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. 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. 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 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 describe a resonator-based optical gyroscope whose sensitivity for measuring absolute rotation is enhanced via use of the anomalous dispersion characteristic of superluminal light propagation. The enhancement is given by the inverse of the group index, saturating to a bound determined by the group velocity dispersion. We also show how the offsetting effect of the concomitant broadening of the resonator linewidth may be circumvented by using an active cavity. For realistic conditions, the enhancement factor is as high as 106. We also show how normal dispersion used for slow light can enhance relative rotation sensing in a specially designed Sagnac interferometer, with the enhancement given by the slowing factor.
Quantum coherence effects in atomic media such as electromagnetically-induced transparency and absorption, lasing without inversion, super-radiance and gain-assisted superluminality have become well-known in atomic physics. But these effects are not unique to atoms, nor are they uniquely quantum in nature, but rather are fundamental to systems of coherently coupled oscillators. In this talk I will review a variety of analogous photonic coherence phenomena that can occur in passive and active coupled optical resonators. Specifically, I will examine the evolution of the response that can occur upon the addition of a second resonator, to a single resonator that is side-coupled to a waveguide, as the coupling is increased, and discuss the conditions for slow and fast light propagation, coupled-resonator-induced transparency and absorption, lasing without gain, and gain-assisted superluminal pulse propagation. Finally, I will discuss the application of these systems to laser stabilization and gyroscopy.