Fiber optic gyroscope with alternating output signal

A Sagnac rotation sensing interferometer that uses a Mach-Zehnder interferometer to provide incident light beams that counter-propagate through an optical-fiber loop. The Sagnac interferometer operates at maximum sensitivity for zero rotation rates when the Mach-Zehnder is adjusted so that the intensities of the incident light beams are equal. By peiodically varying the position of a mirror in the Mach-Zehnder the interferometer is switched into and out of quadrature so that the amplitude of the interferometer output signal is modulated at frequency f.sub.o. Phase sensitive detection at 2f.sub.o or multiples thereof reduces the background noise level several orders of magnitude below the level for dc operation.

BACKGROUND OF THE INVENTION 
The present invention relates generally to Sagnac fiber-optic 
rotation-sensing interferometers and more particularly to a Sagnac 
fiber-optic rotation-sensing interferometer which produces an alternating 
output signal. 
The Sagnac ring interferometer, which employs a long 
single-mode-optical-fiber loop, has shown promise as a passive gyroscope 
for navigational purposes. The properties of Sagnac fiber-optic gyroscopes 
are described in an article by Rashleigh and Burns entitled "Dual-Input 
Fiber-Optic Gyroscope", Optics Letters, Vol. 5, No. 11, p. 482, Nov. 1980. 
Typical Sagnac fiber-optic gyroscopes include means for introducing 
counter-propagating light beams into both ends of a fiber-optic loop and 
photodectors for measuring the intensities of the output light beam. This 
intensity detection then gives a measure of the relative phase shift 
between the counterpropagating beams in the fiber-optic loop in order to 
determine the rate of rotation about an axis perpendicular to the plane of 
the fiber-optic loop. An optical coupler/divider splits an incoming light 
beam into the counter propagating beams in the fiber-optic loop and later 
combines the output light beam exiting the fiber-optic loop, allowing them 
to interfere. 
Two problems associated with the operation of typical interferometers are 
low sensitivity at near-zero rotation rates and the effect of noise on 
intrinsic dc operation. 
Recently several interferometers have been developed which operate at 
maximum sensitivity, or quadrature, for near-zero rotation rates. However, 
these devices produce a dc signal which limits sensitivity due to high 
intrinsic, low-frequency noise levels in the photodetectors. 
Since noise generally has a broad power spectrum, the power of the noise at 
a given frequency, for example f.sub.o, is low. If the output signal is 
periodically varied at f.sub.o and amplified by a phase-locked amplifier, 
then much of the noise is eliminated and an improvement of several orders 
of magnitude in the sensitivity of the interferometer is achieved. Also, 
since noise is superimposed upon the output signal, it is desirable to 
achieve a signal of high average power in order to maximize the signal to 
noise ratio and to minimize loss of sensitivity. 
Several methods of producing an alternating output signal from an 
interferometer have been developed whereby the intensity of the input beam 
to the interferometer is periodically varied. However, since power is 
switched into and out of the interferometer the average power level of the 
output signal is low and sensitivity is not maximized. 
OBJECTS OF THE INVENTION 
Accordingly, one object of this invention is to provide a novel Sagnac 
rotation-sensing interferometer having maximum sensitivity at near-zero 
rotation rate while producing an alternating output signal. 
A further object is to provide a Sagnac rotation-sensing interferometer 
that produces a periodically varying output signal with a high average 
power level so that the signal to noise ratio is high. 
SUMMARY OF THE INVENTION 
Accordingly, the above and other objects are realized in the present 
invention comprising a new and improved Sagnac interferometer including 
means for switching the interferometer into and out of quadrature by 
varying the phase of the light beams in the interferometer thereby 
producing an alternating interferometer output signal. Since no input 
power is switched out of the interferometer, the average power of the 
output signal at the photodetectors is not reduced thereby assuring high 
sensitivity due to the high signal to noise ratio. The interferometer 
output signal is processed by a phase-locked amplifier to produce a final 
output signal.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The present invention produces a low-noise electrical signal that is a 
function of the rate of rotation, .OMEGA., about a given axis. Prior art 
rotation sensing interferometers have been developed that operate a 
quadrature, the maximum sensitivity point, when .OMEGA.=0 but those Sagnac 
interferometers produce a dc signal with an inherently low signal to noise 
ratio. 
Briefly stated the present invention modulates the intensities, I.sub.3 and 
I.sub.4, of the output beams of a prior art Sagnac interferometer by 
switching the interferometer into and out of quadrature; electronically 
measures the intensities, I.sub.3 and I.sub.4, and processes the resulting 
signals into the form S.sub.I =(I.sub.3 -I.sub.4)/(I.sub.3 +I.sub.4); and 
provides for phase-sensitive detection, at the modulation frequency of 
S.sub.I or multiples thereof. The resulting detected signal, S.sub.F, 
exhibits a signal-to-noise ratio several orders of magnitude greater than 
prior art devices. 
The application of the principles of the present invention to three prior 
art Sagnac rotation-sensing interferometers is set out below. 
Referring now to the drawings, wherein like reference numerals designate 
identical or corresponding parts throughout the several views, and more 
particularly to FIG. 1 thereof, a prior art interferometer that operates 
in quadrature, when controlled by the circuit of FIG. 2, is depicted. 
The Sagnac interferometer of FIG. 1 comprises an optical light path circuit 
10, such as a coil of single-mode optical fiber, and an optical coupler 
including a Mach-Zehnder interferometer 12. The optical coupler divides an 
input beam 14 from a light source 16 into two incident beams 18, 20 that 
counterpropagate through the optical light path circuit and combines the 
Sagnac phase shifted output beams 22, 24 to produce beams 26, 28 with 
intensities that are a function of the Sagnac phase shift. 
The circuit of FIG. 2 is interconnected with and adjusts the Mach-Zehnder 
so that the Sagnac interferometer is in quadrature, notwithstanding the 
presence of air current in the Mach-Zehnder. 
More specifically, an input light beam 14 is split by a first beamsplitter 
30 into a first input beam component 32 which propagates along a first 
light path 34 and a second input beam component 36 which propagates along 
a second light path 38. The light paths 34, 38 include mirrors for 
directing the input beam components to a second beamsplitter 40 which 
splits the first input beam component into a third input beam component 
and fourth input beam component and splits the second input beam component 
into a fifth and a sixth input beam component. The third and fifth input 
beam components combine to form a first incident beam 18 of intensity 
I.sub.1, which propagates through an optical light path circuit 10 in a 
counterclockwise direction while the fourth and sixth input beam 
components combine to form a second incident beam 20, of intensity 
I.sub.2, which propagates through the optical light path circuit 10 in a 
clockwise direction. 
The normalized intensities of the incident beams 18, 20 are: 
EQU I.sub.1,2 =1/2(1.+-.cos.theta.) (1) 
where .theta. the is the relative phase difference between the first and 
second input beam components and where .theta. is the sum of .psi., the 
phase difference introduced by the first beam splitter 30, and .delta., 
the phase difference caused by the relative path length difference between 
the first and second light paths 34, 38. Note that I.sub.1 =I.sub.2 =1/4 
when .theta.=.pi./2 and the Sagnac interferometer is in quadrature. 
The light beam in the first light path 34 is directed from the first 
beamsplitter 30 to the second beamsplitter 40 by an adjustable mirror 42. 
By controlling the position of the adjustable mirror to very the relative 
path length difference, .delta. is adjusted so that 
.theta.=.delta.+.psi.=.pi./2, I.sub.1 =I.sub.2 =1/2, and the Sagnac 
interferometer is in quadrature. The adjustment of the relative path 
length difference is achieved by mounting the adjustable mirror on a 
piezoelectric cylinder 43 which is driven to change the position of the 
adjustable mirror 42. 
Beamsplitters 44, 46 are disposed to pick-off a small portion of the first 
and second incident beams 18, 20 so that the intensities, I.sub.1 and 
I.sub.2 may be measured by photodetectors 48, 50. The resulting voltage 
signals from these two detectors may be compared and utilized to produce a 
compensating voltage for driving the piezoelectric cylinder to adjust the 
phase shift, .delta., so that I.sub.1 =I.sub.2. 
In this air-mirror design, air currents tend to change the optical path 
lengths in the interferometer. Accordingly, continuous adjustment of the 
phase shift, .delta., is typically necessary. In order to implement such a 
continuous adjustment of the phase shift, the circuit of FIG. 2 is set 
forth. The detectors 48 and 50 merely direct their voltage outputs to the 
inputs of a differential amplifier 60. The compensating voltage output 
from this differential amplifier is then applied to control the 
piezoelectric driver 62 for the mirror 42. In this manner, the intensities 
of the incident beams upon the ends of the light path circuit 10, I.sub.1 
and I.sub.2, are automatically adjusted to be equal and to remain so. 
The incident light beams counterpropagate through the optical light path 
circuit 10 and exit therefrom as first and second output beams 22, 24. The 
first output beam 22 is split by the second beamsplitter 40 into a third 
output beam component that propagates through the first light path 34 and 
a fourth output beam component that propagates through the second light 
path 38. Likewise, the second output beam is split into fifth and sixth 
components that propagate through the first and second light paths 34, 38 
respectively. The third and fourth output beam components in the first 
light path 34 combine to form a third output beam 26 of intensity I.sub.3 
while the fourth and sixth output beam components in the second light path 
combine to form a fourth output beam 28 of intensity I.sub.4. 
The normalized intensities of the output beams, I.sub.3 and I.sub.4, after 
propagating through the optical light path circuit 18, which rotates at 
angular velocity, are: 
EQU I.sub.3,4, =1/2(1.+-.sin.theta.sin2.phi.) (2) 
where 
EQU 2.phi.=8.pi.NA.OMEGA./.lambda.c (3) 
.OMEGA. being the rotation rate about the axis perpendicular to the plane 
of the optical light path circuit, NA being the total area enclosed by the 
optical light path circuit 10, and c being the free-space wavelength and 
the light-velocity, respectively, of the input beam. 
Beamsplitters 64, 66 are positioned in the first and second light paths 34, 
38 to pick off portions of the third and fourth output beams 26, 28 and 
direct the picked-off beams to photodetectors 68, 70. Signals are produced 
by the photodetectors 68, 70 proportional to I.sub.3 and I.sub.4. 
Note that when .theta.=.pi./2 eq. (3) becomes: 
EQU I.sub.3,4 =1/2(1.+-.sin 2.phi.) (4) 
and if .OMEGA.=0 then I.sub.3 =I.sub.4 so that the interferometer operates 
at quadrature, or maximum sensitivity. 
The noise and minimum-detectable rotation rate are of particular importance 
in any fiber-optic gyroscope. Electronic processing of the detected 
signals in the form 
EQU S.sub.I =(I.sub.3 -I.sub.4)/(I.sub.3 +I.sub.4)=sin.theta.sin 2.phi.) (5) 
where S.sub.I is designated the interferometer output signal, removes the 
dependence of the gyroscope output signal on laser power fluctuations. 
When .theta.=.pi./2, S.sub.I =sin2.phi. and .OMEGA. may be calculated 
utilizing eq. (3). 
It is to be noted that S.sub.I is a dc signal subject to intrinsic dc noise 
limitations. 
The physical principles underlying the operation of the present invention 
can be understood by examining eqs. (1) and (2). As described above, 
.delta. may be changed by varying the relative path length difference 
between the first and second light paths of the Mach-Zehnder 
interferometer. Adjusting .delta. so that .theta.=.pi./2 by means of a 
piezoelectric driver 84 brings the gyroscope into quadrature so that 
I.sub.1 =I.sub.2 =1/2 and S.sub.I =sin 2.phi.. However, if the relative 
path length difference is adjusted so that .theta.=0 or .pi., the 
gyroscope is completely out of quadrature, and its sensitivity is zero 
with I.sub.1 =1, I.sub.2 =0, I.sub.3 =I.sub.4 =1/2, and S.sub.I =0, 
independently of any rotation. In this case, light travels in one 
direction only in the optical light path circuit 10. 
The alternating interferometer output signal of the present invention is 
produced by periodically varying the adjustable path length difference so 
that .theta. switches from .pi./2 to 0 or .pi.. Thus, the Sagnac 
interferometer is switched into and out of quadrature and the amplitude of 
the interferometer output signal, S.sub.I, is modulated between sin2.phi. 
and 0 at frequency f.sub.o. The modulated interferometer output signal is 
then processed by a phase locked amplifier at twice the modulation 
frequency or multiples thereof to provide a final output signal, S.sub.F 
=sin 2.phi., with a high signal-to-noise ratio. Since power is not 
switched out of the Sagnac interferometer to achieve ac modulation the 
average power in the photodetectors is high thereby further increasing the 
signal-to-noise ratio. 
A detailed description of the operation of an embodiment of the present 
invention comprising the dual input interferometer of FIG. 1 controlled by 
the circuit of FIG. 3 follows. FIG. 3 depicts a circuit for switching the 
interferometer of FIG. 1 into and out of quadrature. 
More specifically, FIG. 3 is a schematic diagram depicting a circuit for 
cancelling low frequency phase fluctuations that would cause I.sub.1 and 
I.sub.2 to be unequal, for creating a high frequency amplitude modulation 
of S.sub.I, and for phase sensitive detection of S.sub.I to provide a 
low-noise, final output signal S.sub.F =sin 2.phi.. 
In order to facilitate description of the operation of the circuit of FIG. 
3 a dashed line 90 divides FIG. 3 into two parts; the upper part is 
designated the dc circuit 92 and the lower part the ac circuit 94. The dc 
circuit performs substantially the same function as the circuit depicted 
in FIG. 2, i.e., to sample I.sub.1 and I.sub.2 and cancel phase 
fluctuations between the input beam components that cause I.sub.1 and 
I.sub.2 to be unequal. The functions of the low-pass filters 96, 98 and ac 
signal generator 100 input to the piezoelectric driver 62, not present in 
the circuit of FIG. 2 are explained below. 
A signal, at frequency f, from the ac signal generator 100 to the 
piezoelectric driver 62 will cause the position of the adjustable mirror 
42 to vary periodically at frequency f. Thus, the path length difference 
varies periodically causing .delta. and .theta., since 
.theta.=.delta.+.psi., to also be periodic functions of time. .theta.(+) 
may be expressed as: 
EQU .theta.(t)=.theta..sub.dc +.theta..sub.ac (6) 
where .theta..sub.dc is the time average of .theta.(t). 
The periodic variation of .theta. will cause the values of I.sub.1 and 
I.sub.2 to be modulated at frequency f.sub.o. This modulation of I.sub.1 
and I.sub.2 is critical to the production of the modulated interferometer 
output signal S.sub.I. Therefore, the dc circuit 92 is designed so the ac 
fluctuations of I.sub.1 and I.sub.2 are not cancelled by the compensating 
voltage signal to the adjustable mirror 42. The frequency components of 
air turbulance in the light path of Mach-Zehnder are concentrated below 
one kHz. By selecting the ac frequency, f, to be above one kHz and 
designing the low pass filters 96, 98 to cut off frequency components 
below one kHz the ac fluctuation of I.sub.1 and I.sub.2 are isolated from 
the dc circuit. Thus the dc circuit will only cancel low frequency phase 
variations due to air currents and will continually adjust the relative 
path length difference so that .theta..sub.dc =.pi./2. Eq. (6) thus 
becomes: 
EQU .theta.(t)=.theta..sub.dc +.theta..sub.ac =.pi./2+.theta..sub.ac (7) 
and eq. (5) becomes: 
EQU S.sub.I 
=sin.theta.sin2.phi.=sin(.pi./2+.theta..sub.ac)sin2.phi.=cos(.theta..sub.a 
c)sin2.phi.. (8) 
Therefore, the time dependence of S.sub.I depends on the form of 
.theta..sub.ac. 
The ac circuit of FIG. 3 includes an arithmetic circuit 104 for processing 
the signals, representing I.sub.3 and I.sub.4, from the detectors 68, 70 
to form a new signal S.sub.I =(I.sub.3 -I.sub.4)/(I.sub.3 +I.sub.4). The 
noise component of S.sub.I generally has a broad power spectrum. Since the 
component of S.sub.I carrying the information pertaining to .OMEGA. is 
modulated, phase-sensitive detection at multiples of twice the modulation 
frequency will increase the signal-to-noise ratio. To achieve 
phase-sensitive detection S.sub.I is processed by a phase-locked amplifier 
106 to produce the final output signal S.sub.F. S.sub.F is measured by 
standard electronic instruments such as, for example, an oscilloscope. The 
variation of I.sub.1, I.sub.2, I.sub.3, I.sub.4 and S.sub.I for the 
illustrative case where .theta. is pulsed at fixed time intervals is 
depicted in FIG. 4. 
FIG. 4 comprises a series of graphs relating to the operation of the 
present invention when .theta. is pulsed. FIG. 4(a) depicts .theta. vs. 
time while 4(b) depicts the corresponding dependence of I.sub.1 and 
I.sub.2. 
Turning to FIG. 4(b), when .theta.=.pi./2 the input power is equally 
divided between the two incident beams, i.e. I.sub.1 =I.sub.2 =1/2. 
However, when .theta. is switched to .theta.=0 all the power is in the 
first incident beam, i.e., I.sub.1 =1, I.sub.2 =0. 
FIG. 4(c) depicts the values of I.sub.3 and I.sub.4 for the corresponding 
values of .theta. in FIG. 4(a). Note that when .OMEGA.=0, I.sub.3 =I.sub.4 
=1/2 for all .theta.. This follows from eq. (2) : 
EQU I.sub.3,4 =1/2(1.+-.sin.theta.sin2.phi.)=1/2 
since when .OMEGA.=0, sin 2.phi.=0. For non zero .OMEGA., when 
.theta.=.pi./2 
EQU I.sub.3,4 =1/2(1.+-.sin2.phi.)=1/2.+-.1/2sin2.phi., 
and when .theta.=0 
EQU I.sub.3,4 =1/2. 
Thus, when 2.phi. is near zero, for small rotation rates, the switching of 
.theta. induces a small modulation in the output signal of each detector 
from the constant value 1/2, so that the average signal power in each 
detector is about 1/2 the input power. 
The signal-to-noise ratio of the detector is low for a near zero signal. In 
the present invention, the average signal power in the detectors may be 
increased to a level with a high signal-to-noise ratio by adjusting the 
intensity of the input beam. 
FIG. 4(d) depicts the value of the interferometer output signal, S.sub.I, 
for the corresponding value of .theta. in FIG. 4(a). Note that S.sub.I is 
modulated between 0 and sin 2.phi. at the same frequency at which .theta. 
is modulated. 
In the embodiment of the invention actually reduced to practice .theta. was 
varied according to: 
EQU .theta.(t)=.theta..sub.dc +.theta..sub.ac =.pi./2+.theta., sin2.pi.ft, 
thus from eq. 2 
EQU I.sub.3,4 =1/2(1.+-.cos[.theta., sin2.pi.ft]sin2.phi.) (9) or 
EQU I.sub.3 =1/2{1=J.sub.0 (.theta..sub.1)sin2.phi.+2J.sub.2 
(.theta..sub.1)cos[2.pi.(2f)t]sin2.phi.+2J.sub.4 
(.theta..sub.1)cos[2.pi.(4f)t]sin2.phi.+2J.sub.6 
(.theta..sub.1)cos[2.pi.(6f)t]sin2.phi.t . . . } 
EQU I.sub.4 =1/2{1-J.sub.0 (.theta..sub.1)sin2.phi.-2J.sub.2 
(.theta..sub.1)cos[2.pi.(2f)t]sin2.phi.-2J.sub.4 
(.theta..sub.1)cos[2.pi.(4f)t]sin2.phi.-2J.sub.6 
(.theta.)cos[2.pi.(6f)t]sin2.phi.-. . . } 
where J.sub.0, J.sub.2, J.sub.4, J.sub.6, . . . are Bessel functions. Thus, 
modulation products occur at frequencies corresponding to 2Nf, where N is 
an integer. If phase sensitive detection is chosen to be at 2f, the 
J.sub.4 and higher order terms of the Bessel function expansion of 
cos(.theta..sub.1 sin2.pi. ft) may be neglected, so that: 
EQU I.sub.3 =1/2{1+J.sub.0 (.theta..sub.1)sin2.phi.+J.sub.2 
(.theta..sub.1)cos[2.pi.(2f)t]sin2.phi.} (10.1) 
EQU I.sub.4 =1/2{1-J.sub.0 (.theta..sub.1)sin2.phi.-J.sub.2 
(.theta..sub.1)cos[2.pi.(2f)t]sin2.phi.} (10.2) 
and 
EQU S=J.sub.0 (.theta..sub.1)sin2.theta.+2J.sub.2 
(.theta..sub.1)cos[2.pi.(2f)t]sin2.phi. (11) 
Note that in this instance the a.c. term depends on cos[2.pi.(2f)t] so that 
phase sensitive detection is possible at 2f. Of course, as equations 9.1 
and 9.2 illustrate, .theta..sub.1 may be chosen to permit phase sensitive 
detection at any desired frequency corresponding to 2Nf, where N is an 
integer. 
The actual detected signal of the interferometer is depicted in FIG. 5. 
FIG. 5(a) represents the final output signal, when the interferometer is 
operated with zero ac signal and FIG. 5(b) represents the final output 
signal for operation with a non-zero ac signal. Note the dramatic 
reduction of noise for ac operation. 
The fiber length employed was 420 m, the coil diameter was 29 cm and the 
mirror was driven sinusoidally at 3 kHz with .theta..sub.1 =3 rad. This 
modulation scheme reduced the short term noise by approximately a factor 
10 while allowing the gyroscope to operate at maximum sensitivity. 
The arithmetic circuit actually constructed included a Burr Brown 3660 with 
attendent resistor network for forming the sum of the signals representing 
I.sub.3 and I.sub.4, a Fairchild 741 with attendent circuitry for forming 
the difference, and an ICL 8013 Special Electronic 4 Quadrant Analogue 
Multiplier for forming the quotient of the difference and the sum of 
I.sub.3 and I.sub.4. Phase sensitive detection was accomplished by use of 
an Ithaco, Model 393 phase-locked amplifier. 
It is understood by persons of ordinary skill in the art that the above 
described embodiment of the invention is not limited to the use of the 
air-mirror light paths 34,36 in the Mach-Zehnder 12. Alternatively, the 
Mach-Zehnder 12 could be fabricated on a dielectric substrate with light 
paths comprising channel waveguides, beamsplitters comprising directional 
couplers and phase-adjusting means comprising electrodes disposed about a 
channel waveguide. Discrete optical fibers may also be employed with 
phase-adjusting means comprising a fiber-stretcher. 
The circuit of FIG. 3 would be interconnected with either of the above 
described Mach-Zehnders in a manner analogous to the Mach-Zehnder depicted 
in FIG. 2. The ac signal generator 100 would be connected to the 
phase-shifter and the photodetectors of the ac and dc circuits 92, 94 
would be disposed to measure the intensities of the appropriate light 
beams. 
FIG. 6 depicts an alternate embodiment of the present invention wherein a 
fiber-optic gyroscope with a (3.times.3)-(2.times.2) coupler 118, as 
disclosed by Sheem, K. in U.S. patent application Ser. No. 356,590, is 
interconnected with the ac circuit depicted in FIG. 3. FIG. 7 depicts a 
(3.times.3) coupler 120 comprising an input waveguide 122 disposed between 
two first output waveguides 124, 126 and a (2.times.2) coupler 128 
comprising two second output waveguides 130, 132 wherein the first output 
waveguides are coupled to the second output waveguides by two intermediate 
waveguides 140, 142. The waveguides may be channel waveguides fabricated 
on a dielectric substrate or discrete optical fibers. The second output 
waveguides 130, 132 are optically coupled to the ends of the optical light 
path circuit 10, the input waveguide 122 is coupled to an external light 
source 16 such as a laser, the first output waveguides 124, 126 are 
coupled to photodetectors 68, 70 and the first output waveguides 124, 126 
are coupled to the second output waveguides 130, 132 by the intermediate 
waveguides 140, 142. 
The input beam launched into the input waveguide 122 is split into two 
light beams which counterpropagate through the optical light path circuit 
10 and return to the photodetectors 48, 46 via the second output 
waveguides 130, 132 the intermediate waveguides 140, 142 and the first 
output waveguides 124, 126. The intensities of the returning output beams 
are equal for zero rotation rate due to the symmetry of the 
(3.times.3)-(2.times.2) coupler 118. Therefore, the interferometer 
operates at maximum sensitivity for near-zero rotation rates and only the 
ac circuit of FIG. 3 is required. 
A phase shifter 144, being either a pair of electrodes for channel 
waveguides or a fiber-stretcher for discrete optical fibers, is disposed 
across one of the intermediate waveguides 142. An ac signal from the ac 
signal generator of the circuit depicted in FIG. 3 applied to the 
phase-shifter 144 will shift the interferometer into and out of 
quadrature, thereby causing the power of the output signal, S.sub.I, to be 
modulated. Therefore, the interferometer depicted in FIG. 6 controlled by 
the ac circuit of FIG. 3, wherein the piezoelectric driver and cylinder is 
replaced by the phase-shifter, provides an ac interferometer output 
signal, S.sub.I, with high average output power. Phase sensitive detection 
thereof is provided, as set out above, and the noise suppression 
advantages described above are realized. 
FIG. 7 depicts a second alternate embodiment of the present invention 
wherein a (3.times.2) optical coupler 146, as disclosed by Burns in U.S. 
patent application Ser. No. 353,677, now U.S. Pat. No 4,445,780, is 
interconnected to the ac circuit depicted in FIG. 3. In FIG. 7 a central 
two-mode channel waveguide 148 branches at one end into three one-mode 
input channel waveguides, wherein a middle input waveguide 150 is disposed 
between two outer input waveguides 152, 154, and at the other end into two 
one-mode output channel waveguides 156, 158. The output waveguides 156, 
158 are optically coupled to the ends of the optical light path circuit 
10, the middle input waveguide 150 is optically coupled to an external 
light source 16 such as a laser, and the outer input waveguides 152, 154 
are optically coupled to photodetectors 68, 70. The waveguides of 
(3.times.2) coupler 146 are fabricated on the planar surface of a 
dielectric and are symmetrically disposed about an axis 159 through the 
central waveguide. Electrode means 160, 162 are disposed relative to the 
central waveguide 148 for generating an electric field in the central 
waveguide 148. 
The input beam launched into the middle input waveguide 150 is split into 
two light beams which counterpropagate through the optical light path 
circuit 10 and return to the photodetectors 48, 50 via output waveguides 
156, 158, the central waveguide 148 and the outer input waveguide 152, 
154. The intensities of the returning output beam are equal for zero 
rotation-rate due to the symmetry of the (3.times.2) coupler 146. 
Therefore, the interferometer operates at maximum sensitivity for near 
zero rotation rates so that only the ac circuit of FIG. 3 is required. 
FIG. 7 depicts the excitement of the two modes 164, 166 of the central 
waveguide by the Sagnac phase shifted counterpropagating light beams 
exiting the optical light path circuit 10. Note that the difference in 
amplitude of the output signals in the outer input waveguides 152, 154 is 
due to the interference between the modes at the point where the central 
waveguide 148 branches into the input waveguides 150, 152, 154. For the 
phase relationship illustrated in FIG. 7 there is constructive 
interference in the outer input waveguide 152 positioned above the axis 
159 and destructive interference in the outer input waveguide 154 below 
the axis 159. The output signal S=(I.sub.3 -I.sub.4)/(I.sub.3+I.sub.4) is 
a maximum when the difference between I.sub.3 and I.sub.4 is a maximum. 
Thus, S will be maximized if the interference between the modes is a 
maximum at the branching point. 
If .beta..sub.1 and .beta..sub.2 are the propagation constants of the 
symmetric and anti-symmetric modes 164, 166, respectively, and L is the 
length of the central waveguide 148, then interference is maximized when 
EQU (.beta..sub.1 -.beta..sub.2)L=.pi./2. (11) 
and the interferometer operates a quadrature. 
A potential difference impressed upon the electrodes 160, 162 creates an 
electric field across the central waveguide 148. .beta..sub.1 and 
.beta..sub.2 are affected differently by the applied electric field since 
the modes have different transverse intensity distributions. Thus, in the 
presence of the applied field, .beta..sub.1 and .beta..sub.2 no longer 
satisfies eq. (11), interference at the branching point is no longer 
maximized, and the amplitude of S decreases from its maximum value. The 
amplitude of S will alternate if an alternating signal from the ac 
generator of the circuit depicted in FIG. 3 is impressed upon the 
electrodes. Therefore, the interferometer depicted in FIG. 7 controlled by 
the ac circuit of FIG. 3 will provide an ac output signal with high 
average power. Phase-sensitive dection is provided as set out above and 
the advantages of noise suppression as described above are realized. 
Obviously, numerous additional modifications and variations of the present 
invention are possible in light of the above teachings. It is therefore to 
be understood that within the scope of the appended claims, the invention 
may be practiced otherwise than as specifically described herein.