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Self-pumped phase-conjugate fiber-optic gyro

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Optics Letters
Authors:
Ian McMichael
Ian McMichael
Ian McMichael
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Pochi Yeh at University of California, Santa Barbara
Pochi Yeh
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Abstract and Figures

We describe a new type of phase-conjugate fiber-optic gyro that uses self-pumped phase conjugation. The self-pumped configuration is simpler than externally pumped configurations and permits the use of sensing fibers longer than the coherence length of the laser. A proof-of-principle demonstration of rotation sensing with the device is presented.
Schematic of a self-pumped phase-conjugate fiber-optic gyro. Light from a laser is split by beam splitter BS into two fibers F1 and F2 that are coiled such that light travels clockwise in F1 and counterclockwise in F2. Light traversing the fibers experiences phase shifts due to thermal, mechanical, and rotational effects. The self-pumped phase-conjugate mirror PCM produces time-reversed waves that compensate for the reciprocal phase changes produced by thermal and mechanical effects but do not compensate for the nonreciprocal phase shift produced by rotation (Sagnac effect). Therefore rotation can be sensed by measuring the interference between the recombining waves at detector D.
Schematic of a self-pumped phase-conjugate fiber-optic gyro. Light from a laser is split by beam splitter BS into two fibers F1 and F2 that are coiled such that light travels clockwise in F1 and counterclockwise in F2. Light traversing the fibers experiences phase shifts due to thermal, mechanical, and rotational effects. The self-pumped phase-conjugate mirror PCM produces time-reversed waves that compensate for the reciprocal phase changes produced by thermal and mechanical effects but do not compensate for the nonreciprocal phase shift produced by rotation (Sagnac effect). Therefore rotation can be sensed by measuring the interference between the recombining waves at detector D.
… 
Experimental setup of the self-pumped phase-conjugate fiber-optic gyro. Instead of the two fibers shown in Fig. 1, the experimental setup shown here uses the two polarization modes of the polarization-preserving fiber-optic coil. Light from the laser is incident upon polarizing beam splitter PBS1 with its polarization at 45° to the plane of the page. The components reflected and transmitted by PBS1 travel clockwise and counterclockwise, respectively, in the fiber coil. The two beams recombine at PBS1 and are then split at PBS2. One of the beams has its polarization rotated by PR, and both beams are incident upon a barium titanate crystal such that self-pumped phase conjugation occurs. The reflected waves retraverse the fiber in an opposite sense, recombine at PBS1, and travel back toward the laser with a phase difference ϕ, which is proportional to the rotation rate. These waves are sampled by the beam splitter BS2, and an additional phase delay of π/2 rad is impressed on them when they propagate through the quarter-wave retarder λ/4. The half-wave retarder is oriented such that the intensities of the interferences measured by detectors D1 and D2 are proportional to sin ϕ and −sin ϕ, respectively.
Experimental setup of the self-pumped phase-conjugate fiber-optic gyro. Instead of the two fibers shown in Fig. 1, the experimental setup shown here uses the two polarization modes of the polarization-preserving fiber-optic coil. Light from the laser is incident upon polarizing beam splitter PBS1 with its polarization at 45° to the plane of the page. The components reflected and transmitted by PBS1 travel clockwise and counterclockwise, respectively, in the fiber coil. The two beams recombine at PBS1 and are then split at PBS2. One of the beams has its polarization rotated by PR, and both beams are incident upon a barium titanate crystal such that self-pumped phase conjugation occurs. The reflected waves retraverse the fiber in an opposite sense, recombine at PBS1, and travel back toward the laser with a phase difference ϕ, which is proportional to the rotation rate. These waves are sampled by the beam splitter BS2, and an additional phase delay of π/2 rad is impressed on them when they propagate through the quarter-wave retarder λ/4. The half-wave retarder is oriented such that the intensities of the interferences measured by detectors D1 and D2 are proportional to sin ϕ and −sin ϕ, respectively.
… 
Measurement of the Sagnac phase shift in the self-pumped phase-conjugate fiber-optic gyro. This figure shows a chart recording of the output of a differential amplifier connected to detectors D1 and D2 in the experimental setup of a self-pumped phase-conjugate fiber-optic gyro shown in Fig. 2. For t < 0, the gyro was stationary. At t = 0, the gyro was rotated first clockwise, then counterclockwise in a square-wave fashion for four cycles with an amplitude of approximately 6°/sec. The experimentally measured phase shift is in good agreement with the predicted phase shift of 0.04 rad.
Measurement of the Sagnac phase shift in the self-pumped phase-conjugate fiber-optic gyro. This figure shows a chart recording of the output of a differential amplifier connected to detectors D1 and D2 in the experimental setup of a self-pumped phase-conjugate fiber-optic gyro shown in Fig. 2. For t < 0, the gyro was stationary. At t = 0, the gyro was rotated first clockwise, then counterclockwise in a square-wave fashion for four cycles with an amplitude of approximately 6°/sec. The experimentally measured phase shift is in good agreement with the predicted phase shift of 0.04 rad.
… 
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686 OPTICS LETTERS / Vol. 11, No. 10 / October 1986
Self-pumped phase-conjugate fiber-optic gyro
Ian McMichael and Pochi Yeh
Rockwell International Science Center, 1049 Camino Dos Rios,
Thousand Oaks, California
91360
Received June 2, 1986; accepted July 30, 1986
We describe a new type of phase-conjugate fiber-optic gyro that uses self-pumped phase conjugation. The self-
pumped configuration
is simpler than externally pumped configurations
and permits the use of sensing fibers
longer
than the coherence length of the laser. A proof-of-principle demonstration of rotation sensing with the device is
presented.
Several types of phase-conjugate gyro
are described in
the literatures and we recently reported on the first
demonstration to our knowledge of rotation sensing
with a phase conjugate gyro.
5The passive phase-
conjugate fiber-optic gyros described in Refs. 3 and 5
are Michelson interferometers in which the arms con-
tain fiber-optic coils that are terminated by externally
pumped phase-conjugate mirrors. Since the phase-
conjugate mirrors produce time-reversed waves, all
reciprocal phase changes in the optical paths are com-
pensated for and do not effect the output of the inter-
ferometer. However, since the phase shift produced
by the Sagnac effect is nonreciprocal, the output of the
interferometer is sensitive to rotation and can be used
as a gyro.
Standard fiber-optic gyros6are Sagnac interferome-
ters that are inherently insensitive to reciprocal phase
changes and sensitive to nonreciprocal phase changes.
This is true only when their operation is restricted to a
single polarization mode,7and the best fiber-optic gy-
ros use polarization-preserving fibers and couplers.8
However, if the phase-conjugate mirrors in the phase-
conjugate fiber-optic gyro
preserve polarization,9then
nonpolarization-preserving single-mode fibers, and
even multimode fibers, can be used in the gyro.
In the externally pumped configurations described
in Ref. 3 and 5, the fiber-optic coils can be no longer
than the coherence length of the laser. This limits the
sensitivity of the device. It is true that longer coils
can
be used if a polarization-preserving fiber of equal
length is used to carry the pumping waves to the
phase-conjugate mirrors. However, this defeats the
above-mentioned advantage in that the phase-conju-
gate gyro can use inexpensive multimode fibers and
couplers. In this Letter we describe and demonstrate
a self-pumped configuration of the phase-conjugate
fiber-optic gyro
that is not only simpler than the exter-
nally pumped configurations but also allows for the
use of fiber-optic coils that are longer than the coher-
ence length of the laser.
Figure 1 shows a schematic of a self-pumped phase-
conjugate fiber-optic gyro. Light from a laser is split
by beam splitter BS into two fibers, Fl and F2. Fibers
F1 and F2 are coiled such that light travels clockwise
in F1 and counterclockwise in F2. Light waves tra-
versing fibers F1 and F2 experience reciprocal phase
shifts
O,= J k1d1
1, ¢kr
2= J k2d12,(1)
respectively, where d1l and d1
2are elements of length
along Fl and F2, and kl,2= 27rnl,
2/X. In addition, the
nonreciprocal phase shifts
qnrl =+27rR1LW/Xc, q5n,2
= -27rR 2L2Q/XC (2)
are due to the Sagnac effect, where R1,2and L1,2are the
radii and lengths of the fiber loops, respectively, and Q
is the rotation rate. The net phase shifts are then Gr1
+ 0,,, and 0r2 + Cknr2.On reflection of the light from
the phase-conjugate mirror, the phase shifts become
-br1-knr 1and -0r2-,nr 2, where we have dropped the
phase shift of the phase conjugator
1 0"' since it is com-
mon to both waves and we are interested only in the
phase difference. It should be noted that the phase
shift of the phase conjugator is common to both waves
D
/PCM
M
Fig. 1. Schematic of a self-pumped phase-conjugate fiber-
optic gyro. Light from a laser is split by beam splitter BS
into two fibers F1 and F2 that are coiled such that light
travels clockwise in F1 and counterclockwise in F2. Light
traversing the fibers experiences phase shifts due to thermal,
mechanical, and rotational effects. The self-pumped
phase-conjugate mirror PCM produces time-reversed waves
that compensate for the reciprocal phase changes produced
by thermal and mechanical effects but do not compensate
for the nonreciprocal phase shift produced by rotation (Sag-
nac effect). Therefore rotation can be sensed by measuring
the interference between the recombining waves at detector
D.
0146-9592/86/100686-03$2.00/0 © 1986, Optical Society of America
... A variety of nonlinear interactions have been used to produce coherent combination, including stimulated Brillouin scattering,'-3 four-wave mixing (FWM), and selfpumped phase conjugation in photorefractive materials.-10 For some applications, including coupling laser amplifiers, 9 fiber-optic gyros, 6 and image subtraction, 5 7 not only must the beams be coherent but the piston component of the phase difference between the beams must also be conjugated so that they recombine in phase at a reference plane. ...
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