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Advances in Optics and Photonics

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  • Editor: Bahaa E. A. Saleh
  • Vol. 2, Iss. 3 — Sep. 30, 2010
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Photonic technologies for angular velocity sensing

Caterina Ciminelli, Francesco Dell’Olio, Carlo E. Campanella, and Mario N. Armenise  »View Author Affiliations


Advances in Optics and Photonics, Vol. 2, Issue 3, pp. 370-404 (2010)
http://dx.doi.org/10.1364/AOP.2.000370


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Abstract

Photonics for angular rate sensing is a well-established research field having very important industrial applications, especially in the field of strapdown inertial navigation. Recent advances in this research field are reviewed. Results obtained in the past years in the development of the ring laser gyroscope and the fiber optic gyroscope are presented. The role of integrated optics and photonic integrated circuit technology in the enhancement of gyroscope performance and compactness is broadly discussed. Architectures of new slow-light integrated angular rate sensors are described. Finally, photonic gyroscopes are compared with other solid-state gyros, showing their strengths and weaknesses.

© 2010 Optical Society of America

1. Introduction

Only a few years after the experimental demonstration of the first laser, photonics permitted the development of very sensitive gyroscopes (here also called gyros) based on the Sagnac effect. This physical effect induces either a phase or a frequency shift between two optical signals counterpropagating in clockwise (CW) and counterclockwise (CCW) directions within an appropriate optical path.

Two possible configurations can be identified for optical gyroscopes, passive and active. In passive gyroscopes the laser source is external, while in active gyroscopes the two beams are generated within the optical path.

In passive phase-sensitive gyros, the phase shift between two broadband optical beams counterpropagating in a ring interferometer is exploited to sense rotation. This phase shift is measured by analyzing the interference pattern.

Frequency-sensitive gyros can be active or passive. Active frequency-sensitive gyros are based on a ring laser in which CW and CCW signals are excited. In these devices the beating signal generated by the interference between CW and CCW lasing modes is measured to derive the angular velocity estimation. Passive frequency-sensitive gyros are based on an optical resonator excited by a very coherent external laser source. In this case, the resonance splitting provides a measure of the angular velocity. Operating principles of the three basic classes of photonic angular velocity sensor are summarized in Table 1.

In past years, the replacement of the He–Ne gain medium with a solid-state one in the RLG and the use of air-core photonic bandgap fibers in the FOG have been proposed to enhance the performance of these devices and to reduce their cost.

Integrated optoelectronics for angular rate sensing may solve some open issues in gyro technology, such as the need to reduce weight and size, lower costs, decrease power consumption, limit thermal effects, and increase reliability. Photonic technologies could allow the integration of a gyroscope on a single chip, and this possibility can surely be pointed out as a very interesting research target, especially in the framework of microsatellite and nanosatellite development.

In active integrated optical gyros, two resonant modes are excited within a semiconductor ring laser (SRL), and they experience a rotation-induced frequency shift that can be measured by the read-out optoelectronic circuit integrated into the same substrate on which the ring laser is fabricated.

In passive integrated optical angular rate sensors, an optical cavity is excited by two signals propagating in CW and CCW directions. When the gyro rotates, the resonance frequencies of the cavity relevant to the two propagation directions are not equal. The difference between them is proportional to the angular rate. The sensor architecture typically includes a passive integrated optical resonator (sensing element), a laser source for cavity excitation, and an optoelectronic read-out system that permits the estimation of the difference between resonance frequencies. The integrated optical resonator can be realized as a single long-length ring or spiral, a number of evanescently coupled rings, or a photonic crystal cavity.

In this paper the most promising emerging photonic technologies for angular rate sensing are reviewed. Recent results in the field of active and passive optical gyros are reported. The main features of bulk-optic RLGs are briefly discussed with special attention to the recently proposed solid-state RLG. Some architectures of fully integrated active optical gyros based on a SRL are presented, and we point out the physical effects limiting their performance. High-performance FOGs exploiting very sophisticated read-out techniques and innovative optical fibers are reported. Recent achievements in the field of passive integrated optical gyros realized by low-loss technology are reviewed, and we show that the simultaneous excitation of the sensing element by two beams enhances the overall gyro performance. Encouraging theoretical results about the feasibility of an InP-based photonic integrated circuit (PIC) serving as a passive gyro are reported. The possibility of using innovative passive integrated optical cavities to sense rotation is briefly discussed. Finally, the performance achievable by photonic angular rate sensors is compared with that of other solid-state gyros, such as the hemispherical resonant gyroscope (HRG) and gyroscopes based on microelectromechanical systems (MEMS).

2. Active Gyroscopes

In active gyroscopes two counterpropagating beams are excited within a ring laser. According to the Sagnac effect, when the sensor rotates, the paths of the two beams are different, and this difference induces a change of the resonant frequency of each propagating mode. The resultant frequency shift is proportional to the angular rate of the device. When CW and CCW optical signals are outcoupled and are allowed to interfere, a beat signal is generated. From the measurement of the frequency of the beat signal, the angular velocity can be estimated.

The He–Ne RLG, which has been a well-established commercial device for several decades, is a bulk-optic active gyroscope based on a triangular or square active optical cavity formed by high-quality mirrors. Optical gain within the laser is provided by a He–Ne gas mixture contained inside a discharge tube equipped with electrodes to supply electrical power.

This sensor exhibits very good performance, but its volume exceeds 2000cm3, its weight is about 3kg, and its power consumption is in the range 1015 W.

Unfortunately, the lifetime and the reliability of the He–Ne RLG are limited by the degradation of the He–Ne gas mixture. The use of a solid-state gain medium instead of a gaseous one may improve the reliability and the lifetime of the RLG. This is why new bulk-optic solid-state RLGs have been both experimentally and theoretically investigated in recent years.

In the past two decades intense research effort has been spent to miniaturize the RLG by using integrated optics. The objective of this research activity has been the demonstration of a very compact RLG fully integrated on a single chip.

According to [4

4. P. G. Eliseev, “Theory of nonlinear Sagnac effect,” Opto-Electron. Rev. 16, 118–123 (2008). [CrossRef]

], in active gyroscopes the rotation-induced frequency difference is inversely proportional to the group index (ng=cvg, with the c speed of light in vacuum and vg the group velocity) of the counterpropagating beams. This effect also implies the possibility of increasing the Sagnac response by generating fast light [5

5. C. Ciminelli, C. E. Campanella, F. Dell’Olio, and M. N. Armenise, “Fast light generation through velocity manipulation in two vertically-stacked ring resonators,” Opt. Express 18, 2973–2986 (2010). [CrossRef] [PubMed]

].

The main critical aspect of all active gyroscopes is the mode locking (or lock-in effect), which corresponds to a null frequency difference between counterpropagating beams for small rotation rates.

2.1. Lock-in Effect

In active gyroscopes, the power exchange between CW and CCW beams generated within the ring laser induces the lock-in effect, which occurs when the angular velocity Ω is below a critical value ΩL.

If the angular velocity is less than ΩL, counterpropagating beams oscillate at the same frequency, making the frequency difference between CW and CCW beams equal to zero. This is responsible for a deadband on the input-output characteristic of the gyro.

The coupling between the counterpropagating waves is due to the backscattering of a small fraction of the optical power carried by each wave. In the bulk-optic RLG, imperfections in mirrors or other intracavity optical elements cause backscattering; so, to reduce the detrimental influence of this physical effect, the mirror fabrication technology has to be particularly accurate. In active integrated optical gyroscopes based on a SRL, the backscattering is due to the roughness on sidewalls of the laser waveguide and to the spatial hole burning. A gain grating is induced in the active medium because of this last physical effect, which generates coupling between CW and CCW resonant modes.

The most straightforward technique to avoid the lock-in is the introduction of an externally controlled constant bias to let the active gyro always operate in the unlocked region. In this case the total rotation rate is defined by two contributions, one from the actual angular velocity and the other from the bias rate. A number of techniques have been proposed to produce the constant bias in the He–Ne RLG. Among them we mention the Faraday cell technique [6

6. J. Krebs, W. Maisch, G. Prinz, and D. Forester, “Applications of magneto-optics in ring laser gyroscopes,” IEEE Trans. Magn. 16, 1179–1184 (1980). [CrossRef]

] and magnetic [7

7. D. A. Andrews and T. A. King, “Sources of error and noise in a magnetic mirror gyro,” IEEE J. Quantum Electron. 32, 543–548 (1996). [CrossRef]

] or multiple-quantum-well (MQW) mirror technology [8

8. F. A. Karwacki, M. Shishkov, Z. Hasan, M. Sanzari, and H. L. Cui, “Optical biasing of a ring laser gyroscope by a quantum well mirror,” in IEEE 1998 Symposium on Position Location and Navigation (IEEE,1998), pp. 161–168.

]. A magnetic mirror has a multilayer structure including a thin film of a magneto-optic material such as iron garnet. When used in a He–Ne RLG, this mirror is properly designed to provide a phase shift between the two reflected beams. Since this phase shift depends on the incidence direction, an optical path difference between counterpropagating beams is generated. In MQW mirrors the reflection plane may be vertically moved by an electric field, which is able to change the refractive index because of the quantum-confined Stark effect.

A constant bias may not be successful because of the great difficulty of ensuring its stability. For typical ΩL values, the bias would have an order of magnitude of 106degh, which is a value incompatible with bias drift less than the 0.01degh usually required for high-performance gyros.

With a time-varying bias obtained by applying a sinusoidal driving signal, a decrease of lock-in can still be observed. A mechanical technique can be used to produce this alternating bias. In this case the gyro is rotated alternately in one direction and then in the opposite. This approach, called mechanical dithering, is usually implemented by mounting the gyro on a rotating system that oscillates by means of a piezoelectric transducer.

The introduction of a time-varying alternating bias induces the so-called dynamic lock-in, which implies that for certain ranges of input rates the gyro output follows the dither input rate and is not responsive to the angular velocity. To overcome this problem, a random variation of the initial phase relevant to every dither bias cycle has been proposed [9

9. J. Killpatrick, “Random bias for laser angular rate sensor,” U.S. patent 3,467,472, Sept. 16, 1969.

]. This solution can be implemented by adding amplitude noise to the pure sine dithering signal.

Lock-in can be significantly reduced by using an active ring cavity supporting four resonant modes, two propagating in the CW direction and the other two propagating in the opposite direction [10

10. W. W. Chow, J. B. Hambenne, T. J. Hutchings, V. E. Sanders, M. Sargent, and M. O. Scully, “Multioscillator laser gyros,” IEEE J. Quantum Electron. QE-16, 918–936 (1980). [CrossRef]

]. One of the CW beams is right-circularly polarized, and the other one is left-circularly polarized. CCW beams have the same polarizations. A reciprocal bias produced by a polarization rotator or a nonplanar cavity is used to obtain right- and left-circularly polarized modes, whereas a Faraday rotation induced by the Zeeman effect separately splits the resonant frequency corresponding to right-circularly polarized and left-circularly polarized beams into two frequencies, one for the CW mode and one for the CCW mode.

2.2. Bulk-Optic Solid-State Ring Laser Gyro

Unlike in the He–Ne ring laser, in the Nd:YAG one the simultaneous excitation of CW and CCW resonant modes is not easy to achieve, and so this kind of laser usually operates unidirectionally [13

13. A. Siegman, Lasers (University Science Books, 1986).

]. This is why an inhomogeneous saturation of the gain medium arises, which produces a population inversion grating and thus a strong coupling between the two counterpropagating modes. Therefore, to realize a bidirectional Nd:YAG ring laser, an additional coupling source between CW and CCW modes is required. In the device shown in Fig. 1, this coupling term is induced by optical losses that are different for CW and CCW signals. Thus the resonant mode with the highest power level suffers from the largest loss. The difference in optical losses of the two counterpropagating waves is induced by
  • A polarizing effect obtained by using a polarizing mirror in one of the cavity vertices;
  • A reciprocal (affecting CW and CCW modes in the same manner) polarization rotation achieved by a slightly nonplanar resonant cavity;
  • A nonreciprocal polarization rotation obtained by a solenoid placed around the Nd:YAG rod (with the current flowing through the solenoid, and so the polarization rotation proportional to the difference between power levels of the two resonant modes).
For angular rate values larger than 3.6×105degh, the fabricated devices, having a perimeter of 25cm and an area around 34cm2, are capable of effectively sensing the rotation. In the range between 6.8×104 and 3.6×105degh the sensor linearity is quite limited, and for angular velocities less than 6.8×104degh some instabilities in counterpropagating modes intensity have been observed, and no beat signal has been measured. In [14

14. S. Schwartz, F. Gutty, G. Feugnet, P. Bouyer, and J.-P. Pocholle, “Suppression of nonlinear interactions in resonant microscopic quantum devices: the example of the solid-state ring laser gyroscope,” Phys. Rev. Lett. 100, 183901 (2008). [CrossRef]

, 15

15. S. Schwartz, F. Gutty, G. Feugnet, and J. Pocholle, “Fine tuning of nonlinear interactions in a solid-state ring laser gyroscope,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (Optical Society of America, 2008), paper CMU7.

] the effect of the Nd:YAG crystal sinusoidal vibration with a frequency of 40kHz and an amplitude around 1μm on this solid-state RLG was investigated. This crystal vibration along the optical axis of the resonant cavity causes a decrease of minimum detectable angular velocity up to 3.6×104degh. This sensitivity is significantly worse than that of the conventional He–Ne RLG.

2.3. Semiconductor-Ring-Laser-Based Gyroscopes

The architecture of active integrated optical gyros includes a SRL and some read-out optoelectronic components. When the gyro rotates, counterpropagating beams generated within the laser exhibit a frequency difference that is proportional to the angular rate. This shift can be measured by the read-out optical circuit. The quantum-noise-limited minimum detectable angular rate of active integrated optical gyros (quantum limit) is given by [16

16. T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980). [CrossRef]

]
δΩ=δνSPoutBhcηλ×180×3600π(degh),
(1)
where S is the gyro scale, which is given by the ratio between the ring diameter and the laser operating wavelength (for circular ring lasers), δν is the linewidth of laser generated beams, Pout is the output laser power, η is the photodetector efficiency, B is the sensor bandwidth, λ is the laser operating wavelength, c is the speed of light in vacuum, and h is Planck’s constant.

In active optical gyroscopes, the angle random walk (ARW) is given by [16

16. T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980). [CrossRef]

]
ARW=δΩ60B=δνSPouthcηλ×180×60π(degh),
(2)
where δΩ is expressed in degrees per hour.

To minimize δΩ and ARW, scale factor and Pout maximization and laser linewidth minimization are needed. Then the basic requirements for a SRL to be used in a medium- to high-performance (δΩ<5degh, ARW<0.02degh) optical gyroscope are the following:
  • Laser radius at least in the range of millimeters (to ensure a sufficient scale factor value);
  • Narrow linewidth of lasing emission (<1MHz);
  • Single-longitudinal-mode operation.
The design and fabrication of a fully integrated active optical gyro exploiting a large-radius SRL as sensing element has been considered a very interesting research target for the past decade.

A fully integrated active optical gyroscope based on a MQW SRL operating at 845nm was proposed, designed, and accurately modeled in [17

17. M. N. Armenise, V. M. N. Passaro, F. De Leonardis, and M. Armenise, “Modeling and design of a novel miniaturized integrated optical sensor for gyroscope applications,” J. Lightwave Technol. 19, 1476–1494 (2001). [CrossRef]

]. The sensor architecture (shown in Fig. 2) was also patented [18

18. M. N. Armenise, M. Armenise, V. M. N. Passaro, and F. De Leonardis, “Integrated optical angular velocity sensor,” European patent EP1219926 (July 3, 2002).

]. The gyro, designed to be integrated on a 15mm wide and 3mm long GaAs substrate, includes

  • A GaAsAlGaAs MQW circular SRL (radius 1.5mm), which generates the two counterpropagating optical signals,
  • A curved directional coupler (bending radius 150μm, coupling efficiency about 0.2%) which extracts the optical beams from the SRL,
  • An electro-optic phase modulator inducing a π2 phase shift between the two optical signals generated by the laser,
  • A Y junction permitting the interference of the two optical signals coming out from the laser,
  • A photodetector (PD) located at the output of the Y junction.
In the MQW ring laser, optical gain is larger for quasi-TE than for quasi-TM modes. This means that the ring laser emits only a quasi-TE mode. This intrinsic effect of polarization selection leads to the absence of any coupling between the two polarizations. The guiding structure adopted in the laser includes an Al0.2Ga0.8As barrier that separates the two GaAs quantum wells, two cladding layers to be realized in Al0.2Ga0.8As, and a Al0.73Ga0.27As buffer. When the sensor rotates with respect to the axis perpendicular to the substrate surface (z axis in Fig. 2), the two beams interfering in the Y junction have different frequencies; so the optical signal coming from the Y junction has an amplitude oscillating with a frequency that is equal to the rotation-induced frequency shift. The device angular rate can be estimated by measuring the frequency of the electrical signal generated by the photodiode.

The main critical point of this fully integrated optoelectronic sensor is the lock-in effect. For angular rate values less than ΩL=210degh, the frequency difference between counterpropagating optical waves vanishes because of the coupling between the beams that is due to waveguide sidewalls roughness. Thus, in the lock-in operating condition, is not possible to measure the angular rate by estimating the frequency of the electrical signal generated by the photodetector.

As pointed out in [17

17. M. N. Armenise, V. M. N. Passaro, F. De Leonardis, and M. Armenise, “Modeling and design of a novel miniaturized integrated optical sensor for gyroscope applications,” J. Lightwave Technol. 19, 1476–1494 (2001). [CrossRef]

], for angular rates less than the threshold value ΩL, the two beams excited within the ring laser have the same frequency but exhibit a rotation-induced phase shift ψr. This phase shift is a measure of the angular rate in the lock-in operating region. For Ω<ΩL, no beat signal can be observed at the Y-junction output, but the intensity of the optical signal coming out from the junction depends on the phase shift ψ between the two interfering beams.

In the lock-in operating region, the current i generated by the photodetector located at the output of the Y junction is given by
i=i0[1+cos(ψ)],
(3)
where i0 is a constant proportional to the incident optical power.

The derivative of i with respect to ψ is maximum when ψ is close to π2. This condition is achieved by adding a fixed phase shift equal to π2 to the rotation-induced phase-shift ψr. In this manner the phase shift ψ between the beams interfering in the Y junction is equal to ψr+π2, and so it is always close to π2.

The electro-optic phase modulator imposes a constant phase shift of π2 between the two signals phase shifted by rotation. This enhances the accuracy of rotation-induced phase shift measurement, which is used when Ω<ΩL to overcome the lock-in detrimental effect. Unfortunately, the rotation-induced phase shift depends on a number of SRL technological parameters such as the ring radius and the backscattering coefficient. Thus, for low angular rate values, the sensor accuracy strongly depends on the accuracy in the estimation of these parameters. If we assume that the minimum detectable angular rate of the integrated gyro is limited by the quantum noise, the sensor resolution is estimated as around 0.01degh, under the lossless operating condition [17

17. M. N. Armenise, V. M. N. Passaro, F. De Leonardis, and M. Armenise, “Modeling and design of a novel miniaturized integrated optical sensor for gyroscope applications,” J. Lightwave Technol. 19, 1476–1494 (2001). [CrossRef]

]. In [17

17. M. N. Armenise, V. M. N. Passaro, F. De Leonardis, and M. Armenise, “Modeling and design of a novel miniaturized integrated optical sensor for gyroscope applications,” J. Lightwave Technol. 19, 1476–1494 (2001). [CrossRef]

] an explanation of how the rotation sense is derived by using the electro-optic modulator is also reported.

The possibility to detect the frequency shift due to the Sagnac effect by measuring only the spectral components of the voltage signal between the terminals of a SRL was demonstrated for the first time in [19

19. K. Taguchi, K. Fukushima, A. Ishitani, and M. Ikeda, “Optical inertial rotation sensor using semiconductor ring laser,” Electron. Lett. 34, 1775–1776 (1998). [CrossRef]

]. According to this approach, a SRL without any other optical component may serve as active integrated optical gyro. To verify this fascinating hypothesis, an experimental setup (shown in Fig. 3) consisting of an InGaAsPInP Fabry–Perot laser, a single-mode fiber, and the laser driving circuit was used. Different values of the loop diameter, i.e., 21.6, 24.8, and 27.2cm, were used in the experiments [20

20. K. Taguchi, K. Fukushima, A. Ishitani, and M. Ikeda, “Self-detection characteristics of the Sagnac frequency shift in a mechanically rotated semiconductor ring laser,” Measurement 27, 251–256 (2000). [CrossRef]

]. While keeping the laser injection current constant, the voltage between the laser terminals was measured through use of a capacitor, a broadband amplifier, and a spectrum analyzer. When a constant rotation rate is applied to the system, a peak in correspondence of the beat frequency appears in the spectrum of the voltage signal measured between the laser terminals. This gyroscopic system exhibits an experimentally measured lock-in limited minimum detectable angular rate of 100degh.

A PIC for rotation sensing based on two SRLs was proposed and fabricated in [21

21. M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically integrated twin ring diode lasers for rotation sensing applications,” J. Cryst. Growth 288, 144–147 (2006). [CrossRef]

]. The integrated device (see Fig. 4) includes
  • Two unidirectionally operating SRLs;
  • Two directional couplers with a reduced efficiency (1%), which extract the optical beams from the SRLs;
  • A Y-junction that combines CW and CCW waves;
  • Seven photodetectors (electrically isolated by deeply etched isolation trenches) used to monitor device performance.
Racetrack-shaped ring lasers (bending radius 1mm and straight sections of length 1mm) having a MQW and a quantum dot active region have been fabricated. Ring laser unidirectionality can be achieved by a forward biased (injection current 60mA) S-section waveguide connecting the two straight sections of the racetrack-shaped cavity. To tune resonant frequencies of the two SRLs, two heaters are placed along the inner sides of ring ridges. Frequency beating between optical signals generated by the two SRLs was experimentally observed in [22

22. H. Cao, A. L. Gray, G. A. Smolyakov, L. F. Lester, P. G. Eliseev, and M. Osinski, “Microwave frequency beating between integrated quantum-dot ring lasers,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CThGG1.

]. The spectrum of photocurrent generated by the photodiode at the output of the Y junction exhibits a peak at 12.2GHz (the peak linewidth is around 4MHz) resulting from the different wavelengths of the two optical signal entering the Y junction (these wavelengths can be finely tuned by two heaters).

The quantum limit of the proposed gyroscope has been estimated as equal to 270300degh by using experimentally measured performance parameters of the two SRLs as in [21

21. M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically integrated twin ring diode lasers for rotation sensing applications,” J. Cryst. Growth 288, 144–147 (2006). [CrossRef]

].

If the two lasers are not exactly identical it is quite difficult to distinguish between the frequency splitting due to rotation and that induced by laser differences. A comparison between the PICs for gyro applications proposed in [17

17. M. N. Armenise, V. M. N. Passaro, F. De Leonardis, and M. Armenise, “Modeling and design of a novel miniaturized integrated optical sensor for gyroscope applications,” J. Lightwave Technol. 19, 1476–1494 (2001). [CrossRef]

, 21

21. M. Osiński, H. Cao, C. Liu, and P. G. Eliseev, “Monolithically integrated twin ring diode lasers for rotation sensing applications,” J. Cryst. Growth 288, 144–147 (2006). [CrossRef]

] is reported in Table 2.

An innovative approach to realize a SRL for rotation sensing was proposed in [23

23. J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, “InGaAsP annular Bragg lasers: theory, applications, and modal properties,” IEEE J. Sel. Top. Quantum Electron. 11, 476–484 (2005). [CrossRef]

]. Bragg reflection instead of total internal reflection was used as the radial confinement mechanism, and a circular guiding defect was located within a medium that consists of annular Bragg layers. The resonator supports azimuthally propagating modes with energy concentrated within the defect region. The lasing structure, schematically shown in Fig. 5, was realized by InGaAsPInP technology, and the active layer includes six quantum wells. The radius of the guiding defect is around 5μm, and five internal and ten external Bragg layers were employed to confine generated optical power into the defect. The laser is pumped by optical pulses at 890nm and emits at 1559nm (emission direction is perpendicular to the substrate). Threshold power is around 0.7mW.

When the laser rotates, a very interesting dependence of both threshold optical power and gain on angular rate is observed [24

24. J. Scheuer, “Direct rotation-induced intensity modulation in circular Bragg micro-lasers,” Opt. Express 15, 15053–15059 (2007). [CrossRef] [PubMed]

]. This effect may allow rotation to be sensed by measuring only the optical power coming from the circular Bragg microlaser in the direction perpendicular to the substrate. To the best of our knowledge, no data about the minimum detectable angular rate of this device are available. Electrical pumping of this laser has not been achieved.

Typically it is difficult to measure angular rates less than 100degh by active integrated optical gyros because the SRL linewidth is about 40MHz. Moreover, complex and expensive techniques to avoid lock-in have to be employed in these sensors.

3. Passive Gyroscopes

In passive gyros, the optical source generating the beams used to measure the angular velocity is outside the sensing element consisting of either a ring interferometer or an optical cavity.

Fiber optic technology allows the fabrication of both phase and frequency-sensitive passive gyros. They are called interferometric and resonant FOGs, respectively. Interferometric FOGs are surely better performing than resonant FOGs, and, for this reason, all commercially available FOGs are phase sensitive.

Passive integrated optical gyros are frequency sensitive and based on an optical cavity excited by an external narrow-linewidth laser. Recently, phase-sensitive integrated optical rotation sensors based on slow-light structures have been proposed.

In passive frequency-sensitive gyros a power exchange between the two beams counterpropagating in the resonator can occur because of backscattering phenomena. It is well known that this effect can be avoided simply by phase modulating one of the two beams exciting the cavity [25

25. F. Zarinetchi and S. Ezekiel, “Observation of lock-in behavior in a passive resonator gyroscope,” Opt. Lett. 11, 401–403 (1986). [CrossRef] [PubMed]

, 26

26. R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. 8, 644–646 (1983). [CrossRef] [PubMed]

, 27

27. Y. Yi, K. Shi, W. Lu, and S. Jin, “Phase modulation spectroscopy using an all-fiber piezoelectric transducer modulator for a resonant fiber-optic gyroscope,” Appl. Opt. 34, 7383–7386 (1995). [CrossRef] [PubMed]

]. In this way the coupling of the two resonant modes within the optical cavity can be easily inhibited in passive frequency-sensitive angular velocity sensors. In this section recent achievements of FOG technology and passive integrated optical angular rate sensors are reviewed.

3.1. Recent Advances in Fiber Optic Gyro Technology

According to the Sagnac effect, rotation induces a phase difference Δφ between two counterpropagating optical signals traveling in a fiber coil. This phase difference is proportional to the angular rate Ω.

In the interferometric FOG, an optical signal from a light source is divided into two different beams by a beam splitter, which are then launched into the two ends of a multiple-turn fiber coil. The counterpropagating signals emerging from the two fiber ends are combined by the beam splitter, and the optical signal resulting from the interference is sent to the photodetector. The relationship between the phase difference Δφ and the angular rate Ω is given by
Δφ=8π2R2cλkΩ=4πLRcλΩ=SΩ,
(4)
where S is the scale factor, λ is the sensor operating wavelength, R is the fiber coil radius, k is the number of coil turns, and L is the total fiber length.

The optical signal at the photodetector input is the result of the interference between the two counterpropagating waves. The time-dependent power (Ppd) of the signal entering the photodetector is given by the following expression:
Ppd(t)=Pin2{1+cos[Δϕ(t)]},
(5)
where Pin is the optical power of the input signal and Δϕ(t) is the time-dependent phase shift between the two interfering signals. If Δϕ(t)=Δφ, the FOG has really low sensitivity to reduced angular rate values. The maximum sensitivity of the output photocurrent with respect to angular rate variation is obtained when Δϕ(t) is close to ±π2. By applying a phase modulation to CW and CCW signals it is possible to keep the gyro operating point where the sensitivity to rotation is maximum, i.e., where the interference plot shows maximum slope.

The FOG open-loop configuration, in which the phase modulator is not included in the feedback loop, exhibits a lack of linearity for large Ω values (>36,000degh), mainly because of the laser source fluctuations and operation characteristics of system components. Since a good scale factor linearity over the whole dynamic range has to be ensured in high-performance FOGs, the open-loop configuration is not used when high performance is required.

In Fig. 6 the closed-loop configuration of the FOG is illustrated [28

28. J. L. Davis and S. Ezekiel, “Closed-loop, low-noise fiber-optic rotation sensor,” Opt. Lett. 6, 505–507 (1982). [CrossRef]

]. The FOG includes a feedback loop connecting the photodetector and the phase modulator. The role of this feedback loop is to generate a feedback phase shift that is opposite to the rotation-induced phase shift.

The FOG’s measurement capability is limited by the presence of the possible nonreciprocal effects in the fiber coil due to the Kerr-like nonlinearity of silica, the time-varying temperature gradient along the fiber coil (Shupe effect), and vibration of the fiber coil.

Rayleigh scattering is a typical loss effect in all optical fibers. It is due to local microscopic fluctuations in silica density. This kind of scattering phenomenon is elastic in the sense that scattered light has the same frequency as incoming light. Since a fraction of scattered power propagates in the backward direction, Rayleigh scattering may produce a power exchange between CW and CCW beams, which obviously may degrade the gyro’s performance [29

29. C. C. Cutler, S. A. Newton, and H. J. Shaw, “Limitation of rotating sensing by scattering,” Opt. Lett. 5, 488–490 (1980). [CrossRef] [PubMed]

]. Because of the elastic feature of Rayleigh scattering, the noise contribution due to it can be effectively reduced by using a broadband light source.

Finally, if standard single-mode telecommunication fibers are utilized, polarization instabilities in CW and CCW beams occur, which degrade FOG performance. The use of polarization-maintaining fibers allows us to solve this problem but at the expenses of a cost increase.

Polarization-maintaining single-mode fiber enables us to achieve better accuracy with than with standard single-mode fiber, and so it is always used in high-performance FOGs. The use of single-mode air-core photonic bandgap fibers to replace conventional fibers in FOGs was recently proposed [30

30. H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Air-core photonic-bandgap fiber-optic gyroscope,” J. Lightwave Technol. 24, 3169–3174 (2006). [CrossRef]

, 31

31. S. Blin, H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Reduced thermal sensitivity of a fiber-optic gyroscope using an air-core photonic-bandgap fiber,” J. Lightwave Technol. 25, 861–865 (2007). [CrossRef]

]. Because in air-core photonic bandgap fibers most of the optical power is confined in air, Kerr and Shupe effects are significantly reduced. This is because the refractive index of air is less sensitive to temperature and optical power than the refractive index of silica.

In FOGs, the broadband (emission spectrum width around 3050nm) light sources are always utilized to strongly reduce effects of Rayleigh backscattering and Kerr effect on accuracy. Then superluminescent diodes (emitting around 0.8μm) or sources based on amplified spontaneous emission in erbium-doped fibers (emitting around 1.55μm) [32

32. P. F. Wysocki, M. J. F. Digonnet, B. Y. Kim, and H. J. Shaw, “Characteristics of erbium-doped superfluorescent fiber sources for interferometric sensor applications,” J. Lightwave Technol. 12, 550–567 (1994). [CrossRef]

] are typically used. In high-performance FOGs, broadband sources based on erbium-doped fibers are preferred especially because of their higher stability with respect to temperature changes.

The phase shifts between CW and CCW beams induced by time-varying temperature gradients, vibrations, polarizations instabilities, Rayleigh backscattering, and the Kerr effect represent noise sources that limit the FOG minimum detectable angular rate. Currently, FOG development and optimization is focused on the reduction of all the noise sources below photodetector shot noise, so that the FOG can operate in a shot-noise-limited mode. In this case the minimum detectable angular rate can be estimated by following expression [33

33. R. A. Bergh, H. C. Lefèvre, and H. J. Shaw, “An overview of fiber-optic gyroscopes,” J. Lightwave Technol. LT-2, 91–107 (1984). [CrossRef]

]:
δΩ=c4RLBhcληPpd×3600×180π(degh),
(6)
where Ppd is the optical power at the input of the photodetector, η is the photodetector quantum efficiency, B is the sensor bandwidth, and h is Planck’s constant. From Eq. (6), we observe that the minimum detectable angular rate is inversely proportional to the product RLPpd; so this product needs to be increased to enhance gyro sensitivity.

For a FOG having a bandwidth of 20Hz and operating at 1.55μm, δΩ dependence on the product R×L and Ppd has been plotted in Fig. 7. In the contour plot, level curves corresponding to δΩ values of 0.02, 0.03, 0.04, 0.05, and 0.08degh are shown. A Ppd increase enhances gyro sensitivity, but values that are too large may increase the sensor inaccuracy owing to the Kerr effect. The minimum detectable angular rate monotonically increases when the R×L product is increased. The typical value of R is around 510cm, whereas L, usually of the order of kilometers, depends on the required FOG sensitivity. For example, if R=5cm and Ppd=0.3mW, the minimum detectable angular rate ranges from 0.06 to 0.015degh when L increases from 1 to 4km.

High-performance FOGs fabricated in recent years include (see Fig. 8) [34

34. T. Buret, D. Ramecourt, J. Honthaas, Y. Paturel, E. Willemenot, and T. Gaiffe, “Fibre optic gyroscopes for space application,” in Optical Fiber Sensors, OSA Technical Digest (Optical Society of America, 2006) paper MC4.

]
  • A broadband light source based on amplified spontaneous emission in an erbium-doped fiber;
  • A power control loop serving to adjust optical power of the signal generated by the light source;
  • Two fiber couplers;
  • A multifunction integrated optic chip
  • A fiber coil composed of a polarization maintaining single-mode fiber;
  • A photodetector;
  • An analog-to-digital converter (ADC), an application-specific integrated circuit (ASIC), and a digital-to-analog converter (DAC), forming the feedback loop generating the modulating signal.
The broadband light source includes a pump laser diode operating at 980nm, two fiber Bragg grating reflecting the pump signal and the generated signal (centered around 1550nm), an erbium doped fiber, and an isolator. The power control loop is realized by a photodetector (PD) and an electronic circuit providing the injection current to the pump laser diode. The LiNbO3 integrated optical chip includes a polarizing waveguide, a Y-junction coupler, and a phase modulator.

By the first fiber coupler, a small fraction (1%–5%) of the optical signal generated by the light source is sent to the power control loop, whereas the remaining part is directed toward the integrated optical circuit, which splits the incoming beam into two signals. After the modulation and propagation in the fiber coil, CW and CCW beams come back in the integrated optical circuit, where they are combined. The signal resulting from the interference between CW and CCW beams is sent to the photodetector. By using the electrical signal generated by this photodetector, the feedback loop generates the modulating signal and the sensor output.

The performance achieved by commercially available FOGs in recent years is very high, e.g., bias stability less than 0.0003degh and an angle random walk ARW<8×105degh [35

35. S. Divakaruni and S. Sanders, “Fiber optic gyros: a compelling choice for high precision applications,” in Optical Fiber Sensors, OSA Technical Digest (Optical Society of America, 2006), paper MC2.

]. However, the problem of the FOG’s higher sensitivity to external perturbation with respect to that of the He–Ne RLG has not been solved at the moment. The dominion of the He–Ne RLG in the high-performance gyro market is essentially due to this FOG drawback and to the simpler read-out electronics required by the RLG.

Currently, high-performance FOGs use polarization-maintaining fibers, so a very attractive research target for FOG development may be the realization of a high-performance gyro employing standard telecom fibers. This might allow significant FOG cost reduction.

3.2. Low-Loss Technologies for Integrated Optical Gyros

Passive integrated optical gyros typically employ a large-radius ring resonator having a high quality factor (Q) as the sensing element. The product between the resonator quality factor and the ring diameter (d) strongly influences the sensitivity and the ARW of a passive angular rate sensor. These two performance parameters are given by [36

36. S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” App. Phys. Lett. 30, 478–480 (1977). [CrossRef]

]
δΩ=1dQPpd2Bhc3λη×(3600×180π)(degh),
(7)
ARW=1dQPpd2hc3λη×(60×180π)(degh),
(8)
where Ppd is the optical power at the input of the photodetector included in the read-out system, η is the photodetector efficiency, B is the measurement bandwidth, λ is the sensor operating wavelength, c is the speed of light in vacuum, and h is Planck’s constant.

To achieve a minimum detectable angular rate less than 10degh, typically d and Q have to be larger than 10mm and 106, respectively. The Q factor of a ring resonator is defined as the ratio between the resonance wavelength and the resonance spectral width (usually designated the full width at half-maximum, FWHM) and it can be enhanced by decreasing loss experienced by the resonant mode within the optical cavity and by increasing the ring diameter [37

37. C. Ciminelli, C. E. Campanella, and M. N. Armenise, “Optical angular velocity sensor based on the optimized design of a waveguide ring resonator,” presented at Future in Light, Metz, France, March 26–27, 2009.

].

Silica-on-silicon technology allows very low-loss (<0.1dBcm) optical waveguides operating at 1.55μm to be fabricated. These waveguides can be realized through a combination of flame hydrolysis deposition and reactive ion etching. Propagation loss in these waveguides strongly depends on the index contrast Δ between the guiding and the cladding layer. A propagation loss around 0.010.03dBcm has been achieved for Δ<1%. The bending loss suffered by these waveguides exponentially decreases on increasing the curvature radius. To achieve negligible bending loss, a curvature radius larger than a few millimeters is required.

Some ring resonators having a very large quality factor have been fabricated by silica-on-silicon technology. The largest experimentally measured quality factor has been obtained by a resonator operating at 1.55μm and employing a waveguide with a 5μm×5μm square core region realized depositing a phosphorus doped SiO2 core layer and a boron and phosphorus doped glass top cladding layer on thermally grown silicon oxide. The waveguide index contrast may be less than 1%, and an estimated propagation loss is of the order of 0.01dBcm. This ring cavity has a radius of 30mm and exhibits a quality factor equal to 2.3×107 [38

38. R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994). [CrossRef]

].

To further enhance the quality factor of resonators in silica-on-silicon technology, the integration of two semiconductor optical amplifiers (SOAs) within a silica-on-silicon ring resonator has been proposed [39

39. C. Ciminelli, F. Peluso, and M. N. Armenise, “A new integrated optical angular velocity sensor,” Proc. SPIE 5728, 93–100 (2005). [CrossRef]

, 40

40. C. Ciminelli, “Innovative photonic technologies for gyroscope systems,” presented at EOS Topical Meeting—Photonic Devices in Space, Paris, Oct. 18–19, 2006.

, 41

41. C. Ciminelli, F. Peluso, E. Armandillo, and M. N. Armenise, “Modeling of a new integrated optical angular velocity sensor,” presented at Optronics Symposium (OPTRO), Paris, May 8–12, 2005.

, 42

42. C. Ciminelli, F. Peluso, N. Catalano, B. Bandini, E. Armandillo, and M. N. Armenise, “Integrated optical gyroscope using a passive ring resonator,” presented at ESA Workshop, Noordwijk, The Netherlands, Oct. 3–5, 2005.

] (see Fig. 9). The SOAs compensate for optical loss suffered by the resonant mode, and so a very high quality factor could be expected. In compensated ring resonators, the amplified spontaneous emission noise generated by the SOAs imposes the ultimate limit on the sensor resolution. For a ring radius equal to 10mm and a coupling efficiency between the straight waveguides and the ring resonator equal to 0.1%, a quality factor equal to 2.9×108 has been calculated. This value, obtained by neglecting the effect of amplified spontaneous emission noise, is more than 1 order of magnitude larger than that obtained by the uncompensated silica-on-silicon resonator reported in [38

38. R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994). [CrossRef]

], which has a ring radius three times larger than that of the compensated ring. Taking into account, also, the effect of amplified spontaneous emission noise, a minimum detectable rotation rate as low as 10degh has been calculated for using a compensated spiral resonator having a total length of about 40cm as building-block in a passive integrated optical gyroscope [43

43. European Space Agency (ESA), IOLG project 1678/02/NL/PA, Final Report, Dec. 2008.

]. Parameters of the amplifier assumed in the numerical estimation of gyro resolution are those typical of a commercial C-band SOA for telecom applications.

The SOAs, realized by types III–V semiconductor technology, cannot be monolithically integrated into the ring, and this may produce some problems in the power transfer between the ring and the amplifiers and may generate backreflections at the interfaces between the silica ring and the SOAs.

Effects of the interaction between two counterpropagating waves having the same frequency in a silica-on-silicon ring resonator, to be exploited as sensing element in a gyro, were investigated in depth in [44

44. C. Ciminelli, C. E. Campanella, and M. N. Armenise, “Design of passive ring resonators to be used for sensing applications,” J. Eur. Opt. Soc. 4, 09034 (2009). [CrossRef]

, 45

45. C. Ciminelli, C. E. Campanella, and M. N. Armenise, “Optimized design of integrated optical angular velocity sensors based on a passive ring resonator,” J. Lightwave Technol. 27, 2658–2666 (2009). [CrossRef]

]. The passive ring was assumed to be evanescently coupled to two straight bus waveguides. Because of the superposition of the two single beams, the counterpropagating traveling waves generate a resonant standing wave that couples with the two bus waveguides. If the two input beams have the same amplitude, the generated wave has an amplitude double that of each traveling wave mode. While in the well-known single-beam case (traveling wave case) the coupler holds the spatial directionality, in the resonant standing wave case the coupler loses this directionality, and an evanescent standing mode is created in the coupling region. This mode, in turn, generates two counterpropagating traveling waves in each bus waveguide.

The developed model suggests a very attractive strategy to improve the sensitivity of passive integrated optical gyros including a ring resonator excited by two simultaneously propagating signals. By using a silica-on-silicon ring with a perimeter of 14.4cm, the optimized design of the gyro provides a numerically predicted resolution enhancement to values as low as a few degrees per hour.

A PIC properly designed to sense rotation by an integrated ring resonator was reported in [46

46. K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18, 66–72 (2000). [CrossRef]

]. The PIC was realized through silica-on-silicon technology to achieve very low propagation loss (around 0.01dBcm). The passive integrated gyro includes (see Fig. 10)
  • A 14.8cm long integrated ring resonator,
  • Two straight bus waveguides,
  • An integrated phase modulator based on the thermo-optic effect used to limit power transfer between CW and CCW beams in the ring,
  • Integrated switches based on Mach–Zehnder interferometers employed to alternatively lock the laser frequency to CW and CCW resonance frequencies.
This is not a fully integrated sensor because the laser source (a tunable distributed feedback laser), the photodetectors, and the read-out electronic circuitry are out of chip. The gyro operates at 1.55μm, and its shot-noise-limited theoretical resolution is 10degh. The experimentally measured resolution is about 14×105degh(=40degs).

More recently another PIC for rotation sensing including a ring resonator having a radius of 9.5mm, three couplers, and only one bus waveguide was realized through silica-on-silicon technology [47

47. H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45, 080506 (2006). [CrossRef]

]. The employed guiding structure exhibits very low loss, and so the resonator quality factor is quite large (3.12×106). The sensor minimum detectable angular rate has been theoretically estimated as about 15degh. This value is quite large with respect to that exhibited by the gyroscope reported in [46

46. K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18, 66–72 (2000). [CrossRef]

]. The entire read-out system, including a fiber laser, two phase modulators, two acousto-optic frequency shifters, two polarization controllers, two photodetectors, and two lock-in amplifiers, is out of chip. To enhance the gyroscope’s sensitivity, a multiple-turn ring resonator in silica-on-silicon technology with total length as great as 77cm has been proposed [48

48. H. Ma, S. Wang, and Z. Jin, “Silica waveguide ring resonators with multi-turn structure,” Opt. Commun. 281, 2509–2512 (2008). [CrossRef]

]. The optical cavity includes a number of crossed waveguides that have been investigated in depth, demonstrating that optimum the intersection angle is close 90°. A minimum detectable angular rate in the range 0.11degh was theoretically predicted for a passive gyro including this multiple-turn resonator. A spiral passive resonator based on a silica-on-silicon waveguide to be used as key element of an integrated optical gyroscope was investigated in [49

49. C. Ciminelli, C. E. Campanella, F. Dell’Olio, V. M. N. Passaro, and M. N. Armenise, “A novel passive ring resonator gyroscope,” presented at 2009 DGaO/SIOF Joint Meeting, Brescia, Italy, June2–5, 2009.

]. A resolution in the range 10100degh can be achieved by using a silica-on-silicon waveguide with propagation loss equal to 0.1dBcm. We have calculated a resolution value in the range 110degh with a propagation loss of 0.01dBcm.

A high-quality-factor LiNbO3 integrated optical circular ring resonator designed for optical angular rate sensing was reported in [52

52. C. Vannahme, H. Suche, S. Reza, R. Ricken, V. Quiring, and W. Sohler, “Integrated optical Ti:LiNbO3 ring resonator for rotation rate sensing,” in European Conference on Integrated Optics (ECIO), 2007, paper WE1.

]. The resonator, which exhibits a radius of 30mm and a quality factor of 2.4×106, was fabricated in a Z-cut LiNbO3 substrate by thermal indiffusion (1060°C) of 7μm wide, 100nm thick Ti stripes. The optical loss within the resonator was estimated as around 0.03dBcm.

The adoption of this ring resonator for rotation sensing has been investigated by the experimental setup shown in Fig. 11. Two optical signal are launched (simultaneously or not) into the bus waveguide ends, and spectral responses at the two through ports are measured. In the case of simultaneous excitation, two circulators are employed to use each bus waveguide end as input and output port. The theoretical minimum detectable angular rate is around 7degh.

Using silver ion exchange in a commercially available silicate glass (Schott IOG-10), a circular ring resonator operating at 1.55μm and having a radius of 8mm was designed and realized in [53

53. G. Li, K. A. Winick, B. R. Youmans, and E. A. J. Vikjaer, “Design, fabrication and characterization of an integrated optic passive resonator for optical gyroscopes,” presented at Institute of Navigation’s 60th Annual Meeting, Dayton, Ohio, 2004.

] to be employed in a passive integrated optical gyro. The fabrication process includes electron-beam evaporation used to deposit a 150nm thick layer of titanium onto the glass substrate, conventional photolithography used to pattern the titanium with 2μm wide channel openings, ion exchange performed in a mixed melt of silver nitrate and sodium nitrate, and the final thermal annealing. Propagation loss within the resonator is around 0.1dBcm, and the quality factor has been calculated as 2×106.

Recently a hybrid PIC for rotation sensing realized by sputtering deposition of glass and reactive ion etching was developed [54

54. A. Duwel and N. Barbour, “MEMS development at Draper Laboratory,” presented at SEM Annual Conference, Charlotte, N.C., June 2–4,2003.

]. The system includes a ring resonator and a tunable optically pumped laser realized by doping glass with rare earths. At the best of our knowledge, no data about gyro performance are available.

To achieve Q values larger than 107 by a ring resonator realized by ion exchange in glass, propagation loss compensation by the optical gain induced by a pump signal is required. In [55

55. H. Hsiao and K. A. Winick, “Planar glass waveguide ring resonators with gain,” Opt. Express 15, 17783–17797 (2007). [CrossRef] [PubMed]

] a compensated resonator realized by using a neodymium doped-silicate glass as substrate has been reported. The fabricated racetrack-shaped resonator operates at 1.02μm and has a total length of 56.07mm. The pump signal, having a power of 150mW, is provided by a laser diode operating at 0.83μm. The device architecture includes two bus waveguides, one for the signal (used to excite the resonator and to measure resonator spectral response) and the other for the pump signal (see Fig. 12). The waveguide was realized in a glass substrate doped with 2 wt. % Nd2O3 by ion-exchange performed in a mixed melt of silver nitrate and sodium nitrate. The compensation of propagation loss allows one to obtain a very large finesse and quality factor (F=250, Q=1.89×107). As discussed in [55

55. H. Hsiao and K. A. Winick, “Planar glass waveguide ring resonators with gain,” Opt. Express 15, 17783–17797 (2007). [CrossRef] [PubMed]

], the latter parameter is ultimately limited by spontaneous emission noise generated by the gain medium.

3.3. InP-Based Photonic Integrated Circuit for Angular Rate Sensing

As discussed in [57

57. C. Ciminelli, F. Dell’Olio, V. M. N. Passaro, and M. N. Armenise, “Low-loss InP-based ring resonators for integrated optical gyroscopes,” presented at Caneus 2009 Workshop, NASA Ames Research Center, Moffett Field, Calif., March 1–6, 2009.

], InP-based PIC technology can also be effectively exploited to realize a compact and reliable passive optical gyro having the architecture shown in Fig. 13. The sensor includes a large-radius ring resonator serving as sensing element, a tunable laser source having a linewidth in the range 15MHz, some optical components processing the beams that excite the sensing element, and the read-out optoelectronic circuit.

As previously pointed out, loss within the ring resonator has to be minimized to enhance the gyro sensitivity. Loss experienced by an optical mode propagating in a curved InP-based waveguide is due to interband absorption, free-carrier absorption, bending loss, and scattering loss. All of these loss sources, except for scattering loss, can be made negligible by appropriately choosing the materials forming the waveguide and the bending radius. Scattering loss due to sidewall roughness can be minimized by optimizing geometrical and physical parameters of the waveguide. An efficient and accurate three-dimensional algorithm for estimating scattering loss suffered from curved waveguides was reported and validated in [58

58. C. Ciminelli, V. M. N. Passaro, F. Dell’Olio, and M. N. Armenise, “Three-dimensional modelling of scattering loss in InGaAsPInP and silica-on-silicon bent waveguides,” J. Eur. Opt. Soc. Rapid Publ. 4, 09015 (2009). [CrossRef]

]. This modeling technique, based on the volume current method, has been used to investigate scattering loss dependence on both width of the waveguide and index contrast. An optimized InP-based buried waveguide exhibiting a propagation loss equal to 0.3dBcm has been designed.

The Q factor of the resonator exploiting the optimized waveguide has been calculated as depending on the ring diameter d, assuming that only one input–output straight bus waveguide is evanescently coupled to the ring resonator and that the optical cavity is excited by the quasi-TE mode. Considered d values are quite large (>10mm) because it is necessary to keep the d value of the order of centimeters to achieve a sensitivity value less than 10degh. The Q factor of the InGaAsPInP buried ring resonator employing the optimized waveguide slowly increases as d increases. A d increase of five times induces a Q increase of less than 7%. The waveguide optimization makes it possible to reach Q values around 1.5×106 for d=4cm.

Performance of the passive integrated optical gyro exploiting the optimized InP-based resonator as sensing element has been theoretically estimated as dependent on the ring diameter and the optical power at the photodetectors included in the readout system. For Ppd=3mW and d=4cm, a gyro resolution of 10degh, a bias drift lower than 0.3degh, and an angle random walk equal to 0.05degh have been predicted [57

57. C. Ciminelli, F. Dell’Olio, V. M. N. Passaro, and M. N. Armenise, “Low-loss InP-based ring resonators for integrated optical gyroscopes,” presented at Caneus 2009 Workshop, NASA Ames Research Center, Moffett Field, Calif., March 1–6, 2009.

]. These encouraging theoretical results make the possibility of developing a quite compact InP-based PIC for angular rate sensing very attractive.

3.4. Slow-Light Structures for Angular Velocity Sensing

Integrated optical ring resonators have been widely employed to slow light by decreasing its group velocity. Two structures have been used for this purpose: the coupled-resonator optical waveguide (CROW) [59

59. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999). [CrossRef]

] and the side-coupled integrated spaced-sequence of resonators (SCISSOR) [60

60. J. E. Heebner, R. W. Boyd, and Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002). [CrossRef]

, 61

61. J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics,” J. Opt. Soc. Am. B 21, 1818–1832 (2004). [CrossRef]

]. CROW consists of a chain of resonators where light propagates because of the coupling between adjacent resonators. SCISSOR consists of a sequence of resonators evanescently coupled to a bus waveguide. The resonators are sufficiently close to the bus waveguide to achieve evanescent coupling, but they are spaced far enough from one another that resonator-to-resonator coupling can be considered negligible.

According to the Sagnac effect, if two optical beams counterpropagate along a closed loop, a phase shift between the beams is induced by rotation. Measuring this phase shift allows the angular rate of the structure including the closed loop to be estimated. Rotation-induced phase shift is proportional to the ratio between the group index and the effective index of light in the guiding structure in which the propagation take place. The phase shift induced by rotation is enhanced if the two beams counterpropagate in a closed loop realized by a CROW or a SCISSOR because the group index of light propagating in these structures may be significantly large [62

62. C. Peng, Z. Li, and A. Xu, “Rotating sensing based on slow light coupled resonator structure with EIT-like property,” Proc. SPIE 6722, 67222F (2007). [CrossRef]

, 63

63. C. Peng, Z. Li, and A. Xu, “Rotation sensing based on a slow-light resonating structure with high group dispersion,” Appl. Opt. 46, 4125–4131 (2007). [CrossRef] [PubMed]

, 64

64. U. Leonhardt and P. Piwnicki, “Ultrahigh sensitivity of slow-light gyroscope,” Phys. Rev. A 62, 055801 (2000). [CrossRef]

].

3.4a. CROW-Based Gyros

In [65

65. J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. 96, 053901 (2006). [CrossRef] [PubMed]

] a phase-sensitive CROW-based passive integrated optical gyro was theoretically proposed (the device architecture is shown in Fig. 14). A laser-generated optical beam is split into two signals by a 3dB power divider based on a directional coupler. The so obtained signals are launched into the ends of a CROW, which is wrapped around itself. During the propagation in the CROW, the two signals acquire an identical phase shift if the gyro is at rest. When the gyro rotates, this phase shift is different for the two signals propagating in CW and CCW directions; so they are not in phase after propagation in the CROW. Signals coming from the CROW (exhibiting a rotation induced phase shift Δφ) interfere at the directional coupler. The power of optical signals coming from the two coupler ports depends on Δφ according to the following equations:
Pout,1=Pincos2(Δφ2),Pout,2=Pinsin2(Δφ2),
(9)
where Pin is the power of the light source.

Measuring the power at the output of the two coupler branches, it is possible to estimate Δφ and then the rotation rate. In a CROW including nine rings having a radius of 25μm, an angular rate of 1degh induces a 4% change in Pout,2. Unfortunately, to achieve this performance, the quality factor of each ring resonator has to be around 107. This high a quality factor value has been achieved only by large-radius silica-on-silicon ring resonators and not by microrings realized, for example, in silicon-on-insulator technology. A decrease in the ring quality factor to values around 104105 significantly degrades the sensor sensitivity.

As proved in [66

66. M. A. Terrel, M. J. F. Digonnet, and S. Fan, “Coupled resonator optical waveguide sensors: sensitivity and the role of slow light,” Proc. SPIE 7316, 73160I (2009). [CrossRef]

], decreasing the coupling coefficient between the rings increases the total length of the gyro, and then its sensitivity improves to values comparable with those of a conventional FOG.

A quite similar integrated optic rotation sensor was proposed in [67

67. Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372, 5848–5852 (2008). [CrossRef]

]. In this device, also, the phase shift between two counterpropagating beams is measured to sense rotation. The integrated passive gyroscope includes (see Fig. 15) a directional coupler, a U-shaped curved waveguide, and a ring-in-ring optical resonator including two coupled rings having a different radii (the smallest ring is realized within the largest one to minimized the occupied area). An optical signal is lunched into one of the two ends of the coupler, which acts as 3dB power divider. The beams coming from the coupler are coupled within the ring-in-ring resonator. After propagation in the cavity, CW and CCW beams propagate along the U-shaped waveguide and then come back into the coupler. If the sensor is rotating, the beams coming into the coupler are not in phase (their phase shift is Δφ), and the powers of beams coming from the two branches of the coupler are given by Eq. (9). The phase shift Δφ is equal to
Δφ=ngneff×8π2R12cλΩ,
(10)
where ng is the group index of light in the ring-in-ring resonator and neff is the effective index of the optical signals propagating in the sensor, λ is the device’s operating wavelength, and R1 is the radius of the largest ring.

The gyro scale factor is the product of the typical scale factor of a phase-sensitive gyroscope (such as the FOG) and the ratio ngneff. This ratio can be written as
ngneff=Tϕϕ1,
(11)
where
ϕ1=β1(2πR1)
(12)
with β1 the propagation constant within the largest resonator. Tϕ is the phase shift induced in the incoming signal by the ring-in-ring resonator. It is defined as
Tϕ=arg[EinEout],
(13)
where Ein and Eout are the complex amplitudes of signals at the two ports of the ring-in-ring resonator (as indicated in the inset of Fig. 15). The Tϕ dependence on ϕ1 exhibits the maximum slope at the resonance wavelength of the largest ring. Then the ratio ngneff can be maximized if the sensor’s operating wavelength corresponds exactly to this resonance wavelength.

For the sensor proposed in [67

67. Y. Zhang, N. Wang, H. Tian, H. Wang, W. Qiu, J. Wang, and P. Yuan, “A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency,” Phys. Lett. A 372, 5848–5852 (2008). [CrossRef]

] having R1=16.4cm and the radius of the smallest resonator equal to R12, the ratio ngneff is about 50 if λ=1.55 (the operating wavelength corresponds to the resonance wavelength of the largest resonator). Rotation-induced phase shift is quite modest in this structure. For example, a rotation of 10degh induces a phase shift of 4.6×107rad in the sensor. In the architecture shown in Fig. 15, the ring-in-ring resonator may be replaced by the CROW structure including a certain number of identical coupled rings proposed in [68

68. C. Peng, Z. Li, and A. Xu, “Optical gyroscope based on a coupled resonator with the all-optical analogous property of electromagnetically induced transparency,” Opt. Express 15, 3864–3875 (2007). [CrossRef] [PubMed]

].

The effect of rotation on the spectral response of a CROW including a large number of coupled integrated optical resonators was investigated in [69

69. B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B 24, 1216–1224 (2007). [CrossRef]

] (see Fig. 16). Each resonator forming the CROW supports two resonant modes (CW and CCW) resonating at the same frequency if the CROW is at rest. The CW resonant mode in even-numbered resonators couples to the CCW resonant mode in odd-numbered resonators. When the CROW rotates, the frequencies of the two resonant modes in each resonator become different as a result of the Sagnac effect, and a periodic alternation of resonant mode frequencies is induced in the structure. Reciprocal and nonreciprocal effects are not clearly described in [69

69. B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B 24, 1216–1224 (2007). [CrossRef]

].

The spectral response at the drop port of a CROW that is at rest exhibits a periodic sequence of transmission bands and forbidden bands (numerically calculated responses of two CROWs including 11 and 17 rings are shown in Fig. 17). Rotation of the structure induces further forbidden bands in the CROW response. The width and the dip of these additional forbidden bands are directly proportional to the CROW angular rate. The scale factor relating the width of rotation-induced forbidden bands and the angular rate (in radians per second) is equal to 67.5 for a CROW including 29 ring resonators having a radius of 25μm and made of a material having a refractive index of 1.5 (the coupling coefficient between two adjacent cavities is equal to 1%) [69

69. B. Z. Steinberg, J. Scheuer, and A. Boag, “Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: optical gyroscopes with exponential sensitivity,” J. Opt. Soc. Am. B 24, 1216–1224 (2007). [CrossRef]

]. To observe the presence of the rotation-induced forbidden band a very large angular velocity is required. For example, in the device including 29 rings, a rotation rate of about 108rads (=2×1013degh) is required in order to begin to observe the presence of the rotation-induced forbidden band.

3.4b. SCISSOR-Based Gyros

A phase-sensitive passive integrated gyro based on a SCISSOR structure was theoretically proposed in [70

70. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004). [CrossRef]

] (see Fig. 18). The sensor includes a circular waveguide coupled to a quite large number of high-Q microresonators. The two beams counterpropagating in the circular waveguide acquire a rotation-induced phase shift. This phase shift is enhanced by the reduced group velocity of light in its circular path within the sensor. No data about the device’s performance are provided in [70

70. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004). [CrossRef]

].

3.5. Photonic-Crystal-Based Gyros

Photonic crystals (PhCs) are ordered structures in which two media with different refractive indices are arranged in a periodic form (the periodicity is of the order of hundreds of nanometers). These submicrometer structures can be designed so that frequency bands within which the optical propagation is inhibited for all propagation directions are induced [71

71. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals-Molding the Flow of Light (Princeton Univ. Press, 1995).

]. Depending on the spatial periodicity dimensionality of the structure, we distinguish one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) PhCs.

A very attractive structure for PhCs fabrication is a thin semiconductor slab waveguide perforated with a 2D periodic lattice of air holes. In this structure light confinement in the vertical direction is obtained by total internal reflection, and in-plane light confinement is due to the 2D lattice of holes [72

72. F. Krauss, R. M. de la Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996). [CrossRef]

]. By introducing a single point defect in this structure (by modifying the radius of one hole or eliminating one hole), a high-Q optical microcavity can be realized [73

73. M. Lončar and A. Scherer, “Microfabricated optical cavities and photonic crystals,” in Optical Microcavities, E. Vahala ed. (World Scientific, 2004).

]. For example, by creating a hexagonal 2D array of air holes (hole radius equal to 140nm and lattice constant equal to 475nm) in a thin InGaAsP slab waveguide and removing one hole, an optical cavity resonating at 1.5548μm was demonstrated in [74

74. O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999). [CrossRef]

]. The cavity supports two TE-polarized degenerate modes having the same resonance frequency and two different spatial distributions of the electromagnetic field. The quality factor of the degenerate resonant modes was estimated as about 2×105.

Very recently, it was numerically predicted that in a PhC microcavity supporting two degenerate resonance modes a symmetrical splitting of the degenerate resonance frequency ν0 into two distinct resonance frequencies ν0±Δν2 is induced by rotation [75

75. B. Z. Steinberg and A. Boag, “Splitting of microcavity degenerate modes in rotating photonic crystals-the miniature optical gyroscopes,” J. Opt. Soc. Am. B 24, 142–151 (2007). [CrossRef]

], where Δν is proportional to the angular rate of the PhC cavity. Δν was estimated numerically and analytically for the PhC microcavity reported in [74

74. O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999). [CrossRef]

], yielding that, in this case, the scale factor relating Δν and angular rate Ω (in radians per second) is 1.6×102. This very reduced value of the scale factor calls for further investigation with regard to the PhC microcavity’s practical employment for sense rotation.

Some improvement was achieved in [76

76. A. Shamir and B. Z. Steinberg, “On the electrodynamics of rotating crystals, micro-cavities, and slow-light structures: from asymptotic theories to exact Green’s function based solutions,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA 09) (IEEE, 2007), pp. 45–48.

]. In fact, for 12 coupled microcavities, a scale factor less than 3 was numerically calculated. However, this value is still very far from the typical scale factor values of passive integrated optical gyros.

4. Performance Comparison with Other Solid-State Technologies

Solid-state vibratory gyroscopes based on the Coriolis effect have been investigated in recent years, and they could represent a competing technology for photonic gyros.

The HRG (hemispherical resonant gyroscope) is a high-performance vibratory gyro including a high-Q-factor mechanical resonator (Q107), a forcer that induces and sustains a standing wave in the resonator, and a pick-off that senses (by some electrodes) the position of nodes and antinodes in the standing wave [1

1. D. Titterton and J. Weston, Strapdown Inertial Navigation Technology (Institution of Electrical Engineers, 2004). [CrossRef]

]. The device is in quartz, and it exploits an electrostatic charge between metal-coated surfaces of the resonator to produce the standing wave and to sense the shift in its vibration pattern. This gyro has an ARW of 0.001degh, δΩ=0.1degh, and a bias stability of 0.01degh. This performance is quite better than that achievable by the He–Ne RLG. The HRG is more expensive, heavier, and larger than the RLG.

In the past decade, an intense research effort has been spent to achieve better performance by a MEMS gyro. For example, the European Space Agency funded the development (started in 2005) of a European silicon MEMS rate sensor. The project objective is the realization of a low-cost gyro for space application having an ARW<0.2degh and a bias stability of about 510degh. The sensor prototype is close to the target specifications, exhibiting a bias stability in the range of 1020degh and an ARW equal to 0.04degh [78

78. R. Durrant, H. Crowle, J. Robertson, and S. Dussy, “SIREUS—status of the European MEMS rate sensor,” presented at 7th International ESA Conference on Guidance, Navigation & Control Systems, Tralee, Ireland, June 2–5, 2008.

]. Recently a prototype of a tuning fork MEMS gyroscope fabricated on a silicon-on-insulator substrate having ARW=0.003degh and a bias stability of 0.15degh was demonstrated [79

79. M. F. Zaman, A. Sharma, Z. Hao, and F. Ayazi, “A mode-matched silicon-yaw tuning-fork gyroscope with subdegree-per-hour Allan deviation bias instability,” J. Microelectromech. Syst. 17, 1526–1536 (2008). [CrossRef]

].

MEMS gyros have worse performance than FOGs and He–Ne RLGs, but they are surely cheaper and more compact. PICs for angular rate sensing and, in general, passive integrated optical gyros have a theoretical sensitivity typically in the range 110degh. This sensitivity range is quite close to that recently achieved by MEMS angular rate sensors having δΩ10degh. So MEMS and integrated optical technologies are two closely competing approaches for the fabrication of gyros having a resolution around 10degh. MEMS gyros are probably cheaper than integrated optical gyros, but they could not fulfil some of the requirements typical of some military or space applications for angular rate sensors. Moreover, high-performance MEMS gyros require complex read-out electronics and expansive vacuum packaging.

Table 3 summarizes the comparison among RLGs, FOGs, passive integrated optical gyros, MEMS gyros, and HRGs in terms of best achievable sensitivity and bias stability.

5. Conclusion

Recently developed optical gyroscopes have been critically reviewed in this paper. Integrated optical gyros exhibit a theoretically predicted resolution in the range of 110degh, and so they can compete with MEMS gyros in the medium-accuracy gyro market. Advantages and disadvantages of both integrated photonic gyroscopes and MEMS angular rate sensors have been pointed out and discussed. Integrated optical gyros are expected to be more reliable and more immune to disturbances than MEMS angular rate sensors. An accurate cost comparison between MEMS and integrated optical technologies for gyroscope realization, taking into account also the complexity of the read-out electronics, should be the topic of future investigations.

The RLG and the HRG compete in the high-performance gyro market. A comparison between the two devices in terms of the key performance parameters has been reported, too. Recently fabricated and commercialized HRGs have better performance but are also larger than RLGs. Unlike the He–Ne RLG, which is widely used in the aeronautic industry, the HRG has found application only in the space market, where price is not a determining factor and reliability is very important.

Recently achieved theoretical results about the feasibility of a compact InP-based PIC for angular rate sensing with a resolution less than 10degh make the experimental investigation of performance achievable by this technology attractive.

Acknowledgments

This work has been partially funded by the European Space Agency (ESA) under IOLG project 1678/02/NL/PA, in the framework of ESA-Politecnico di Bari agreement 20199/06/NL/PA.

Tables and Figures

Table 1. Basic Classes of Photonic Gyroscopes

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Table 2. Fully Integrated Active Optical Gyros: Performance and Geometrical Parameters

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Table 3. Performance Comparison among RLGs, FOGs, Passive Integrated Optical Gyros, MEMS gyros, and HRGs

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Fig. 1 Architecture of the bulk-optic solid-state RLG (PD, photodetector) [11].
Fig. 2 Active integrated optical gyroscope proposed in [17].
Fig. 3 Experimental setup adopted to detect the frequency shift due to the Sagnac effect in the spectrum of the voltage signal between the terminals of a SRL [19].
Fig. 4 PIC for rotation sensing, including two unidirectional SRLs, two directional couplers (DCs), seven photodiodes (PDs), and a beam combiner [21].
Fig. 5 Circular Bragg microlaser for rotation sensing [23].
Fig. 6 FOG closed-loop configuration [28].
Fig. 7 Minimum detectable angular rate of the FOG as dependent on R×L and optical power coming in the photodetector.
Fig. 8 Typical architecture of high-performance FOGs [34].
Fig. 9 Ring resonator compensated with two SOAs.
Fig. 10 Passive integrated optical gyro in silica-on-silicon technology [46].
Fig. 11 Readout system for a passive gyroscope based on a lithium niobate resonator [52].
Fig. 12 Compensated ring resonator realized by ion exchange in glass [55].
Fig. 13 Architecture of the InP-based PIC for angular rate sensing (PD, photodetector).
Fig. 14 CROW-based integrated gyro architecture [65].
Fig. 15 Architecture of the phase-sensitive gyroscope including a ring-in-ring resonator [67].
Fig. 16 Coupling between CW and CCW resonant modes in a CROW.
Fig. 17 Forbidden and transmission bands in a CROW spectral response at the drop port and rotation-induced additional forbidden band.
Fig. 18 Passive integrated optical gyro including a circular waveguide coupled to high-Q microresonators [70].
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70.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107–112 (2004). [CrossRef]

71.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals-Molding the Flow of Light (Princeton Univ. Press, 1995).

72.

F. Krauss, R. M. de la Rue, and S. Brand, “Two-dimensional photonic bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996). [CrossRef]

73.

M. Lončar and A. Scherer, “Microfabricated optical cavities and photonic crystals,” in Optical Microcavities, E. Vahala ed. (World Scientific, 2004).

74.

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75.

B. Z. Steinberg and A. Boag, “Splitting of microcavity degenerate modes in rotating photonic crystals-the miniature optical gyroscopes,” J. Opt. Soc. Am. B 24, 142–151 (2007). [CrossRef]

76.

A. Shamir and B. Z. Steinberg, “On the electrodynamics of rotating crystals, micro-cavities, and slow-light structures: from asymptotic theories to exact Green’s function based solutions,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA 09) (IEEE, 2007), pp. 45–48.

77.

Honeywell, “HG1900 MEMS IMU,” http://www.honeywell.com

78.

R. Durrant, H. Crowle, J. Robertson, and S. Dussy, “SIREUS—status of the European MEMS rate sensor,” presented at 7th International ESA Conference on Guidance, Navigation & Control Systems, Tralee, Ireland, June 2–5, 2008.

79.

M. F. Zaman, A. Sharma, Z. Hao, and F. Ayazi, “A mode-matched silicon-yaw tuning-fork gyroscope with subdegree-per-hour Allan deviation bias instability,” J. Microelectromech. Syst. 17, 1526–1536 (2008). [CrossRef]

aop-2-3-370-i001 Caterina Ciminelli received the Laurea degree in electronic engineering and the Ph.D. degree in electronic engineering [working on fabrication and characterization of ion exchange optical waveguides, design, fabrication and characterization of liquid crystal optical switches, and modeling of distributed feedback (DFB) lasers] from Politecnico di Bari, Bari, Italy, in 1996 and 1999, respectively. In 1999, she worked on modeling and design of DFB lasers for six months at the Research Center of Alcatel in Marcoussis. In December, 1999, she joined Pirelli Optical Systems and in February, 2000, moved to Cisco Photonics Italy, doing research on new optoelectronic technologies. Currently, she is University Researcher and Lecturer in Electronics at the Politecnico di Bari. She is author or coauthor of more than 120 journal articles and conference papers. Her scientific interests are in photonic bandgap devices, ring lasers, SOAs, and optical sensors.

aop-2-3-370-i002 Francesco Dell’Olio was born in Terlizzi, Bari, Italy, in April 1981. He received, in 2005 and 2010, the Laurea degree (cum laude) in electronic engineering and the Ph.D. degree in information engineering both from the Politecnico di Bari, Bari, Italy. His research interests include the fields of integrated optical sensors, especially angular velocity and chemical sensors, silicon photonics and InP-based photonic integrated circuits. He is the coauthor of more than 10 papers published in international refereed journals. He has coauthored more than 30 papers published in conference proceedings. Dr. Dell’Olio is a member of the Optical Society of America and Italian Society of Optics and Photonics (SIOF), Italian branch of the European Optical Society (EOS).

aop-2-3-370-i003 Carlo Edoardo Campanella received the Laurea degree in electronic engineering from Politecnico di Bari, Bari, Italy, in 2007, where he is currently working toward the Ph.D. degree. He is coauthor of more than 20 journal articles and conference papers. His research interests are focused mainly on modeling, design, and simulation of integrated optical devices, such as optical sensors and photonic-crystal based components, SOAs, and lasers.

aop-2-3-370-i004 Mario Nicola Armenise received the Laurea degree in electrical engineering from the University of Bari, Bari, Italy. He has been a Full Professor of Optoelectronics since 1986 at Politecnico di Bari. He has been Deputy Rector of the Politecnico di Bari from 1994 to 1997. He has been Deputy Chair of the Consortium of the Apulian Universities (CIRP), from 1995 to 1997, and since 2004 he has been the Chair. He is author or coauthor of about 300 journal articles and conference presentations, and coinventor of two international patents. His current research interests include fabrication and characterization techniques of optical waveguides and devices, design and simulation of guided-wave devices and circuits for telecommunications, optical signal processing, optical computing, and sensing. He has been visiting professor in several universities and has been invited to give seminars in Europe, the U.S., Japan, and former Eastern European countries. Dr. Armenise currently serves as a referee of a number of international journals. He is an advisory Member of the Institute of Electronics, Information and Communication Engineers—Japan (IEICE) Transactions on Electronics. He was member of the Scientific Council of the Department of Science and Technology of Communications and Information of the French National Committee of Scientific Research. He is a member of the Scientific Council of the Department of Materials and Technologies of the Italian National Council of Research. He has been Chair, Cochair, or Member of the Program Committees of numerous international conferences. He has given invited talks at many international conferences. He has been scientific coordinator of several national and international research projects. He is Past President of the Italian Optics and Photonics Society, and Fellow of the European Optical Society.

ToC Category:
Integrated Optics Devices

History
Original Manuscript: November 18, 2009
Revised Manuscript: April 30, 2010
Manuscript Accepted: May 8, 2010
Published: June 2, 2010

Virtual Issues
(2010) Advances in Optics and Photonics

Citation
Caterina Ciminelli, Francesco Dell’Olio, Carlo E. Campanella, and Mario N. Armenise, "Photonic technologies for angular velocity sensing," Adv. Opt. Photon. 2, 370-404 (2010)
http://www.opticsinfobase.org/aop/abstract.cfm?URI=aop-2-3-370


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