Towards a solid-state ring laser gyroscope

Abstract

In this paper, we report our recent progress towards a solid-state ring laser gyroscope (RLG), where mode competition is circumvented by active control of differential losses, and nonlinear effects are mitigated by longitudinal vibration of the gain medium. The resulting dynamics is significantly different from that of a classical helium–neon RLG, owing in particular to parametric resonances that occur when the Sagnac frequency is an integer multiple of the crystal vibration frequency. We describe the main experimental and theoretical results obtained so far, and the prospects of practical applications in the near future.

Full text

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Contents lists available at ScienceDirect
Comptes Rendus Physique
www.sciencedirect.com
The Sagnac effect: 100 years later / L’effet Sagnac : 100 ans après
The fiber-optic gyroscope, a century after Sagnac’s
experiment: The ultimate rotation-sensing technology?
Le gyromètre à fibre optique, cent ans après l’expérience de Sagnac :
la technologie ultime de mesure inertielle de rotation ?
Hervé C. Lefèvre ∗
iXBlue SAS, 52, avenue de l’Europe, 78160 Marly-le-Roi, France
a r t i c l e i n f o a b s t r a c t
Article history:
Avail able online xxxx
Keywords:
Fiber-optic gyroscope
Ring-laser gyroscope
Sagnac effect
Inertial navigation
Mots-clés :
Gyromètre à fibre optique
Gyromètre laser
Effet Sagnac
Navigation inertielle
Taking advantage of the development of optical-fiber communication technologies, the
fiber-optic gyroscope (often abbreviated FOG) started to be investigated in the mid-1970s,
opening the way for a fully solid-state rotation sensor. It was firstly seen as dedicated to
medium-grade applications (1◦/hrange), but today, it reaches strategic-grade performance
(10−4◦/hrange) and surpasses its well-established competitor, the ring-laser gyroscope,
in terms of bias noise and long-term stability. Further progresses remain possible, the
challenge being the ultimate inertial navigation performance of one nautical mile per
month corresponding to a long-term bias stability of 10−5◦/h. This paper is also the
opportunity to recall the historical context of Sagnac’s experiment, the origin of all optical
gyros.
©2014 Published by Elsevier Masson SAS on behalf of Académie des sciences.
r é s u m é
Profitant du développement des technologies de télécommunication à fibre optique, le
gyromètre à fibre optique a commencé à être étudié au milieu des années 1970, ouvrant
la voie à un gyromètre entièrement à état solide. Il a d’abord été considéré comme
seulement adapté aux applications de moyenne performance (de l’ordre de 1◦/h), mais
atteint aujourd’hui des performances de classe stratégique (de l’ordre de 10−4◦/h) et
surpasse, en termes de bruit et de dérive à long terme du biais, son concurrent établi, le
gyromètre laser. Des progrès supplémentaires restent possibles, le défi étant la performance
ultime de navigation inertielle au nautique par mois, qui correspond à une stabilité de
dérive de 10−5◦/h. Cet article offre aussi l’opportunité de rappeler le contexte historique
de l’expérience de Sagnac, qui est à l’origine de tous les gyros optiques.
©2014 Published by Elsevier Masson SAS on behalf of Académie des sciences.
*Tel.: +33 1 30 08 88 88; fax: +33 1 30 08 88 00.
E-mail address: herve.lefevre@ixblue.com.
http://dx.doi.org/10.1016/j.crhy.2014.10.007
1631-0705/©2014 Published by Elsevier Masson SAS on behalf of Académie des sciences.

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Fig. 1. Original Sagnac’s setup [1] of a ring interferometer to demonstrate sensitivity to rotation rate (S stands for surface, which means “area” in French).
1. Introduction
Both optical gyroscopes, the ring-laser gyro (RLG) and the fiber-optic gyro (FOG), are based on the same Sagnac effect [1],
which shows that light travelling along a closed-ring path in opposite directions allows one to detect rotation with respect
to inertial space. Over one turn as in the original Sagnac’s experiment, a century ago [2], the effect is extremely weak but
it can be increased with recirculation in the resonant cavity of a ring laser or using the numerous loops of a fiber coil. The
RLG was demonstrated only a few years after the invention of the laser in 1960, and it is based on helium–neon (He–Ne)
technology. It became very successful in the 1980s and has since overcome classical spinning-wheel mechanical gyroscopes
because of its improved lifetime and reliability. It also provided an excellent scale factor performance, making strap-down
navigation systems possible. Earlier mechanical systems used a stabilized gimbaled platform where the gyros work only
around zero to stabilize the attitude of the platform; a strap-down system avoids the delicate mechanics of the gimbaled
approach but the gyros are attached directly to the vehicle, and then they have to follow precisely the whole dynamical
range of the vehicle rotation, which requires a very good stability of the scale factor. It was clear progress over mechanical
gyroscopes, but gas lasers still have several drawbacks such as high-voltage discharge electrodes that tend to wear out over
the long term or the need for perfect sealing of the gas enclosure. The advent of low-attenuation optical fiber and efficient
semiconductor light source developed for optical communications in the 1970s opened the way for a fully solid-state device.
Then, however, the FOG was seen as an approach dedicated to medium performance, and unable to compete with the RLG
for top-grade applications. As we shall see, this is not the case anymore. This paper is also the opportunity to recall the
historical context of Sagnac’s experiment and to outline the early theoretical contribution of Max von Laue [3].
2. Historical context of Sagnac’s experiment
If Huygens proposed in the 17th century a wave theory of light, Newton imposed his views of a corpuscular theory
in the early 18th century. It is only in the early 19th century that Young’s double-slit experiment reopened the wave
theory, knowing that it was not easily admitted: you did not contradict Newton! It required the exceptional quality of the
theoretical and experimental work of Fresnel to convince the physicist community.
However, for the minds of that time, a wave needed some kind of propagation medium, as for acoustic waves. It was
called “luminiferous Aether”, and light was seen as propagating at a constant velocity cwith respect to this fixed Aether.
Even when Maxwell showed in 1864 the electromagnetic nature of light wave, Aether was not questioned. It required
the famous Michelson and Morley experiment in 1887 to have a clear demonstration that the concept of Aether should
be revised, and this yielded, in 1905, the special theory of Relativity, when, based on earlier theoretical works of Lorentz,
Poincaré, Planck and Minkowski, Einstein abandoned the concept of Aether and stated that light is propagating at the same
velocity cin any inertial frame of reference in linear translation, despite its own velocity.
This revolutionary conceptual leap was very difficult to admit, and Sagnac’s experiment [Fig. 1], the base of present
optical gyroscopes, was actually performed to demonstrate that Aether did exist as clearly stated in the title of his publica-
tion [2]: “The luminiferous Aether demonstrated by the effect of the relative wind of Aether in an interferometer in uniform rotation”.
Sagnac’s experiment, which takes place in a vacuum (actually in air, but it can be considered as in a vacuum), can be
either explained by special Relativity or classical Aether theory, and does not allow one to demonstrate which theory is
right or wrong. It was explained clearly by von Laue in 1911 [3] [Fig. 2], two years before Sagnac’s publication, and maybe
the Sagnac effect should be renamed the Sagnac–Laue effect!

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Fig. 2. Explanation of “Sagnac–Laue” effect in von Laue publication of 1911 [3].
Another important point of Aether theory was the hypothesis made by Fresnel in 1818 of the drag of Aether by matter,
which was demonstrated experimentally by Fizeau in 1851 [4]. The velocity vof a wave that propagates in a medium of
index nthat moves at a speed vmis not c/nanymore, but:
v=c
n+1−1
n2vm(2.1)
Note that in Fizeau’s experiment, one has to take into account the dispersion of the index, since the wave frequency seen
by the medium is not the same in both directions because of the Doppler effect, but in a fiber gyro both opposite waves
have the same frequency in the frame of the medium and there is no dispersion effect [5].
This Fresnel–Fizeau drag effect was explained by von Laue in 1907 [6] as resulting from the law of combination of speeds
of Special Relativity:
v=v1+v2
1+v1v2
c2
(2.2)
where v1is the speed of a mobile in a frame moving at v2with respect to the “rest” frame, and vis the speed of this
mobile in this “rest” frame. One sees that Eq. (2.2) yields Eq. (2.1) to first order in vm, considering v1=c/n, v2=vmand
vmc. The Fresnel–Fizeau drag effect is actually a relativistic effect!
The important point is that, because of the Fresnel–Fizeau drag effect, the Sagnac effect does not depend on the index
of refraction of the corotating propagation medium as it was stated by von Laue [7] as early as in 1920, and as it is clearly
experienced in a fiber-gyroscope [5]. If the Sagnac effect in a vacuum can be explained by Aether theory, the Sagnac effect
in a medium is related to the Fresnel–Fizeau drag effect and is then also a relativistic effect.
3. What are we looking for? Single-mode reciprocity is key
Going back to present optical gyros, despite their difference of principle, RLGs and FOGs have similar theoretical noises
for the same single-turn enclosed area and the same number of recirculations [8]. The typical RLG perimeter is 20 to 30 cm
with on the order of 104recirculations in the high-Q mirror cavity [Fig. 2]. An FOG coil of 104loops of 10 cm in diameter
(i.e. 3 km long and typically 3dB of attenuation) has the same potential. Today, RLGs are in the so-called navigation-grade
performance range needed for airliners, i.e. below 10−2◦/hin term of long-term bias stability, while highest-performance
FOGs are in the so-called strategic-grade performance range needed for very long-term marine and submarine navigation,
i.e. at least ten times better, below 10−3◦/h. Translated in path length difference induced by the Sagnac effect, it means a
relative change on the order of 10−18 for the RLG, and 10−19 to 10−20 for the FOG! These incredible numbers may look
unrealistic, but there is the fundamental principle of reciprocity of light propagation which acts as a perfect common-mode
rejection between both counter-rotating waves, when there is single-mode propagation. Because of single-mode reciprocity,
the transit time of both counterpropagating waves can be perfectly balanced, leaving out only the Sagnac effect. The quality
of the residual bias instability (zero instability) depends on the residual lack of reciprocity.
A detailed analysis of the principle of RLG can be found in a work by F. Aronowitz [9], one of the pioneers of this
technology. The RLG has naturally “quasi-reciprocity” because it operates in a single transverse laser mode as well as a

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Fig. 3. Symmetrical discharge to balance. Fresnel–Fizeau drag effect due to the ionic flow in an RLG.
single longitudinal mode and the reflection birefringence of the mirrors due to the large angle of incidence ensures a single
polarization in the cavity, but its reciprocity is not perfect. The electrical discharge creates an ionic flow, and because of the
Fresnel–Fizeau drag effect, this matter flow yields a velocity difference between counterpropagating waves [9]. It is only on
the order of 10−15 in terms of relative velocity, but it creates a spurious non-reciprocal effect equivalent to about 1◦/h. It
is counterbalanced by using a common cathode and two symmetrical anodes [Fig. 3], but this balancing cannot be perfect
and there is a residual bias instability on the order of a few thousandths of degree per hour. One could think: why does
not one use a solid-state laser to avoid this drag effect? After all, since the early 1960s, when the He–Ne laser gyro was
invented, numerous kinds of lasers have been developed, but there is a key problem in laser behavior: mode competition!
In principle, a CW ring laser should not work because both directions have the same lasing conditions and they “compete”,
i.e. it is unstable. He–Ne ring lasers work because of a very subtle effect: with the flow, the moving amplifying ions see
different frequencies for both opposite directions because of the Doppler effect, and the use of 20Ne and 22 Ne isotopes
with gain curves shifted in frequency allows one to get two “superimposed” lasers: one isotope amplifying one direction
and the other one the opposite one, which avoids mode competition. “Magic”... but within the limit of the Fresnel–Fizeau
drag-induced non-reciprocity!
In the case of FOG, reciprocity was much more difficult to get, mainly because of the residual birefringence of the fiber. As
it is well known, a single-mode fiber has actually two orthogonal polarization modes that propagate with slightly different
velocities because of fiber birefringence. One understands that if one direction uses one mode and the opposite one uses
the crossed mode, there is a non-reciprocal phase difference. It was shown very early [10] that reciprocity does not require
true single-mode propagation along the entire interferometer and that a single-spatial mode/single-polarization mode filter
at the common input–output of the ring interferometer is sufficient. However, the requirement on polarizer rejection to
fully suppress the problem can be very stringent. Because of coherence effects, the residual phase non-reciprocity in radian
may be equal to the amplitude rejection of the polarizer [11], i.e. a very good rejection of −80 dB may yield a phase
non-reciprocity as high as 10−4rad, but today the problem is solved with the progress of the components and the use
of decoherence [12,13]. Proton-exchanged lithium niobate (LiNbO3) integrated-optics yields a single-polarization waveguide
that provides excellent polarization rejection (as good as −80/–90 dB), and a polarization-maintaining (PM) fiber limits the
amount of light in the crossed polarization mode, but it would not be sufficient by far. One has also to take advantage
of decoherence/depolarization effects with the use of a broadband source which has a short coherence time. Because of
the birefringence of PM fiber and LiNbO3crystal, the spurious crossed polarization propagates at a different speed from the
main signal and loses its coherence with respect to this main signal, which drastically reduces the parasitic effect. To further
reduce defects, one can also take advantage of the natural unpolarization of ASE (Amplified Spontaneous Emission) sources
based on telecom diode-pumped EDFA (erbium-doped fiber amplifier) technology. The crossed component of the input
unpolarized light (the component orthogonal to the polarizer axis) compensates for the residual nonreciprocity of the main
component [12,13]. Because of the residual polarization dependent loss of the components, the actual input unpolarization
is not perfect, but in practice the degree of polarization of the input ASE light is only few percent and this brings an
additional 30-fold reduction of polarization non-reciprocities.
Now, light travelling in a dense medium and with high-power density because of the guidance, one could have faced
nonlinear effect destroying reciprocity [14] which is based on the linearity of propagation equation, but the power fluctu-
ation statistics of broadband source happens to balance this effect perfectly [12,13]. Today, the FOG appears as a unique
sensor that could be just limited by its theoretical white photon shot noise without any source of long-term drift.
Note that the use of a low-temporal-coherence source brings excess relative intensity noise (excess RIN) because of the
random intensity beating of all its spectral components. With an erbium fiber source, it can be as high as 10−6/√Hz, but

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Fig. 4. Principle of digital phase ramp feedback, with τgbeing the transit time through the coil (5 μs/km), which depends on the group’s velocity.
RIN can be reduced by compensation techniques [12], and it is possible to get very close to the theoretical photon shot
noise, which is typically 10−7/√Hz for a returning power of few tens of μW.
Finally, gyroscopes have to operate over a large dynamical range, and this requires signal processing techniques that will
not degrade this intrinsic stability.
4. The other key issue: signal processing techniques
Among the advantages of RLG is its very simple read-out mechanism. As in any laser, there are an integral number
of wavelengths along the cavity path. Path length difference created by the Sagnac effect induces a wavelength difference
between both counterpropagating resonant beams, and therefore a frequency difference. Both output beams are recombined
to interfere [Fig. 2] and yield a frequency beating that is proportional to the rotation rate. A simple counting electronics
provides a linear read-out of the rate over a very large dynamical range.
Note however that at low rate, there is the so-called “lock-in” effect. Both laser beams have very close frequencies: about
1Hz difference for 1◦/h, when light frequency is 500 THz at a He–Ne operating wavelength of 633 nm. Despite impressive
technological progress, there is still some residual mirror backscattering yielding coupling that locks them on the same
frequency. This is eliminated by a mechanical dithering, but it increases the theoretical RLG measurement noise by an order
of magnitude [9].
The FOG is not an active resonator anymore but a passive interferometer with an external light source. It is possible to
get no lock-in, so no need for dithering that avoids its related noise degradation. In particular, the backscattering of a fiber is
higher than the one of RLG mirrors, but the low temporal coherence of the broad-spectrum source of an FOG limit spurious
interferences between this backscattered light and the primary waves. However, the raw response is the nonlinear raised
cosine response of an interferometer. This has been overcome by a very efficient phase modulation technique associated
with a drift-free digital demodulation and a phase feedback. This so-called all-digital phase ramp combines square-wave
biasing modulation and synchronized phase steps generated and demodulated digitally [Fig. 4] [12,13,15].
This sophisticated processing approach is conceptually much more complicated than the simple frequency readout of an
RLG, but it can be easily implemented with present digital electronics. It yields an excellent scale factor linearity of 1 ppm
without any degradation of the basic noise or the reciprocity of the interferometer, and it works without quantization error
despite a limited number of converter bits, because of averaging effects [12,15].
Bias noise and drift are calculated with Allan variance (or deviation, its square root) [12,16] and, in a temperature
stabilized environment, a high-performance FOG does yield the theoretical −1/2power reduction slope of a white noise
over days of measurement without any visible bias stability limitation (no flicker, no rate random walk), down to the
10−5◦/h range, corresponding to an interferometer phase difference close to 10−10 rad, and with a white noise be-
low 10−2(◦/h)/√Hz, which corresponds to an angular random walk in the 10−4◦/√hrange, and a phase noise of few
10−7rad/√Hz. This is absolutely unique, compared to any other inertial sensors, as accelerometers or mechanical and laser
gyros, which all face long term drift, even in a temperature-controlled environment.
There is a residual temperature dependence in FOG that is related to the so-called Shupe effect [12,17] due to temper-
ature transient. However, symmetrical winding techniques [18] as well as careful modeling reduce very significantly the
effect. Typical long-term bias stability specification for a high-performance FOG is in the range of a few 10−4◦/hin an
unstabilized temperature environment.
The scale factor varies also in temperature. It depends on the geometrical area of the gyro coil and on the wavelength.
Temperature modeling allows one to get a reproducible stability of the coil size to an accuracy of 10 ppm, and wavelength
stability may be improved to this same 10 ppm value with internal spectral filtering of an erbium-doped fiber source [12].
5. Configuration of an FOG
Based on solid-state technologies of optical-fiber communications, the FOG yields a high reliability and a very long life
time in addition to its performance. It is composed of (Fig. 5; see for example [12,13]):

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Fig. 5. Configuration of an FOG with a Y junction as the splitter and recombiner of the interferometer, a polarizer and a pair of electro-optic phase
modulators on the multi-function LiNbO3integrated-optic circuit.
Fig. 6. (Color online.) iXBlue MARINS inertial navigation system (400 ×300 ×280 mm3) using gyro coils of 3km over a mean diameter of 170 mm. The
bias stability specification of the gyros over environment is 5 ×10−4◦/h, and the scale factor specification is 10 ppm.
•a broadband source based, for high grade, on EDFA technology at a wavelength of 1550 nm; wavelength stability may
be obtained with internal spectral filtering with a fiber Bragg grating,
•a polarization-maintaining (PM) fiber coil (a few hundred meters for medium grade to several kilometers for very high
grade),
•a LiNbO3integrated-optic circuit with electrodes to generate phase modulation with the electro-optic Pockels effect and
that provides excellent polarization selectivity with proton-exchanged waveguide,
•a fiber coupler (or a circulator for higher returning power) to send to a detector light returning from the common
input–output port of the interferometer;
•an analog–digital (A/D) converter to sample the detector signal;
•a digital logic electronics that generates the phase modulation and the phase feedback through a digital-to-analog (D/A)
converter.
It is important to note that with the adequate design and components, the performance of an FOG is very reproducible
in production, even for the high-performance end. It does not require trimming or selection.
Testament to the quality, accuracy and reliability of the fiber-optic gyro is its growing use for positioning and navigation
instruments in navy [Fig. 6] and space [Fig. 7] applications.
As already discussed, the residual limit of FOG bias stability is the temperature transient, and Fig. 8 shows a promising
laboratory result of longitude error of an iXBlue prototype of inertial navigation system that was performed “at rest” in a
temperature-stabilized environment over more than one month (38 days). The longitude accuracy is in the range of one

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Fig. 7. (Color online.) Four-axis (for redundancy) FOG developed by iXSpace, an iXBlue company, in cooperation with Airbus Defence & Space (formerly
EADS-Astrium) for space applications; the gyro coils are 5km long over a mean diameter of 170 mm. Bias and scale factor specifications are similar to the
ones of MARINS gyros.
Fig. 8. Longitude error of iXBlue’s inertial system prototype, in a temperature controlled environment, over 38 days: 1 nautical mile (Nm) per month.
nautical mile (Nm) over one month! It corresponds to a gyro bias stability of about 10−5◦/h and a gyro scale factor stability
of about 1 ppm!
Understanding this result requires some explanations about inertial navigation. An inertial navigation system (INS) cal-
culates the trajectory with respect to inertial space with the mathematical integration of the measurements of the rate
of rotation by the gyros and of the acceleration by the accelerometers. Note that mathematical integration is similar to
averaging and then it filters out short-term noise to keep only the effect of the long-term drift.
“At rest” with respect to the Earth means actually to follow the movement of rotation of the Earth, which is quite fast.
At the latitude of 48◦where the experiment was performed, the tangential velocity due to the Earth’s rotation is 1100 km/h
and it is measured by the gyros. Over the 38 days of the experiment, the system “at rest” travelled in fact over one million
of kilometers, and its position in longitude is known by the integration of the tangential speed measured with the rotation
rate. The linear component of the mean position drift being less than half a nautical mile (i.e. about one kilometer) over one
million of kilometers, it means the measurement of the 15◦/hof Earth rotation rate is performed with a relative stability
of one millionth, i.e. a 1.5 ×10−5◦/herror combining bias and scale factor. The gyro fiber coils of this experiment being
3 km long over a diameter of 200 mm and the wavelength being 1550 nm, this 1.5 ×10−5◦/herror correspond to a
phase difference error of only 5 ×10−10 rad. Compared to the absolute phase of 2 ×10+10 rad accumulated over 3 km of
propagation in the fiber coil, it yields a relative stability of 2.5 ×10−20 !

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There is also a 24 h oscillation in this experimental result: the modulus of the measurement of the Earth rotation rate
vector by the gyro triad yields, as we just saw, the linear part of the drift, but there is also a residual error in the measured
direction of the axis of this Earth rotation rate vector. At rest with respect to the Earth, the measured inertial movement
should follow a circle with always the same latitude, but with an orientation defect, this measured circle will become
slightly tilted yielding a 24-h oscillation of the position error in latitude and longitude. This error is bounded and then it is
not as harmful as the linear component of the drift in longitude that grows continuously over time.
6. Conclusion
Entering production in the 1980s, the RLG has revolutionized inertial techniques, and it is clearly the technology of
reference today. However, its limited lifetime and its need for dithering have motivated the development of FOG technology
based on a fully solid-state approach. Theoretical performance is similar for both technologies, but it has been more difficult
for FOG to obtain it. It started as a product for medium grade (1◦/h range) applications in the 1990s [19]. However, with
the development of fiber-optic communications components and digital signal processing techniques, it was shown that the
FOG not only brings the expected improvement of lifetime, but does not face the performance limitation of the RLG in terms
of noise and bias stability.
Today there is a clear change of mind, and the FOG is not seen any more as limited to medium grade, as presented
during the last OFS (Optical Fiber Sensor) Conference [20] by Northrop Grumman, Honeywell and iXBlue. As shown in this
paper, it even has the potential to become the “ultimate-performance” gyro that can surpass by at least one if not two
orders of magnitude RLG technology. Results in a temperature-controlled environment are already impressive and the final
challenge is to obtain this performance without this thermal control!
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