Title of Invention: Unidirectional crow gyroscope Abstract: An optical waveguide gyroscope includes at least one optical coupler configured to receive a first optical signal at a first port, to transmit a second optical signal to a second port, and to transmit a third optical signal to a third port. The optical waveguide gyroscope further includes a plurality of resonant waveguides optically coupled to the second port and the third port. The resonant waveguides are generally adjacent to one another and optically coupled to one another. At least a portion of the second optical signal propagates from the second port to the third port by propagating through the plurality of resonant waveguides, and at least a portion of the third optical signal propagates from the third port to the second port by propagating through the plurality of resonant waveguides. The at least a portion of the second optical signal propagates through each resonant waveguide of the plurality of resonant waveguides in a clockwise direction and the at least a portion of the third optical signal propagates through each resonant waveguide of the plurality of resonant waveguides in a counterclockwise direction. Detailed Description: Part general_description_paragraphs: Part CROSS-REFERENCE TO RELATED APPLICATIONS: This application claims the benefit of priority from U.S. Provisional Patent Appl. No. 61/041,567, filed on Apr. 1, 2008, and incorporated in its entirety by reference herein. Part BACKGROUND OF THE INVENTION: 1. Field of the Invention This application relates generally to optical waveguide gyroscopes. 2. Description of the Related Art Recent investigations have shown that slow light can have a profound impact on the optical properties of materials and systems. In particular, under certain conditions, the sensitivity of interferometric sensors can be in principle greatly enhanced by interrogating the interferometer with slow light. See, e.g., M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B Vol. 19, 2052-2059 (2002). This intriguing property has a number of physical origins, depending on the nature of the waveguide and of the perturbation applied to it. However, irrespective of the exact origin, the sensitivity of a number of different sensors has been shown to scale like the reciprocal of the group velocity. Since slow light can be characterized by an extremely large group index (>105), its use can in principle improve the sensitivity of optical sensors by many orders of magnitude. Although not all sensors benefit in terms of sensitivity from this slow-light enhancement, this prospect has far-reaching implications for many applications. Part SUMMARY OF THE INVENTION: In certain embodiments, an optical waveguide gyroscope comprises at least one optical coupler having a first port, a second port, and a third port. The at least one optical coupler is configured to receive a first optical signal at the first port, to transmit a second optical signal to the second port, and to transmit a third optical signal to the third port. The optical waveguide gyroscope further comprises a plurality of resonant waveguides optically coupled to the second port and the third port. The resonant waveguides are generally adjacent to one another and optically coupled to one another. At least a portion of the second optical signal propagates from the second port to the third port by propagating through the plurality of resonant waveguides, and at least a portion of the third optical signal propagates from the third port to the second port by propagating through the plurality of resonant waveguides. The at least a portion of the second optical signal propagates through each resonant waveguide of the plurality of resonant waveguides in a clockwise direction and the at least a portion of the third optical signal propagates through each resonant waveguide of the plurality of resonant waveguides in a counterclockwise direction. In certain embodiments, an optical waveguide gyroscope comprises a plurality of resonant waveguides generally adjacent to one another and optically coupled together. Each resonant waveguide of the plurality of resonant waveguides is configured to allow light to propagate through the resonant waveguide in a generally planar path. The paths of each of the resonant waveguides of the plurality of resonant waveguides are generally parallel to one another. Light propagates along each path in a clockwise direction or along each path in a counterclockwise direction. For purposes of summarizing the invention, certain aspects, advantages and novel features of the invention have been described herein above. It is to be understood, however, that not necessarily all such advantages may be achieved in accordance with any particular embodiment of the invention. Thus, the invention may be embodied or carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other advantages as may be taught or suggested herein. Part DETAILED DESCRIPTION: A parameter that is of particular importance to detect with a high accuracy is rotation rate. Applications of rotation-sensing devices, or gyroscopes, cover a wide range, from inertial navigation of aircraft and automobiles to stabilization of sea oil platforms, guidance of missiles and rockets, etc. A number of optical gyroscope configurations based on coupled resonant optical waveguides (CROW) have been proposed and studied in the literature. See, e.g., J. Scheuer, and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett, Vol. 96, 053901 (2006)); A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. Vol. 24, 711-713 (1999)); M. S. Shahriar et al, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light”, Phys. Rev. A, Vol. 75, 053807 (2007); A. B. Matsko et al., “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107 (2004); Steinberg et al, “Rotation Induced Super Structure in Slow-Light Waveguides with Mode Degeneracy: Optical Gyroscopes with Exponential Sensitivity,” JOSA B, Vol. 25(5), 1216-1224, May 2007; Chao Peng, Zhengbin Li, and Anshi Xu, “Rotation sensing based on a slow-light resonating structure with high group dispersion,” Applied Optics Vol. 46, No. 19, 4125-4131, July 2007; and Chao Peng, Zhengbin Li, and Anshi Xu, “Optical gyroscope based on a coupled resonator with the all-optical analogous property of electromagnetically induced transparency,” Optics Express Vol. 15, No. 7, 3864-3875, 2 Apr. 2007. These references claim that the disclosed gyroscopes have superior sensitivity, either relative to a single resonator structure (in essence a resonant fiber optic gyroscope (RFOG), see, e.g., H. Lefèvre, The Fiber-Optic Gyroscope, Ch. 11, Artech House, Boston (1993)), or relative to a conventional fiber optic gyroscope (FOG) (see, e.g., H. Lefèvre, The Fiber-Optic Gyroscope, Ch. 2, Artech House, Boston (1993)). Such claims are particularly noteworthy because first the fiber-optic gyroscope (FOG) has been for many years the most successful commercial fiber sensors (see, e.g., G. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, Washington, D.C., 2006), MA3), and second because developing an optical gyroscope with a sensitivity greater than possible with a conventional FOG is an appealing prospect that would find several important applications. There is consequently a tremendous interest, both scientific and commercial, in developing a gyroscope with much greater sensitivity, and/or long-term stability, and/or scale factor stability, than the most successful commercial optical gyroscope to date, which is the FOG. FIGS. 1A and 1B schematically show two diagrams of conventional CROW gyroscopes of relevance. The CROW gyroscope of FIG. 1A has a loop comprising a series of N=3 low-loss resonators or resonant waveguides (e.g., rings), and the CROW gyroscope of FIG. 1B has a loop comprising a series of N=7 resonators or resonant waveguides (e.g., rings). The rings are optically coupled to each other with a power coupling ratio κ to form an open loop. This loop is closed with a 3-dB loop coupler to create a Sagnac interferometer. The loop coupler is optically coupled to a light source and a detector (e.g., via a second optical coupler as shown in FIGS. 1A and 1B). As in a conventional FOG, light is launched into the loop coupler, which splits it with equal power into two signals. One signal travels clockwise (cw) around the Sagnac loop, and the other one counterclockwise (ccw). For simplicity, the resonant waveguides can be assumed to be identical rings with the same radius R, and the power coupling coefficient between any two adjacent rings or between the rings and the leads can be assumed to be the same, and equal to κ. These conditions are not necessary for the proper operation of this Sagnac-based CROW gyroscope, or any of the other CROW gyroscopes discussed herein. The conclusions of the following analyses are qualitatively the same when the dimension and/or the coupling coefficient vary from ring to ring. The exact shape of the loop around which the N rings are arranged has also no bearing on the overall behavior of this sensor. For simplicity, it can be assumed throughout that the rings are all centered on a circle of radius R0, and that the leads or injector couplers connecting the rings to the 3-dB coupler comprise circular arcs with the same radius of curvature as the rings (see FIGS. 1A and 1B). To understand the operating principle of the CROW gyroscope, consider first the limit of strong coupling (κ=1). Each ring can support cw and ccw modes. For example, the cw mode in ring j couples to the ccw mode in rings j+1 and j−1. The cw light signal then travels about half way through the first ring to an optical coupler (e.g., a portion of the first ring and the second ring which are strongly optically coupled to one another) at the far end of the first ring, where it is substantially fully coupled to the second ring. The same process takes place in each subsequent ring, until the signal reaches the 3-dB loop coupler. The light signal has therefore traveled around the loop in a “scalloped” pattern that encompasses a certain area B. The ccw signal undergoes the same process, except that it encounters the rings in the reverse order. So it follows the same optical path, but in the opposite direction. Hence as in a conventional FOG, in the absence of rotation and nonreciprocal effects, the two signals experience the same phase shift as they travel around the CROW loop in their respective directions. Consequently, when they recombine at the 3-dB coupler, they interfere constructively into the input arm of the coupler, and all the light (minus what is lost to losses within the loop) is detected at the detector (see FIGS. 1A and 1B). When the loop is rotated at a rate Ω about its main axis (i.e., perpendicular to its plane), as a result of the Sagnac effect light traveling in the direction of the rotation undergoes a stronger phase shift than light traveling in the opposite direction. The two signals are no longer in phase, which translates into a change in the power received by the detector. Except for the scalloped shape of the path followed by the light around the loop, this particular configuration behaves exactly the same way as a conventional FOG. In particular, it has the exact same sensitivity to rotation as a FOG encircling the same area B. Note that, in FIGS. 1A and 1B, for the cw and ccw signals to return to the loop coupler instead of to port C and port D, respectively, which is undesirable, the number of rings is odd. By switching the ports of one of the two injection couplers, a similar configuration is created that supports only an even number of rings, as shown in FIG. 2. Both types of configurations have the same basic properties. The CROW gyroscope starts differing from a FOG and becomes more interesting when κ<1, especially when κ is very weak. Each ring in the Sagnac loop is then a high-finesse resonator. The input laser signal frequency is selected to coincide with a resonance frequency of the (identical) rings at rest (zero rotation). For example, each ring can be considered to be a high Q cavity with low coupling to neighboring rings. At each junction or optical coupler between two neighboring rings, a very small fraction κ of the power passes on to the adjacent ring, while the rest of the power stays in the same ring. Thus, the effective group velocity of a signal propagating from ring to ring can be slow. When the gyroscope is at rest, each signal must thus travel multiple times around each ring, one ring after the other, before reaching the far end of the Sagnac loop and interfering with each other. When a rotation is applied to the Sagnac loop around an axis perpendicular to the plane of the loop, as a result of these multiple passes, each signal accumulates a larger rotation-induced (Sagnac) phase shift in each and every ring than if it were traveling through each ring only once, and the differential phase shift is enhanced. The applied rotation therefore results in a change in the optical power coming out of the Sagnac loop at port A (see FIGS. 1A and 1B), and this power change is larger than if the signals were not resonating around the rings. This enhancement is expected to scale like the number of times each signal travels around each ring, i.e., like 1/κ. For weak coupling (κ<<1), the increase in sensitivity can therefore be quite significant, as is the case in a resonant fiber optic gyroscope (RFOC) (see, e.g., H. Lefèvre, The Fiber-Optic Gyroscope, Ch. 11, Artech House, Boston (1993)). For the CROW gyroscope to work optimally in certain embodiments, (1) all the rings have a common resonance frequency at all time, (2) the frequency of the interrogating light remains tuned to this common resonance frequency at rest, and (3) the linewidth of the light signal is substantially narrower than the linewidth of the resonant modes of each resonant waveguide. Achieving these conditions is done using very tight control of the optical path length, index, and transverse dimensions of all N rings simultaneously. All of these quantities vary when portions or all of the rings are subjected to a temperature change, stresses, and/or vibrations. Therefore, controlling these quantities constitutes a significant engineering challenge in practice. However, such challenges can be in principle met with existing technology. The very small size of some of the CROW gyroscopes considered for rotation-rate detection (rings of only tens of microns in diameter) helps reduce the temperature variations along the rings, and it reduces the thermal mass of the interferometer, two conditions that make it easier to control the temperature of the final structure. Neverthless, because these structures involve multiple resonant waveguides to be stabilized to the same resonant frequency to an extraordinarily high precision, this stabilization process remains a serious engineering difficulty. Certain embodiments described more fully below advantageously satisfy the desired goal of not only offering a higher sensitivity to rotation, but also loosening the technical challenges of stabilizing its optical path. In the original reference which first disclosed the configuration of FIGS. 1A and 1B (J. Scheuer and A. Yariv, “Sagnac effect in coupled-resonator slow-light waveguide structures,” Phys. Rev. Lett. Vol. 96, 053901 (2006)), an expression was presented for its responsivity or sensitivity to rotation. This sensitivity was found to vary as (N+1)2 and as 1/κ. The conclusion that was drawn is that by using a large number of rings and weak coupling, a CROW gyroscope can be made considerably more sensitive than a conventional FOG. The term “slow light” was invoked in that original publication, presumably because the apparent group velocity of the signals traveling through these coupled resonators is greatly reduced (sees e.g., A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. Vol. 24, 711-713 (1999)) as the coupling coefficient κ is varied from 1 to very weak values. In many systems, low group velocity implies high sensitivity, since the phase change can be expressed as: δφ=L·δk≈L·δω·dk/dω=L·δω/vg where vg is the group velocity. A small group velocity does not improve the sensitivity to changes in the length L, but it can improve sensitivity to changes in the refractive index n or the frequency ω. In an optical gyroscope, both signals move with the medium, so δω=0 in the gyroscope frame of reference. Confusion on this point can lead to mistakes (see, e.g., Leonhardt et al., Phys. Rev. A 62, 055801 (2000)). However, as described more fully below, simulations show that in this configuration, slow light has no net benefit, and that this configuration, when properly scaled for fair comparison to a conventional FOG, exhibits at best the same responsivity or sensitivity as a FOG. These simulations were performed in part to assess the best possible rotation sensitivity a CROW gyroscope can have compared to a conventional FOG, assuming similar gyroscope footprints. The responsivity can be expressed as dP(Ω)/dΩ where P(Ω) is the power detected at a rotation rate Ω. These simulations show that although the (N+1)2 dependence of the responsivity or sensitivity predicted by Scheuer et al. is correct, it is only applicable when no external phase bias is applied between the gyroscopes counter-propagating signals. However, it is well known that with such zero phase bias, the sensitivity to first order in rotation rate Ω is zero. Hence the power returning to the detector depends on the next higher (second) order term in the phase difference between the signals, i.e., on the square of the rotation rate. This configuration has therefore a very poor sensitivity to small rotation rates, certainly much poorer than that of a conventional FOG having a coil of similar size. One option explored in the performance limitation discussion below is to supply a suitable phase bias to the CROW gyroscope and hence make the gyroscope signal proportional to Ω. However, as described below, when a proper phase bias is added, the signal does become proportional to N rather than N2. The CROW gyroscope is then more sensitive to small rotation rates, but its sensitivity is no longer proportional to (N+1)2, but rather to N+1. As a result, the biased CROW gyroscope turns out to have a sensitivity to rotation comparable to that of a conventional FOG or RFOG with the same footprint and the same total propagation loss when N=1, and increasingly smaller relative sensitivity as N increases. The number of rings that maximizes the relative sensitivity of the CROW gyroscope of FIGS. 1A and 1B is N=1, and in this configuration the CROW gyroscope looks sensibly like an RFOG. The conclusion is that the CROW gyroscope of FIGS. 1A and 1B has the same one and only benefit over a FOG as a resonant fiber gyroscope, namely it utilizes a shorter length of waveguide. However, it also has the same disadvantages over a FOG as an RFOG, namely the aforementioned stringent thermal and mechanical path-length stabilization requirements. This significant downside adds great engineering complexity and cost, and it certainly does not outweigh the length advantage. Finally, as discussed below in the performance limitation discussion below, unlike the situation implied in the original publication of Scheuer et al., the apparent lower group velocity of the light traveling through a CROW gyroscope has no bearing on its responsivity or sensitivity. Unfortunately, the CROW gyroscope belongs to the class of sensors that are not enhanced by slow light. This conclusion applies to two other configurations as well, illustrated in FIGS. 3 and 4, discussed by Steinberg et al, “Rotation Induced Super Structure in Slow-Light Waveguides with Mode Degeneracy: Optical Gyroscopes with Exponential Sensitivity,” JOSA B, Vol. 25(5), 1216-1224, May 2007. In the CROW gyroscope of FIG. 3, the resonators or resonant waveguides are not arranged in a Sagnac loop but in a straight line. Steinberg et al. also unfortunately makes incorrect predictions about this gyroscope performance. The CROW gyroscope of FIG. 4 is similar; the main difference is that the output signal is collected at the end of the same waveguide that supplies light to the coupled resonant waveguides. Unlike claimed in Steinberg et al., first the sensitivity of this CROW gyroscope is unrelated to group index. Second, its sensitivity scales like the total area of the rings, not like their total length, which implies that reducing the rings' radius while keeping their total length constant will yield a reduced sensitivity. Third, the fact that the transmission varies exponentially with rotation rate has no benefit for the sensitivity. Fourth, the presence of a bandgap in the transmission when the device is rotated is not a novel effect (it is present in classical RFOGs), and for equal total loss and area (the proper metric to compare gyroscopes) it does not result in an improvement in sensitivity over a conventional FOG. Finally, again for equal total loss and area, a CROW gyroscope has the same sensitivity as an RFOG. The bottom line is that even if one were to construct a CROW gyroscope with the world's lowest loss waveguide (silica single-mode fibers around 1.5 μm) and hypothetically lossless fiber couplers, the CROW gyroscope of FIG. 3 would not offer any sensitivity advantage over a conventional FOG. Such a CROW gyroscope would, on the other hand, present several significant disadvantages, including lack of reciprocity and the need to stabilize the resonance frequencies of N coupled rings against environmental perturbations to an extreme degree (as mentioned in relation to the CROW gyroscope of FIGS. 1A and 1B). Several other publications in recent years have described other gyroscope schemes utilizing slow light to purportedly enhance the sensitivity to small rotation rates, and so far most of them have proved to be erroneous. A. B. Matsko et al., “Optical gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 233, 107 (2004)) introduced another concept that was also ultimately proved incorrect (see, e.g., A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, “Erratum to Optical Gyroscope with whispering gallery mode optical cavities,” Opt. Commun. 259, 393 (2006); and M. S. Shahriar et al., “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light”, Phys. Rev. A, Vol. 75, 053807 (2007)). Certain embodiments described herein provide a number of new unidirectional configurations of CROW gyroscopes in which the light travels in the same direction (e.g., cw) in a plurality of adjacent resonant waveguides (e.g., in all or most of the rings). In certain embodiments, these configurations present one significant advantage over all CROW gyroscopes configurations proposed to date, namely a greater sensitivity to rotation rate than a conventional FOG (again, after normalization to the same area and total loss). In addition, in certain embodiments, some of these configurations are folded, as described in greater detail below, which means that they exhibit a smaller footprint and hence easier stabilization of their optical path lengths. These improvements offer the new prospect of optical gyroscopes with performance far superior to that of conventional FOGs. Subsequent publications (see, Chao Peng, Zhengbin Li, and Anshi Xu, “Rotation sensing based on a slow-light resonating structure with high group dispersion,” Applied Optics Vol. 46, No. 19, 4125-4131, July 2007; and Chao Peng, Zhengbin Li, and Anshi Xu, “Optical gyroscope based on a coupled resonator with the all-optical analogous property of electromagnetically induced transparency,” Optics Express Vol. 15, No. 7, 3864-3875, 2 Apr. 2007) have also indicated that unidirectional configurations may provide benefits compared to other configurations. One reason, and perhaps the only reason, why the sensitivity to rotation rate of any of the CROW gyroscopes illustrated in FIGS. 1-4 do not exceed the sensitivity of a conventional FOG is that the light in successive rings travels in opposite directions, namely, alternatively cw and ccw. The implication is that the Sagnac phase shift picked up by the signal as it travels through a given ring is partly cancelled by the Sagnac phase shift picked up by the same signal as it travels through the adjacent ring. The net Sagnac-induced phase shift accumulated by the light signal traveling through the structure (e.g., the clockwise signal in the CROW gyroscope of FIGS. 1A and 1B, or the signal traveling upward through the CROW gyroscope of FIG. 4) is then reduced compared to what it would be if light was to travel in the same direction (e.g., cw), in all or most rings. This can be accomplished by utilizing one of a number of configurations, shown in FIGS. 5A and 6 through 10. FIG. 5A schematically illustrates an example optical waveguide gyroscope 10 in accordance with certain embodiments described herein. The gyroscope 10 comprises at least one optical coupler 20 having a first port 22, a second port 24, and a third port 26. The at least one optical coupler 20 is configured to receive a first optical signal 30 at the first port 22, to transmit a second optical signal 40 to the second port 24, and to transmit a third optical signal 50 to the third port 26. The gyroscope 10 further comprises a plurality of resonant waveguides 60 (e.g., resonant waveguides 60a, 60b, 60c of FIG. 5A) optically coupled to the second port 24 and the third port 26. The resonant waveguides 60 are generally adjacent to one another and are optically coupled to one another. At least a portion of the second optical signal 40 propagates from the second port 24 to the third port 26 by propagating through the plurality of resonant waveguides 60. At least a portion of the third optical signal 50 propagates from the third port 26 to the second port 24 by propagating through the plurality of resonant waveguides 60. The at least a portion of the second optical signal 40 propagates through each resonant waveguide 60 of the plurality of resonant waveguides 60 in a clockwise direction and the at least a portion of the third optical signal 50 propagates through each resonant waveguide 60 of the plurality of resonant waveguides 60 in a counterclockwise direction. In certain embodiments, the at least a portion of the second optical signal 40 is received by the third port 26 and the at least a portion of the third optical signal 50 is received by the second port 24. In certain such embodiments, the at least a portion of the second optical signal 40 and the at least a portion of the third optical signal 50 are combined by the at least one optical coupler 20 and transmitted to the first port 22. In certain embodiments, the gyroscope 10 further comprises at least one injector coupler 70 optically coupling the second port 24 to the plurality of resonant waveguides 60 and at least one injector coupler 70 optically coupling the third port 26 to the plurality of resonant waveguides 60. In certain embodiments, the gyroscope 10 further comprises a plurality of optical couplers 80, with each optical coupler 80 optically coupling two generally adjacent resonant waveguides 60 of the plurality of resonant waveguides 60 to one another. In certain such embodiments, the optical couplers 80 are located between two adjacent resonant waveguides 60 (e.g., between resonant waveguides 60a and 60b, and between resonant waveguides 60b and 60c). In certain embodiments, the at least one optical coupler 20 comprises a 1×2 optical coupler with three ports or a 2×2 optical coupler with four ports. For example, certain embodiments utilize a 3-dB optical coupler. The at least one optical coupler 20 of certain embodiments splits the first optical signal 30 into the second optical signal 40 and the third optical signal 50. For example, in certain embodiments, the at least one optical coupler 20 directs 50% of the first optical signal 30 to the second optical port 24 as the second optical signal 40 and directs 50% of the first optical signal 30 to the third optical port 26 as the third optical signal 50. In certain embodiments, the at least one optical coupler 20 comprises an optical circulator, an optical splitter, or other optical components. In certain other embodiments, free-space coupling can be used and the at least one optical coupler 20 comprises a partially transmitting mirror. Other types of optical couplers 20 are also compatible with certain embodiments described herein. In certain embodiments, the first optical signal 30 is generated by a light source (not shown). Examples of light sources compatible with certain embodiments described herein include, but are not limited to, laser sources. In certain embodiments, the light generated by the light source has a linewidth significantly smaller than the width of the resonances of the CROW. In certain embodiments in which the at least a portion of the second optical signal 40 and the at least a portion of the third optical signal 50 are combined by the at least one optical coupler 20, the resultant optical signal is transmitted to an optical detector (not shown). Examples of optical detectors compatible with certain embodiments described herein include, but are not limited to, photodiodes. In certain embodiments, the resonant waveguides 60 comprise at least one ring waveguide which is configured to allow an optical signal to resonate within (e.g., propagate multiple times around) the resonant waveguide 60. In certain other embodiments, the resonant waveguides 60 comprise at least one microresonator. In certain embodiments, the resonant waveguides 60 can be of one or multiple kinds. For example, at least one of the resonant waveguides 60 can be defined in photonic-bandgap planar structures, conventional waveguides defined by well-established methods such as implantation, diffusion, photolithography, etching, etc., in amorphous, crystalline, or ceramic materials such as silica, phosphate, fluoride, or other glasses, in crystals such as silicon, or in dielectrics or metals. In certain embodiments, the resonant waveguides 60 can also comprise microspheres or conventional optical fiber (e.g., single-mode optical fiber). For silica-based microspheres and silica-based optical fibers, the wavelength range of operation can be about 1.5 μm, a range for which the propagation loss through the silica-based material is minimal, and hence the enhancement in sensitivity described above is at a maximum. Examples of low-loss optical ring resonators compatible with certain embodiments described herein include, but are not limited to, CaF2 resonators, which can have sufficiently low loss (see, e.g., I. S. Grudinin et al., “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006), which is incorporated in its entirety by reference herein). Similarly to the conventional CROW gyroscopes of FIGS. 1A and 1B, in certain embodiments, the number N of resonant waveguides 60 can be odd (e.g., 1, 3, 5, 7, 9). Similarly to the conventional CROW gyroscope of FIG. 2 (e.g., with an appropriate configuration of injector couplers 70), in certain other embodiments, the number N of resonant waveguides 60 can be even (e.g., 2, 4, 6, 8, 10). In certain embodiments, the coupling ratio between adjacent resonant waveguides 60 of the plurality of resonant waveguides 60 is less than one. In certain embodiments, the coupling ratio is comparable to the round-trip loss of the resonant waveguide 60. For example, for low-loss ring resonators (e.g., single-mode alexandersamuel@example.net μm), the round-trip loss and the coupling ratio can be less than 10−4. In certain embodiments, each resonant waveguide 60 of the plurality of resonant waveguides 60 is generally planar, and the resonant waveguides 60 of the plurality of resonant waveguides 60 are generally parallel to one another. For example, each resonant waveguide 60 of the plurality of resonant waveguides 60 can define a normal direction generally perpendicular to the resonant waveguide 60, and the resonant waveguides 60 of the plurality of resonant waveguides 60 can be positioned such that the normal directions are generally parallel with one another. In certain embodiments, each resonant waveguide 60 of the plurality of resonant waveguides is configured to allow light to propagate through the resonant waveguide 60 in a generally planar path, and the paths of each of the resonant waveguides 60 of the plurality of resonant waveguides 60 are generally parallel to one another. In certain such embodiments, each generally planar path has a normal direction generally perpendicular to the path, and the resonant waveguides 60 are positioned such that the normal directions of the paths are generally coincident with one another. In certain embodiments, the resonant waveguides 60 are generally planar with one another. For example, in certain embodiments, the resonant waveguides 60 are positioned such that the generally planar paths of the plurality of resonant waveguides 60 are in a common plane. In certain such embodiments, the resonant waveguides 60 are stacked above one another or folded on top of each other (e.g. the normal directions of the resonant waveguides 60 are coincident with one another). For example, the gyroscope 10 schematically illustrated by FIG. 5A is a folded unidirectional Sagnac-based CROW gyroscope 10 with stacked rings. In certain embodiments, the resonant waveguides 60 lie substantially flat over or on top of each other (e.g., having a zero angle between adjacent resonant waveguides 60). In certain other embodiments, at least two adjacent resonant waveguides 60 have a non-zero angle with respect to each other. FIG. 5A shows a non-zero angle between adjacent resonant waveguides, mostly for clarity of the figure. A small angle between resonant waveguides 60, of any value, is acceptable, however the larger this non-zero angle, the lower the directionality of the gyroscope 10, and the weaker the responsivity or sensitivity of the gyroscope 10. In certain embodiments (see, e.g., FIG. 5A), the at least one injector coupler 70 optically coupling the second port 24 to the plurality of resonant waveguides 60 comprises a portion of a waveguide sufficiently close to a portion of a resonant waveguide 60 to allow at least a portion of an optical signal to propagate between the waveguide portion and the resonant waveguide 60. Similarly, in certain embodiments (see, e.g., FIG. 5A), the at least one injector coupler 70 optically coupling the third port 26 to the plurality of resonant waveguides 60 comprises a portion of a waveguide sufficiently close to a portion of a resonant waveguide 60 to allow at least a portion of an optical signal to propagate between the waveguide portion and the resonant waveguide 60. In certain embodiments (see, e.g., FIG. 5A), the plurality of optical couplers 80 comprises at least one optical coupler 80 comprising portions of two adjacent resonant waveguides 60 (e.g., resonant waveguides 60a and 60b) which are sufficiently close to one another to allow at least a portion of an optical signal to propagate between the two adjacent resonant waveguides 60. The principle of the unidirectional CROW gyroscope 10 of FIG. 5A are similar to that of the configuration of FIGS. 1A and 1B. To understand the configuration of FIG. 5A, reference can be made first to the CROW gyroscope of FIGS. 1A and 1B. For simplicity, while it is not a requirement of the CROW gyroscope of FIGS. 1A and 1B, it can be assumed that the rings or resonant waveguides are all centered on a circle of radius R0, as shown in FIGS. 1A and 1B. As demonstrated in the performance limitation discussion below, the rotation-induced signal in the gyroscope of FIGS. 1A and 1B originates from two components. One is the fact that the counter-propagating signals have traveled around a large loop (circular, and of radius R0, in this example), and thus they have picked up a differential Sagnac phase shift proportional to the area of this loop, which is labeled B as described above. The second contribution is the resonant Sagnac phase shift collected by each of the cw and ccw signals as they propagate through the resonant rings. The performance limitation discussion below shows that provided the coupling ratio between rings is reasonably low, or equivalently that the finesse of the (identical) ring resonators is sufficiently high, this second contribution is much larger than the first contribution. By folding the rings or resonant waveguides 60 as shown in FIG. 5A, the area enclosed by the rings (B) has been reduced to zero, so the first contribution to the rotation-induced signal vanishes, but since it is negligible compared to the resonant contribution, the net rotation-induced signal has not been compromised. In fact, the net rotation-induced signal has increased. The reason is that because of the way the resonant waveguides 60 are arranged in this configuration, the signal traveling, for example, cw around this collapsed loop, travels cw with respect to the direction of the rotation applied to the structure in every single one of the resonant waveguides 60. For example, as schematically illustrated in FIG. 5A, at least a portion 40a of the second optical signal 40 is coupled from the second port 40 into the resonant waveguide 60a, at least a portion 40b is coupled from resonant waveguide 60a into the resonant waveguide 60b, at least a portion 40c is coupled from resonant waveguide 60b into resonant waveguide 60c, and at least a portion 40d is coupled from resonant waveguide 60c into the third port 26. Each of the portions 40a, 40b, and 40c propagating through the resonant waveguides 60a, 60b, and 60c travel is the same direction (e.g., cw) as one another. Therefore instead of partially subtracting from each other, all of these contributions actually add. In turns, everything else being the same (in particular the ring size or area, number of rings, waveguide loss, and coupling ratio κ), this yields a much stronger signal for a given rotation rate than in the configuration of FIGS. 1A and 1B. In conclusion, the unidirectional CROW gyroscope 10 of FIG. 5A has a greater sensitivity than the corresponding conventional FOG (schematically illustrated in FIG. 5B) with a length of fiber wrapped around the same footprint, and with the same total loss. FIG. 6 schematically illustrates another example optical waveguide gyroscope 10 (e.g., a unidirectional Sagnac-based CROW gyroscope) in accordance with certain embodiments described herein. The gyroscope 10 comprises at least one optical coupler 20 and a plurality of resonant waveguides 60 (e.g., resonant waveguides 60a-60d of FIG. 6) generally adjacent to one another and optically coupled to one another. In certain embodiments, each resonant waveguide 60 of the plurality of resonant waveguides 60 is generally planar, and the resonant waveguides 60 of the plurality of resonant waveguides 60 are generally planar with one another. At least one optical coupler 80 of the plurality of optical couplers 80 comprises a coupling portion 90 of a first resonant waveguide 60 (e.g., resonant waveguide 60b) of the plurality of resonant waveguides 60. The coupling portion 90 is generally adjacent to, and optically coupled to, a second resonant waveguide 60 (e.g., resonant waveguide 60a) of the plurality of resonant waveguides 60. The coupling portion 90 of certain embodiments comprises two sections of the first resonant waveguide 60 that cross over one another. For example, as schematically illustrated in FIG. 6, the coupling portion 90 of resonant waveguide 60b comprises a 180 degree twist of the resonant waveguide 60b. In certain such embodiments, the first resonant waveguide 60 is generally planar and generally surrounds a first area, and the coupling portion 90 between the twist and the second resonant waveguide 60 is generally planar and generally surrounds a second area smaller than the first area. For example, in certain embodiments, the second area is less than 10% of the first area. In certain embodiments, the second area is smaller than the first area, but not so small as to induce a significant bending loss in the fiber. For example, in a practical fiber-based device, the minimum diameter for the twisted section of the coupling portion 90 is a few millimeters. In certain embodiments, the sizes of the twisted sections of the coupling portions 90 are substantially equal to one another so that the resonant waveguides 60 are substantially identical to one another. FIG. 7 schematically illustrates another example optical waveguide gyroscope 10 (e.g., a unidirectional Sagnac-based CROW gyroscope) in accordance with certain embodiments described herein. The gyroscope 10 comprises at least one optical coupler 20 and a plurality of resonant waveguides 60 (e.g., resonant waveguides 60a-60d of FIG. 6) generally adjacent to one another and optically coupled to one another. In certain embodiments, each resonant waveguide 60 of the plurality of resonant waveguides 60 is generally planar, and the resonant waveguides 60 of the plurality of resonant waveguides 60 are generally planar with one another. At least one optical coupler 80 of the plurality of optical couplers 80 comprises a ring resonator 92 generally adjacent to, and optically coupled to, a first resonant waveguide 60 (e.g., resonant waveguide 60b) of the plurality of resonant waveguides 60 and a second resonant waveguide 60 (e.g., resonant waveguide 60a) of the plurality of resonant waveguides 60. In certain embodiments, the ring resonator 92 is generally circular, while in certain other embodiments, the ring resonator 92 has other shapes. In certain embodiments, the first resonant waveguide 60 is generally planar and generally surrounds a first area, the second resonant waveguide 60 is generally planar and generally surrounds a second area, and the ring resonator 92 is generally planar and generally surrounds a third area smaller than the first area and smaller than the second area. For example, in certain embodiments, the third area is less than 10% of the first area and the third area is less than 10% of the second area. In certain embodiments, the third area is smaller than either the first area or the second area, but not so small as to induce a significant bending loss. In certain embodiments, the sizes of the ring resonators 92 are substantially equal to one another. The above discussion regarding the propagation of optical signals through the gyroscope 10 is applicable to certain embodiments utilizing the configurations of FIGS. 6 and 7 as well. In FIG. 6, alternating reversal of the direction of rotation of the optical signals propagating through the ring with respect to the direction of the rotation applied to the structure is effected by flipping a portion of every other ring by 180° to create a coupling portion 90. In FIG. 7, it is accomplished by inserting a ring resonator 92 of small diameter between each adjacent ring or resonant waveguide 60. The area of the small ring resonator 92 is negligible compared to the area of the main rings or resonant waveguides 60, for example, only 10% of the area of the main rings or resonant waveguides 60. In certain embodiments, at least one optical coupler 80 of the plurality of optical couplers 80 comprises the ring resonator 92, a portion of the first resonant waveguide 60, and a portion of the second resonant waveguide 60. In certain such embodiments, the optical coupling between the small ring resonator 92 and one of the portions of the two resonant waveguides 60 has a low coupling coefficient κ, determined in the same manner as in the CROW gyroscope of FIGS. 1A and 1B. The optical coupling between the small ring resonator 92 and the other portion of the two portions of the two resonant waveguides 60 has a coupling ratio of substantially 100%. The higher the better; the difference between 100% and the actual value amounts to an undesirable loss, but the device will still function well. In certain embodiments, this additional loss is equal to or smaller than the value of the round-trip loss of the optical signal propagating through a resonant waveguide 60. In this manner, light couples from a first resonant waveguide 60 to the next small ring resonator 92 with a low coupling coefficient κ, and from there on this signal travels in a strongly-asymmetric “figure-8” through the small ring resonator/second resonant waveguide 60. The process repeats itself all the way across the structure. As schematically illustrated in FIGS. 6 and 7 for the cw-traveling signal (e.g., the second optical signal 40 and the portions 40a, 40b, 40c, 40d propagating around each of the resonant waveguides 60a, 60b, 60c, 60d, respectively), light in adjacent resonant waveguides 60 clearly travels in the same direction, namely, cw. For the ccw-traveling signal, not shown for clarity, light in adjacent resonant waveguides 60 also travels in the same direction, but now ccw. FIG. 8 shows another example optical waveguide gyroscope 10 (e.g., a unidirectional linear CROW gyroscope) with folded or stacked resonant waveguides 60 or rings in accordance with certain embodiments described herein. FIG. 9 shows another example optical waveguide gyroscope 10 (e.g., a unidirectional linear CROW gyroscope) with twisted coupling portions 90 in accordance with certain embodiments described herein. FIG. 10 shows another example optical waveguide gyroscope 10 (e.g., a unidirectional linear CROW gyroscope) with small interstitial ring resonators 92 in accordance with certain embodiments described herein. In certain embodiments, the plurality of resonant waveguides 60 are optically coupled to at least one waveguide. For example, as schematically illustrated by FIGS. 8, 9, and 10, one of the resonant waveguides 60 of the plurality of resonant waveguides 60 is optically coupled to a first waveguide 102 and one of the resonant waveguides 60 of the plurality of resonant waveguides 60 is optically coupled to a second waveguide 104. In certain embodiments, the resonant waveguides 60 are positioned along a generally straight line, while in certain other embodiments, the resonant waveguides 60 are positioned along a generally curved line. The same discussion regarding the propagation of optical signals through the gyroscope 10 applies to certain embodiments utilizing the linear CROW gyroscopes 10 of FIGS. 8, 9, and 10. Here again, the rings or resonant waveguides 60 can be stacked, twisted portions 90, or smaller interstitial ring resonators 92 can be added as described above to force light to circulate in the same direction (e.g., cw) in a plurality of resonant waveguides 60 (e.g., in all or most of the resonant waveguides 60). Similar unidirectional optical waveguide gyroscopes 10 can be configured to have a linear array of coupled resonant waveguides 60 with a single waveguide for inputting and outputting signals to the plurality of resonant waveguides 60, in a manner similar to that of the conventional CROW gyroscope of FIG. 4. Such unidirectional optical waveguide gyroscopes 10 look just like the ones shown in FIGS. 8, 9, and 10, except that in each case the second waveguide 104 is not present and the output is read at the port opposite the input port. In certain embodiments, some of the unidirectional configurations described above, for example, those of FIGS. 5A and 8 (as well as FIG. 8 without the second waveguide 104), also exhibit a significant stability improvement over the other unidirectional configurations. The reason is that in these gyroscopes, the rings or resonant waveguides 60 are positioned over (e.g., folded on top of) each other. Consequently, they physically occupy a smaller volume, and it is easier to control their mean temperature and reduce temperature gradients than in other non-folded configurations. Variations in mean temperature and variations in temperature gradients are detrimental in certain embodiments of these sensors because they modify the resonance frequencies of the rings or resonant waveguides 60, which in turn modify the output power at the output port of the sensor in a manner that is undistinguishable from a variation in rotation-induced signal. In certain embodiments, one or more of the CROW gyroscopes 10 shown in FIGS. 5A, 6-10 is operated in a reciprocal mode of operation, namely, through which two signals travel in opposite directions, as well as folded. As a result of the reciprocal operation, the two signals are nominally exposed to the same external reciprocal perturbations. Such perturbations include, but are not limited to, refractive index or length changes in the waveguide(s) due to external temperature changes that are slow compared to the time of flight of light through the structure. This effect is well known in FOGs, as described, for example in H. Lefèvre, The Fiber-Optic Gyroscope, Ch. 6, Artech House, Boston (1993). The structure is then less susceptible to mean temperature variations, and to variations in temperature gradients, as well as acoustic waves and vibrations. The folded configuration, as explained above, makes it easier to stabilize the structure in temperature. FIG. 5A shows an example CROW gyroscope 10 that satisfies this advantageous feature in accordance with certain embodiments described herein. Certain other embodiments utilize a CROW gyroscope 10 having a configuration that includes the second, but not the first, feature, namely, which are folded (e.g., the CROW gyroscopes 10 of FIGS. 5A and 8, and the one of FIG. 8 without the second waveguide 104) but which are not operated in a reciprocal mode. Another significant benefit of certain embodiments of the unidirectional configurations described herein is that they can be designed to be much smaller than a conventional FOG yet exhibit the same sensitivity. In certain such embodiments, the smaller size but comparable sensitivity to conventional FOG systems can be accomplished by reducing the number of coupled rings or resonant waveguides 60. In other words, although certain embodiments can be used to produce a gyroscope with the same footprint as a FOG but a superior sensitivity to rotation, it can also be designed to produce a gyroscope with either a smaller footprint and/or a
{'bibliographic_information': "{'country': 'US', 'doc-number': '12416767', 'kind': 'B2', 'date': '20090401', 'extension': '233', 'invention_title': 'Unidirectional crow gyroscope'}", 'source_file': './grant/2011/ipg111129.xml', 'source_data': 'USPTO-Grant'}