Theoretical and Experimental Investigation of Quantum Noise Induced Sensitivity Limit of a Fast Light Ring Laser Gyroscope

In a Fast-Light Ring Laser Gyroscope (FRLG), the rotation induced shift in the frequency of two counter-propagating lasers is amplified by the inverse of the group index, compared to a conventional ring laser gyroscope (RLG). This scale factor enhancement coefficient (SFEC) can be as high as a million. If the uncertainty in the laser frequency for an FRLG is the same as that for an RLG for otherwise identical conditions, then the factor of enhancement in measurement precision (FEMP) for an FRLG is the same as the SFEC. However, it has been suggested that the frequency uncertainty for an FRLG based on a pair of coupled resonators may be larger than that for an RLG, due to the Petermann factor (PF), thus reducing the FEMP to a value smaller than the SFEC, and possibly to unity. Theoretical investigation in Phase I has shown that when such an FRLG is operated far above threshold, it may be possible to achieve a value of FEMP significantly larger than unity. We will carry out theoretical as well as experimental work to establish the maximum possible value of the FEMP that can be achieved for such an FRLG, employing intracavity gain in one cavity and intra-cavity loss in another, using Raman transitions in Rb. In addition, we will investigate another type of FRLG in which a single ring cavity supports two counter-propagating lasers, without any cross-coupling, also realized using Raman transitions in Rb. For each laser in this system, the nature of the eigenvalues indicates that the FEMP would also be limited by the PF. However, it is not yet clear whether the PF exists in this case. We will explore ways to resolve this issue theoretically, by using the approach of Langevin noise operators. If the PF does not exist, it would indicate that for such an FRLG the FEMP can really be as larger as the SFEC. If the PF does exist, then we will identify conditions under which the FEMP in this case can also be much larger than unity when operated far above threshold. In a Fast-Light Ring Laser Gyroscope (FRLG), the group index is vanishingly small.  The Sagnac effect induced shift in the resonance frequency of each of two counter-propagating lasers, for a given rotation rate, is amplified by a factor equaling the inverse of this group index, compared to that for a conventional ring laser gyroscope (RLG).  This scale factor enhancement coefficient (SFEC) can be as high as a million.  If the quantum noise limited uncertainty in the laser frequency for an FRLG is the same as that for an RLG, this would imply that the factor of enhancement in measurement precision (FEMP) for an FRLG is the same as the SFEC.  However, it has been suggested that the actual value of the FEMP  may be smaller than the SFEC, and currently it is not known as to what the maximum achievable value of the SFEC is.  We will carry out theoretical as well as experimental work to establish the maximum possible value of the FEMP that can be achieved under experimentally achievable conditions.  This will pave the way for miniaturization and commercialization of the FRLG in Phase II. In Phase II, the goal is to determine the maximum possible factor of enhancement in measurement precision (FEMP) for a Fast-Light Ring Laser Gyroscope (FRLG). This would be achieved by carrying out the following tasks: (1)  Construct an FRLG using a pair of coupled ring cavities, one with Raman gain and the other with Raman depletion.  (2) Develop analytic expressions for the saturation behavior for Raman gain and Raman depletion, and use these to predict the Petermann Factors (PFs) for intensity noise and phase noise, for variations around steady state.  Identify optimal operating parameters to maximize the FEMP while operating as a single mode laser outside the dead-band. Use beating with a stable reference laser to measure any frequency shift. (3) Construct another FRLG in which a single cavity supports two counter-propagating lasers, without any cross-coupling, using Raman gain and depletion.  (4) Develop an approach, employing Langevin noise operators, to determine what the PF is for such a laser at threshold as well as in the saturated regime.  (5) For each FRLG, measure the phase noise and intensity noise spectra. Measure Schwalow-Townes Linewidths and compare with values expected from the PFs as well as the noise spectra.   (6) Demonstrate measurement of rotation and determine whether the measured FEMP agrees with theory.  The deliverables will be technical reports.

  • Improved space vehicle positioning and navigation • Ultra-precise pointing and platform stabilization for telescopes • Space vehicle health monitoring • Tests of general relativity via measurement of gravitational frame dragging effect   • Improved positioning and navigation of missiles • Positioning and navigation for atmospheric and ground vehicles in GPS-denied environments • Guidance of unmanned underwater vehicles (UUVs) • Guidance of smart ammunitions • Advanced laser beam pointing/steering systems

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