be understood more fully through
reverence to Figure 14 which shows a vector 90,
representing interference between EKE and Epic and a
vector 92, representing interference between
P to to These vectors 90,92 may be
added to yield an i-mode resultant vector 94, representing
the total intensity of i mode cross-coupled components.
Note that the vector 90 has a phase angle of (pluck
while the vector 92 has a phase angle of (~p3~~q2)~ where
the subscript p indicates the total accumulated phase for
light that is cross coupled from one mode to the other
between the terminals C'' and D'; the subscript q
indicates total accumulated phase for light that is cross
coupled from one mode to the other between terminals C'
~276~
-30-
and D" (Figures 12 and 13~; and the subscripts 1, 2, 3
and 4 denote the branches 1, 2, 3 and 4 (Figures 12 and
13), respectively, traveled by the cross-coupled
components. In general, the phase angles for the vectors
90,92 will be different, so that their vector addition
yields a resultant 94 having a magnitude less than their
algebraic sum.
Similarly, Figure 14 shows a vector 96, representing
interference between components EKE and Eke, and a
vector 98, representing interference between
components Eke and Eke' which victrola add to
provide a j-mode resultant vector 100, representing the
total i mode cross-coupled components. The vectors 96 and
98 have phase angles which are equal and opposite to those
of the vectors 90 and 92, respectively, so that the phase
angles of the resultant vectors 94,100 are also equal and
opposite. In accordance with the principles discussed in
reference to Figures 6 through 9, to the extent that each
of the modes are launched with light having an equal
intensity, the j-mode vector 100 (j mode cross-coupled
components) and the i-mode vector 94 I mode cross-coupled
components) will add victrola to yield a Group III
resultant vector 102, which lies along the real axis, as
illustrated in Figure 14.
because the vectors 94,100 of Figure 14 are each
composed of two vectors having phase angles which, in
general, are different, the magnitude of these vectors
94,100 will be less than they would had the loop 16 not
been divided into plural fiber coherence length
segments. Thus, the vectors 94, 100 will be less in
magnitude than their counterpart vectors 56,58 in Figures
6 and 8. Consequently, the magnitude of the resultant
vector 102 will be less than its counterpart vector 60 in
Figures 7 and 9.
The foregoing principles may be illustrated more
dramatically through reference to Figure 15, which depicts
~;2~76~
a vector diagram for a fiber loop comprised of 10 fiber
coherence length segments, rather than the two segments
depicted in the vector diagram of Figure 14. In
accordance with the present invention, the cross coupled
components on symmetrical segments ox the loop will
interfere with each other but not with components in other
segments of the loop. Thus, assuming the segments are
numbered sequentially from one end of the loop to the
other, light cross coupled in segment 1 will interfere
only with light cross coupled in segment 10; segment 2
light will interfere with segment 9 light, segment 3 light
with segment 8 light, and so on. Consequently, there will
be ten pairs of interfering components for i-mode light
and ten pairs of interfering components for j-mode light,
as represented by the ten vectors 110 and the 10 vectors
112 in Figure 15. The phases of the individual vectors
110,112 are such that they add victrola in a two-
dimensional random walk to yield resultant vectors
114,115, respectively. Thus, there is a "statistical
averaging" of the interference such that the magnitude of
the resultant vectors 114,116 will be lo that of the
algebraic sum of the individual vectors 110,112,
respectively. As the number of segments N in the loop is
increased, the magnitudes of the vectors 112,114 will
further decrease. The vectors 112,114 which have equal
and opposite phase angles, add victrola to yield a
resultant vector 118. Again, the resultant vector 118
will be directed along the real axis only if the light
intensity is equalized for the two modes so that the
vectors 112,114 are equal.
It will be recalled that, in practice, it is difficult
to achieve precisely equal optical intensities, so that
phase errors may be present. Figure 16 shows, in general
terms, the effect on the overall phase error ye) of Group
phase errors eye)- As shown therein, the overall
interference vector Ii is the resultant of a Group
foe
-32-
interference vector It, a Group II interference vector
Ire and a Group III interference vector Ii(III)~ This
Group III interference vector Ii(III) corresponds, e.g., to
the resultant vector 60 of Figures 7 or 9, or the
resultant vectors 102,118 of Figures 14 and 15,
respectively. It is assumed that phase errors due to the
Group I and Group II components have been eliminated, so
that the only phase error is that caused by Group III
components. As the Group III phase error increases, the
overall phase error ye correspondingly increases. For a
given Group III phase error, however, the effect of such
phase error on the overall phase error ye may be reduced
by decreasing the magnitude of the Group III interference
vector Ii(III). The amount of phase error reduction is
proportional to lo where N is the number of fiber
coherence length segments within the loop 16. The phase
error approximation given by equation (10), therefore, may
be further reduced by a factor of lo so that:
Sal sin (~p-~q)[¦Ej¦2-¦Ei¦2] (14)
e ON [YE joy¦ ]
It will be recalled that the maximum phase error
Max occurs when the quantity pi equals 90t and
when either Hi or En is Nero. It follows that:
AL
Max - (15)
ON
Thus, by providing a plural number (N) of fiber
coherence length segments within the loop 16 to reduce the
magnitude of the Group III interference vector, as
demonstrated above in reference to Figures 14 and 15, the
overall phase error may be reduced by lo thereby
increasing rotation sensing accuracy
Using present, state-of-the-art high bire~ringence
fibers and short coherence length light sources, such as
7660
-33-
described above for the fiber 11 and source 10, a fiber
coherence length on the order of loom may be achieved.
For a one kilometer loop length, this yields about 10,000
fiber coherence length segments. Substituting N = 10,000
into equation (14), and assuming that Al is on the order
of 0.01 radians, the maximum phase error will, therefore,
be on the order of 10 4 radians. If the intensities for
the polarization modes are equalized to within one
percent, a further improvement, on the order of a factor
of 100, may be realized, yielding a maximum phase error of
10-6 radians. Thus, by utilizing the high birefringence
fiber in combination with the short coherence length
source 10, and orienting the source polarization at 45
degrees relative to the principle axes of birefrLngence to
equalize the intensities in the polarization modes a
simple, yet highly accurate, rotation sensor may be
provided.
While the present invention has been described in the
context of its use with unpolarized light, it will be
understood that the invention is useful in other types of
rotation sensors which do not utilize unpolarized light.
For example, the above-referenced patent application
entitled "Fiber Optic Rotation Sensor" utilizes a
polarizer to achieve reciprocity, as opposed to utilizing
unpolarized light. In the event a polarizer is used, such
polarizer may be provided between the couplers 12,14 of
Figure 1, at the point labeled 130, so that both the input
wave We and the output wave We pass through the polarizer
as these waves propagate to and from the loop 16. The
I polarizer blocks light in one of the two orthogonal
polarization modes, while passing light in the other, so
that, theoretically, only light propagating through the
loop in one of the polarization modes is detected. In
practice, however, such polarizers are not perfect, and
thus, do not block all of the cross-coupled light, so that
phase errors may still be present. The present invention
~2~7~i61:~
-34-
effectively reduces these phase errors in the same manner
as described above, i.e. by providing plural coherence
length segments within the loops so that light scattered
from one mode to the other at an arbitrary point along the
fiber loop will interfere only with that light which
scatters to the same mode within one fiber coherence
length of the symmetrical point on the other side of the
loop. Thus, the present invention is broadly applicable
to rotation sensing, and may be used in combination with
I other techniques to yield cumulative improvements in
rotation sensing accuracy.
Scale Factor Improvement
Those skilled in the art will understand that,
although the i mode and j mode vectors in Figures 6, 8, 14
and 15 are necessarily drawn in a static position, their
equal and opposite phase angles will vary in time between
zero and 360, Thus, even though the Group III resultant
vectors (i.e., the resultant of the i and j mode vectors,
such as the vector 60 of Figure 9) remain along the real
axis, they may undergo a substantial variation in
magnitude. Figures aye and (b) illustrate the effect of
variations in the Group III resultant or interference
vectors Ii(III) upon the detected intensity of Idol of the
optical output signal Wow (Fig. 1). The i and j mode
vectors, which are illustrated by dotted lines in Figures
aye and (b), are shown as changing phase angles between
time ill [Figure aye t=t2 [Figure 17~b)]. At time
if, their equal and opposite phase angles are small,
resulting in a relatively large Group III inference vector
Ii(III)- However, at time to, the phase angles have
increased substantially, so that the Group III
interference factor has been substantially reduced in
magnitude, even though the magnitude of the i and j mode
vectors remains unchanged. Since the detected optical
intensity Idol is the sum of the DC components,
represented by the vector Id plus all of the individual
foe
~35-
Group interference vectors, a variation in the Group III
interference vector Ii(III) will cause a variation in the
detected optical intensity. While such variation does not
present any phase error problems, it does result in a
scale factor problem, in that the output intensity curve
52 can shrink or expand, as indicated previously in regard
to Figure 10. This scale factor problem is alleviated in
the present invention by reducing the magnitude of the i
and j mode vectors through statistical averaging as
discussed in reference to Figure 15. By reducing the
and j mode vector magnitudes, the range of variation in
the resultant Group III interference vector Ii(III is
necessarily reduced, so that the optical output signal WOW
is more stable. Thus, the present invention not only
reduces phase errors, but also contributes to scale factor
improvements.
The Couplers 12 and I
A preferred fiber optic directional coupler for use as
the couplers 12 and 14 in the rotation sensor or gyroscope
of the present invention is illustrated in Figure I The
coupler includes two exemplar strands AYE and 150B of a
single mode fiber optic material mounted in longitudinal
arcuate grooves AYE and 152B, respectively, formed in
optically flat, confronting surfaces of rectangular bases
or blocks AYE and 153B, respectively. The block AYE
with the strand AYE mounted in the groove AYE will be
referred to as the coupler half AYE, and the block 153B
with the strand 150B mounted in the groove 152B will be
referred to as the coupler half 151B.
The arcuate grooves AYE and 152B have a radius of
curvature which is very large compared to the diameter of
the fibers 150, and have a width slightly larger than the
fiber diameter to permit the fibers 150, when mounted
therein, to conform to a path defined by the bottom walls
US of the grooves 152. The depth of the grooves AYE and
152B varies from a minimum at the center of the blocks
76~
-36-
AYE and 153B, respectively, to a maximum at the edges of
the blocks AYE and 153B, respectively. This
advantageously permits the fiber optic strands AYE and
150B, when mounted in the grooves AYE and 152B,
respectively, to gradually converge toward the center and
diverge toward the edges of the blocks AHAB, thereby
eliminating any sharp bends or abrupt changes in direction
of the fibers 150 which may cause power loss through mode
perturbation. In the embodiment shown, the grooves 152
are rectangular in cross-section, however, it will be
understood that other suitable cross-sectional contours
which will accommodate the fibers 150 may be used
alternatively, such as a U-shaped cross-section or a V-
shaped cross-section.
At the centers of the blocks 153, in the embodiment
shown, the depth of the grooves 152 which mount the
strands 150 is less than the diameter of the strands 150,
while at the edges of the blocks 153, the depth of the
grooves 152 is preferably at least as great as the
diameter of the strands 150. Fiber optic material was
removed from each of the strands AYE and 150B, e.g., by
lapping to form respective oval-shaped planar surfaces,
which are coplanar with the confronting surfaces of the
blocks AHAB. These oval surfaces, where the fiber
optic material has been removed, will be referred to
herein as the fiber "facing surfaces". Thus, the amount
of fiber optic material removed increases gradually from
zero towards the edges of the blocks 153 to a maximum
towards the center of the blocks 153. This tapered
removal of the fiber optic material enables the fibers to
converge and diverge gradually, which is advantageous for
avoiding backward reflection and excess loss of light
energy.
In the embodiment shown, the coupler halves AYE and
151B are identical, and are assembled by placing the
confronting surfaces of the blocks AYE and 153B together,
,766~
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so that the facing surfaces of the strands AYE and 150B
are in facing relationship.
An index matching substance (not shown), such as index
matching oil, is provided between the confronting surfaces
of the blocks 153. This substance has a refractive index
approximately equal to the refractive index of the
cladding, and also functions to prevent the optically flat
surfaces from becoming permanently locked together. The
oil is introduced between the blocks 153 by capillary
action.
An interaction region 154 is formed at the junction of
the strands 150, in which light is transferred between the
strands by evanescent field coupling. It has been found
that, to ensure proper evanescent field coupling, the
amount of material removed from the fibers 150 must be
carefully controlled so that the spacing between the core
portions of the strands 150 is within a predetermined
"critical zone". The evanescent fields extend into the
cladding and decrease rapidly with distance outside their
respective cores. Thus, sufficient material should be
removed to permit each core to be positioned substantially
within the evanescent field of the other. If too little
material is removed, the cores will not be sufficiently
close to permit the evanescent fields to cause the desired
interaction of the guided modes, and thus, insufficient
coupling will result. Conversely, if too much material is
removed, the propagation characteristics of the fibers
will be altered, resulting in loss of light energy due to
mode perturbation. however, when the spacing between the
cores of the strands 150 is within the critical zone, each
strand receives a significant portion of the evanescent
field energy from the other strand, and good coupling is
achieved without significant energy loss. The critical
zone includes that area in which the evanescent fields of
the fibers AYE and 150B overlap with sufficient strength
to provide coupling, i.e., each core is within the
6C~
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evanescent field of the other. However, as previously
indicated, mode perturbation occurs when the cores are
brought too close together. For example, it it believed
that, for weakly guided modes, such as the Hell mode in
single mode fibers, such mode perturbation begins to occur
when sufficient material is removed from the fibers lS0 to
expose their cores. Thus, the critical zone is defined as
that area in which the evanescent fields overlap with
sufficient strength to cause coupling without substantial
JO mode perturbation induced power loss.
The extent of the critical zone for a particular
coupler is dependent upon a number of interrelated factors
such as the parameters of the fiber itself and the
geometry of the coupler, Further, for a single mode fiber
having a step-index profile, the critical zone can be
quite narrow. In a single mode fiber coupler of the type
shown, the required center-to-center spacing between the
strands lS0 at the center of the coupler is typically less
than a few (e.g., 2-3) core diameters.
Preferably the strands AYE and 150B (1) are
identical to each other; (~) have the same radius of
curvature at the interaction region 154; and (3) have an
equal amount of fiber optic material removed therefrom to
form their respective facing surfaces. Thus, the fibers
150 are symmetrical, through the interaction region 154,
in the plane of their facing surfaces, so that their
facing surfaces are coextensive if superimposed, This
ensures that the two fibers AYE and 150B will have the
same propagation characteristics at the interaction region
154, and thereby avoids coupling attenuation associated
with dissimilar propagation characteristics.
The blocks or bases 153 may be fabricated of any
suitable rigid material. In one presently preferred
embodiment, the bases 153 comprise generally rectangular
blocks of fused quartz glass approximately one inch long,
one inch wide, and I inch thick. In this embodiment,
~Z,X~660
-39-
the fiber optic strands 150 are secured in the slots 152
by an ultra-violet light sensitive cement.
The coupler includes four ports, labeled A, B, C, and
D, in Figure 18. When viewed from the perspective of
Figure 18, ports A and C, which correspond to strands AYE
and 150B, respectively, are on the left hand side of the
coupler, while the ports B and D, which correspond to the
strands AYE and 150B, respectively, are on the right-hand
side of the coupler. For the purposes of discussion, it
will be assumed that input light is applied to port A.
This light passes through the coupler and is output at
port B Andre port D, depending upon the amount of power
that is coupled between the strands 150. In this regard,
the term "normalized coupled power" is defined as the
ratio of the coupled power to the total output power. In
the above example, the normalized coupled power would be
equal to the ratio of the power at port D of the sum of
the power output at ports B and D. This ratio is also
referred to as the "coupling efficiency", and when so
used, is typically expressed as a percent. In this
regard, tests have shown that the coupler of the type
shown in Figure 18 has a coupling efficiency ox up to
100%. However, the coupler may be "tuned" to adjust the
coupling efficiency to any desired value between zero and
the maximum, by offsetting the facing surfaces of the
blocks 153. Such tuning is preferably accomplished by
sliding the blocks 153 laterally relative to each other.
The coupler is highly directional, with substantially
all of the power applied at one side of the coupler being
delivered to the other side of the coupler. That is,
substantially all of the light applied to input port A is
delivered to the output ports B and D, without contra-
directional coupling to port C. Likewise, substantially
all of the light applied to input port C is delivered to
the output ports B and D. Further, this directivity is
symmetrical. Thus, light supplied to either input port B
766 [)
--40-
or input port D is delivered to the output ports A and
C. Moreover, the coupler is essentially non-
discriminatory with respect to polarizations, and thus,
preserves the polarization of the coupled light. Thus,
con example, if a light beam having a vertical
polarization is input to port A, thy light coupled from
port A to port D, as well as the light passing straight
through from port A to port B, will remain vertically
polarized.
From the foregoing, it can be seen that the coupler
may function as a beam-splitter to divide the applied
light into two counter-propagating waves Wylie
figure 1). Further, the coupler may additionally
function to recombine the counter-propagating waves after
they have traversed the loop 16 (Figure 1).
In the embodiment shown, each of the couplers 12,14
has a coupling efficiency of So%, as this choice of
coupling efficiency provides maximum optical power at the
photodetector 20 (Figure 1).
When using the above-described coupler in the rotation
sensor of Figure 1, it is preferable to align the
principal axes of birefringence so that the fast axis of
the fiber AYE is parallel to the fast of the fiber 152s
and the slow axis of the fiber AYE is parallel to the
slow axis of the fiber 152B. Such alignment of the
principal axes reduces the coupling between the fast and
slow modes in the coupler, e.g. between the fast mode of
one fiber and the slow mode of the other fiber, and
between the slow mode of one fiber and the fast mode of
I the other fiber, insures that polarization is maintained
as light passes through -the coupler. This reduces phase
errors by reducing mixing of the modes in the coupler.
For unpolarized light operation, the rotation sensor
of Figure 1 may be further simplified by eliminating the
coupler 12 and relocating the detector 20 to receive light
from the end of the fiber portion 17 at port B of the
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1;22'7G60
coupler 14. In this configuration, however, it is
important that the coupler 14 be as loss less as possible,
since coupler losses could result in a phase difference
between the counter-propagating waves WOW when the loop
16 is at rest, and thus, cause phase errors.
Advantageously, the coupler described above has very low
losses, on the order of 2% to 5%, and thus, is also
preferred for this single-coupler configuration,
Additional details of the couplers 12,14 are described
in U.S. Patent No 4,536,058 and U.S. Patent No.
4,493,528. The coupler is also described in an article
entitled "Single rode Fiber Optic Directional Coupler",
published in Electronics Letters, Vol. 16, No. 7 (March
27, 19~0, pp. 260-261),
The Polarizer
A preferred polarizer for use in the rotation sensor
of Figure 1 at the point 130, is illustrated in Figure
19. This polarizer includes a birefringent crystal 160,
positioned within the evanescent field of light
: transmitted by the fiber 11, The fiber 11 is mounted in a
slot 162 which opens to the upper face 163 of a generally
rectangular quartz block 164. The slot 162 has an
arcuately curved bottom wall, and the fiber is mounted in
the slot 162 so that it follows the contour of this bottom
wall. The upper surface 163 of the block 164 is lapped to
remove a portion of the cladding from the fiber 11 in a
region 167, The crystal 160 is mounted on the block 164,
with the lower surface 168 of the crystal facing the upper
surface 163 of the block 164, to position the crystal 160
within the evanescent field of the fiber 112.
The relative indices of refraction of the fiber 11 and
the birefringent material 160 are selected so that the
wave velocity of the desired polarization mode is greater
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~3L;2~7660
in the birefringent crystal 160 than in the fiber 11,
while the wave velocity of an undesired polarization mode
is greater in the fiber 11 than the birefringent crystal
160. The light of the desired polarization mode remains
guided by the core portion of the fiber if, whereat light
of the undesired polarization mode is coupled from the
fiber 11 to the birefringent crystal 160. Thus, the
polarizer 132 allows passage of light in one polarization
mode, while preventing passage of light in the other
orthogonal polarization mode. When a polarizer is used,
the allowed polarization should be aligned with either the
fast or the slow axes of the high birefringence fiber 11
for effective phase error reduction.
Further details of the polarizer are described in U.S.
Patent No. 4,386,822. The polarizer is also described in
an article entitled "Single Mode Fiber Optic Polarizer",
published in Optics Letters, Vol. 5, No. 11 (Nov. 1980),
pp. 479-481.
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