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Journal of the Optical Society of America B

Gain-assisted superluminal propagation in coupled optical resonators

Hongrok Chang, David D. Smith

Published Oct 1, 2005• 34 citations
Publisher

Abstract

We predict transparent superluminal pulse propagation in coresonant coupled optical resonators when a gain element is placed in the resonator closest to the excitation waveguide, provided that the structure is overcoupled, but the resonator farthest from the excitation waveguide is undercoupled sufficiently to avoid lasing at the split modes. The effective steady-state absorptive and dispersive response of coupled resonators are derived, and the coupled-mode approximation is used to determine the conditions for transparent superluminal pulse propagation in these systems. In addition, we find that the effect of pulse compression is minimized when the structure is critically coupled.

DOI
10.1364/josab.22.002237

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We predict transparent superluminal pulse propagation in coresonant coupled optical resonators when a gain element is placed in the resonator closest to the excitation waveguide, provided that the structure is overcoupled, but the resonator farthest from the excitation waveguide is undercoupled sufficiently to avoid lasing at the split modes. The effective steady-state absorptive and dispersive response of coupled resonators are derived, and the coupled-mode approximation is used to determine the conditions for transparent superluminal pulse propagation in these systems. In addition, we find that the effect of pulse compression is minimized when the structure is critically coupled.
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.
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.
We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrödinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.
We demonstrate that a cancellation of absorption occurs on resonance for two (or any even number of) coupled optical resonators, due to mode splitting and classical destructive interference, particularly when the resonator finesse is large and the loss in the resonator farthest from the excitation waveguide is small. The linewidth and group velocity of a collection of such coupled-resonator structures may be decreased by using larger resonators of equal size, by using larger resonators of unequal size where the optical path length of the larger resonator is an integer multiple of that of the smaller one, or by using a larger number of resonators per structure. We explore the analogy between these effects and electromagnetically-induced transparency in an atomic system.