We present an entirely linear all-optical method of dispersion enhancement that relies on mode coupling between the orthogonal polarization modes of a single optical cavity, eliminating the necessity of using an atomic medium to produce the required anomalous dispersion, which decreases the dependence of the scale factor on temperature and increases signal-to-noise by reducing absorption and nonlinear effects. The use of a single cavity results in common mode rejection of the noise and drift that would be present in a system of two coupled cavities. We show that the scale-factor-to-mode-width ratio is increased above unity for this system and demonstrate tuning of the scale factor by (i) directly varying the mode coupling via rotation of an intracavity half wave plate, and (ii) coherent control of the cavity reflectance which is achieved simply by varying the incident polarization superposition. These tuning methods allow us to achieve unprecedented enhancements in the scale factor and in the scale-factor-to-mode-width ratio by closely approaching the critical anomalous dispersion condition.
We present an entirely linear all-optical method of dispersion enhancement using coupled cavities that leads to a substantial increase in system transmission in comparison with atom-cavity systems. This is achieved by tuning the system to an anomalous dispersion condition by under-coupling at least one of the cavities to the other. The intracavity anomalous dispersion is then associated with a dip in reflection (and in turn with a peak in transmission) rather than with an absorption resonance as in the case of the atomic vapor. We find that in contrast with the atom-cavity system where mode reshaping always contributes to the mode pushing, in coupled cavity systems reshaping of the mode profile can either contribute to or oppose the mode pushing, and even reverse it under appropriate conditions leading to a reduced scale factor in transmission. We demonstrate a method for further optimizing the transmission of both atom-cavity and coupled-cavity systems, but show that this leads to a more rectangular mode profile and a reduction in the scale factor bandwidth. We also derive the cavity scale factor in reflection for both atom-cavity and coupled cavity systems and show that in reflection the reshaping of the mode profile can either contribute to or oppose the mode pushing, but cannot reverse it.
We have measured mode pushing by the dispersion of a rubidium vapor in a Fabry-Perot cavity and have
shown that the scale factor and sensitivity of a passive cavity can be strongly enhanced by the presence of
such an anomalous dispersion medium. The enhancement is the result of the atom-cavity coupling, which
provides a positive feedback to the cavity response. The cavity sensitivity can also be controlled and tuned
through a pole by a second, optical pumping, beam applied transverse to the cavity. Alternatively, the
sensitivity can be controlled by the introduction of a second counter-propagating input beam that interferes
with the first beam, coherently increasing the cavity absorptance. We show that the pole in the sensitivity
occurs when the sum of the effective group index and an additional cavity delay factor that accounts for mode
reshaping goes to zero, and is an example of an exceptional point, commonly associated with coupled non-
Hermitian Hamiltonian systems. Additionally we show that a normal dispersion feature can decrease the
cavity scale factor and can be generated through velocity selective optical pumping.
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 show that the dynamics of photons in a ring laser gyro are adequately represented by the damped Rabi problem, and thus demonstrate a variety of photonic coherence phenomena analogous to those that occur in atoms. We discuss methods to circumvent the deleterious consequences and exploit the advantageous consequences of these effects. Specifically, we discuss the use of short pulses for the elimination of the gyro dead-band, the use of the dead-band locking frequency for the hypersensitive measurement of scattering and absorption, and the incorporation of fast and slow light media into the cavity for the enhancement of the gyro response.
We predict the propagation of slow and fast light in two co-resonant coupled optical resonators. In coupled resonators, slow light can propagate without attenuation by a cancellation of absorption as a result of mode splitting and destructive interference, whereas transparent fast light propagation can be achieved by the assistance of gain and splitting of the intracavity resonances, which consequently change the dispersion from normal to anomalous. The effective steady-state response of coupled-resonators is derived using the temporal coupled-mode formalism, and the absorptive and dispersive responses are described. Specifically, the occurrence of slow light via coupled-resonator-induced transparency and gain-assisted fast light are discussed.
An iterative method is applied to the analysis of N-coupled ring resonators. Splitting of the modes into N higher-Q modes occurs when the round-trip phase shifts in each ring are equal, in agreement with results for planar resonators and whispering gallery modes (WGMs) in coupled microparticles. This mode-splitting is, therefore, a universal phenomenon for resonant structures, and can lead to reduced thresholds for nonlinear optical effects.