A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency
Introduction
Since slow light was discovered in electromagnetically induced transparency (EIT) [1], it has been widely investigated in many materials and structures (e.g., atomic vapor [2], [3], [4], [5], photorefractive crystal [6], [7], ruby [8], [9], optical fiber [10] and coupled-resonator structure [11], [12], [13], [14], [15]) because it has potential application in various aspects, such as all-optical buffer, optical delay line, synthetic aperture radar and optical gyroscope. The concept of slow-light gyroscope was originally proposed by Leonhardt and Piwnicki [16]. They predict that “slow light” property induced by electromagnetically induced transparency (EIT) and coherent population trapping (CPT) may greatly boost the gyroscope's sensitivity by as much as light slows. However, they did not indicate concretely how the gyroscope's sensitivity can be enhanced by slow-light technique. After several years, Shahriar et al. [17], [18] proved that this enhancement cannot be achieved for the case of absolute rotation, in which case slow light medium moves together with the rest of gyroscope. They also proved only the case of relative rotation, in which case there is a relative rotation between the slow light medium and the rest of the gyroscope, can enhance the gyroscope's sensitivity. However, the relative rotation between the medium and the rest of the gyroscope, up to now, cannot be used in navigation and aviation. What is needed for these applications is an ability to measure the absolute rotation of the whole gyroscope, including the propagation medium [18]. Therefore, the dispersive medium such as EIT and CPT cannot be utilized to enhance the gyroscope's sensitivity, but the dispersive structure based on photonic crystal or resonator cavities reveals some possibilities. Recently, a series of work aimed to utilized the dispersive structure to enhance gyroscope's sensitivity. Matsko et al. [19], [20] proposed a set of coupled whispering gallery mode resonators to realize a high-sensitivity optical gyroscope, but this structure was modeled as a highly-dispersive conventional waveguide where the slow group velocity of the light in this structure stems from the average interaction of the light with the high-Q resonators. Steinberg et al. [21], [22], [23] studied the Sagnac effect in rotating coupled photonic crystal defect cavities. Yariv et al. [24] presented a coupled-resonator slow-light waveguide structure to realize highly compact integrated rotation sensors and gyroscopes. Moreover, Peng et al. proposed a two-identical-ring planar structure [25] and a two-identical-ring folded structure [26] which can be employed to construct highly sensitive gyroscopes, respectively.
All these works mentioned above aimed to use slow light to improve the sensitivity of optical gyroscope. In this Letter, we proposed a high dispersive ring-in-ring planar structure which belongs to the dispersive structure, and studied the relationships between the effective Sagnac phase shift and the group index in details. In addition, we utilize the ring-in-ring planar structure, measuring absolute rotation, to construct a new high sensitive gyroscope.
Section snippets
Analysis of ring-in-ring planar structure
The ring-in-ring planar structure is constructed by a waveguide coupled with ring-in-ring resonator, as shown in Fig. 1. It would consume less space than that proposed in Refs. [25], [26], where the rings of the former is coupled in tandem to a waveguide, the latter is a folded structure. The radiuses of the two rings in the ring-in-ring resonator, and , satisfy the relation of . The response of the whole structure can be described by the transmission coefficient, , which is
Optical gyroscope based on the ring-in-ring planar structure
The ring-in-ring planar structure has high dispersion at resonance, simultaneity, the group velocity reaches minimum with transparent. This structure can be used in absolute rotation sensing to enhance the sensitivity of optical gyroscope. In previous studies, Peng et al. proposed a two-identical planar ring structure [25] and a folded identical ring structure [26] that can be used in optical gyroscope and rotating senor. However, Peng et al. did not devise the specific structure of optical
Conclusion
In this Letter, a ring-in-ring planar structure with an EIT-like property is proposed to construct an optical gyroscope for measuring absolute rotation. The sensitivity of the proposed gyroscope can be enhanced to orders of magnitude for centimeter scale structure with the proper selected parameters. In addition, the size of the rings should be very accurate for a given optical frequency based on Eq. (8) because achieve maximum at resonance only. In practice, there could be some
Acknowledgements
The research is supported by the National Natural Science Foundation of China under Grant Nos. 60272075 and 60478014, the National High Technology Research and Development Program (″863″Program) of China under Grant No. 2007AA12Z112 and partially supported by the program of the excellent team in Harbin Institute of Technology.
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