We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the output modulation to determine the conditions for enhanced gyroscopic sensitivities. The element is treated as both a phase and amplitude filter, and the time dependence of the cavity field is considered. Both atomic gases (two level and multilevel) and optical resonators (single and coupled) are considered and compared as dispersive elements. We find that it is possible to simultaneously enhance the gyro scale factor sensitivity and suppress the dead band by using an element with anomalous dispersion that has greater loss at the carrier frequency than at the sideband frequencies, i.e., an element that simultaneously pushes and intensifies the perturbed cavity modes, e.g. a two-level absorber or an undercoupled optical resonator. The sensitivity enhancement is inversely proportional to the effective group index, becoming infinite at a group index of zero. However, the number of round trips required to reach a steady state also becomes infinite when the group index is zero (or two). For even larger dispersions a steady state cannot be achieved, and nonlinear dynamic effects such as bistability and periodic oscillations are predicted in the gyro response.
We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the output modulation to determine the conditions for enhanced gyroscopic sensitivities. The element is treated as both a phase and amplitude filter, and the time dependence of the cavity field is considered. Both atomic gases (two level and multilevel) and optical resonators (single and coupled) are considered and compared as dispersive elements. We find that it is possible to simultaneously enhance the gyro scale factor sensitivity and suppress the dead band by using an element with anomalous dispersion that has greater loss at the carrier frequency than at the sideband frequencies, i.e., an element that simultaneously pushes and intensifies the perturbed cavity modes, e.g. a two-level absorber or an undercoupled optical resonator. The sensitivity enhancement is inversely proportional to the effective group index, becoming infinite at a group index of zero. However, the number of round trips required to reach a steady state also becomes infinite when the group index is zero (or two). For even larger dispersions a steady state cannot be achieved, and nonlinear dynamic effects such as bistability and periodic oscillations are predicted in the gyro response.
We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the modulation to determine the conditions for cavity self-stabilization and enhanced gyroscopic sensitivity. We find an enhancement in the sensitivity of a laser gyroscope to rotation for normal dispersion, while anomalous dispersion can be used to self-stabilize an optical cavity. Our results indicate that atomic media, even coherent superpositions in multilevel atoms, are of limited use for these applications, because the amplitude and phase filters work against one another, i.e., decreasing the modulation frequency increases its amplitude and vice-versa. On the other hand, for optical resonators the dispersion reversal associated with critical coupling enables the amplitude and phase filters to work together. We find that for over-coupled resonators, the absorption and normal dispersion on-resonance increase the contrast and frequency of the beat-note, respectively, resulting in a substantial enhancement of the gyroscopic response. Under-coupled resonators can be used to stabilize the frequency of a laser cavity, but result in a concomitant increase in amplitude fluctuations. As a more ideal solution we propose the use of a variety of coupled-resonator-induced transparency that is accompanied by anomalous dispersion.
We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the modulation to determine the conditions for cavity self-stabilization and enhanced gyroscopic sensitivity. Hence, we model cavity rotation or instability by an arbitrary AM/FM modulation, and the dispersive element as a phase and amplitude filter. We find that anomalous dispersion may be used to self-stabilize a laser cavity, provided the magnitude of the group index of refraction is smaller than the phase index of refraction in the cavity. The optimal stabilization is found to occur when the group index is zero. Group indices with magnitudes larger than the phase index (both normal and anomalous dispersion) are found to enhance the sensitivity of a laser gyroscope to rotation. Furthermore, our results indicate that atomic media, even coherent superpositions in multilevel atoms, are not useful for these applications, because the amplitude and phase filters work against one another, i.e., decreasing the modulation frequency increases its amplitude and vice versa, with one exception: negative group indices whose magnitudes are larger than the phase index result in negative, but enhanced, beat frequencies. On the other hand, for optical resonators the dispersion reversal associated with critical coupling enables the amplitude and phase filters to work together under a greater variety of circumstances than for atomic media. We find that for single over-coupled resonators, or in the case of under-coupled coupled-resonator-induced absorption, the absorption and normal dispersion on-resonance increase the contrast and frequency of the beat-note, respectively, resulting in a substantial enhancement of the gyroscopic response. Moreover, for cavity self-stabilization, we propose the use of a variety of coupled-resonator induced transparency that is accompanied by anomalous dispersion.
We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the modulation to determine the conditions for cavity self-stabilization and enhanced gyroscopic sensitivity. We find an enhancement in the sensitivity of a laser gyroscope to rotation for normal dispersion, while anomalous dispersion can be used to self-stabilize an optical cavity. Our results indicate that atomic media, even coherent superpositions in multilevel atoms, are of limited use for these applications, because the amplitude and phase filters work against one another, i.e., decreasing the modulation frequency increases its amplitude and vice-versa. On the other hand, for optical resonators the dispersion reversal associated with critical coupling enables the amplitude and phase filters to work together. We find that for over-coupled resonators, the absorption and normal dispersion on-resonance increase the contrast and frequency of the beat-note, respectively, resulting in a substantial enhancement of the gyroscopic response. Under-coupled resonators can be used to stabilize the frequency of a laser cavity, but result in a concomitant increase in amplitude fluctuations. As a more ideal solution we propose the use of a variety of coupled-resonator-induced transparency that is accompanied by anomalous dispersion.
Introducing active gain in the optical waveguide resonator not only compensates the loss, but also can change the dispersion relationship in the ring resonator. It is demonstrated that the group delay time is negative when the resonator is in the undercoupled condition, which also means the resonator exhibits the fast light effect. Theoretical analysis indicates that fast light effect due to anomalous dispersion, would be manipulated by the gain coefficient controlled by the input pump light power and that fast light would enhance scale factor of the optical resonant gyroscope. Resonance optical gyroscope (ROG)’s scale factor for measuring rotation rate is enhanced by anomalous dispersion with superluminal light propagation. The sensitivity of ROG could be enhanced by anomalous dispersion by coupled resonators even considering the effect of anomalous dispersion and propagation gain on broadened linewidth, and this could result in at least two orders of magnitude enhancement in sensitivity.
The pushing of the modes of a Fabry-Perot cavity by an intracavity rubidium cell is measured. The scale factor of the modes is increased by the anomalous dispersion and is inversely proportional to the sum of the effective group index and an additional cavity delay factor that arises from the variation of the Rb absorption over a free spectral range. This additional positive feedback further increases the effect of the anomalous dispersion and goes to zero at the lasing threshold. The mode width does not grow as fast as the scale factor as the intracavity absorption is increased resulting in enhanced measurement sensitivities. For absorptions larger than the scale factor pole, the atom-cavity response is multivalued and mode splitting occurs.