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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

The maximum group delay in a resonator: an unconventional approach

Andrey B. Matsko, Anatoliy A. Savchenkov, Vladimir S. Ilchenko, Dmitry Strekalov, Lute Maleki

Published Feb 8, 2007• 0 citations
Publisher

Abstract

We introduce a definition of group velocity for a system with a discreet spectrum and apply it to a linear resonator. We show that a positive, negative, or zero group velocity can be obtained for light propagating in the whispering gallery modes of a microspherical resonator. The associated group delay is practically independent of the ring-down time of the resonator. We demonstrate "stopped light" in an experiment with a fused silica microsphere.

DOI
10.1117/12.714218

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We introduce a definition of group velocity for a system with a discreet spectrum and apply it to a linear resonator. We show that a positive, negative, or zero group velocity can be obtained for light propagating in the whispering gallery modes of a microspherical resonator. The associated group delay is practically independent of the ring-down time of the resonator. We demonstrate "stopped light" in an experiment with a fused silica microsphere.
Suitably configured whispering-gallery-mode (WGM) optical resonators have been proposed as delay lines for trains of short light pulses. Until now, it has been common practice to implement an optical delay line as a coiled long optical fiber, which is bulky and tends to be noisy. An alternative has been to implement an optical delay line as a coupled-resonator optical waveguide (a chain of coupled optical resonators), which is compact but limits the width of the pulse spectrum to the width of an optical resonance and thereby places a lower limit on the duration of a pulse. In contrast, a delay line according to the proposal could be implemented as a single WGM resonator, and the pulses delayed by the resonator could be so short that their spectral widths could greatly exceed the spectral width of any single resonance. The proposal emerged from theoretical and experimental studies of the propagation of a pulse train in a WGM resonator. An important element of the theoretical study was recognition that the traditional definition of group velocity in effect, the velocity of a single pulse comprising a packet of waves propagating in a medium, the responsivity of which is a monotonous function of frequency does not necessarily apply in the case of a WGM resonator or other medium having a spectrum consisting of discrete resonance peaks at different frequencies. A new definition of group velocity, applicable to a train of pulses propagating in such a medium, was introduced and found to lead to the discovery of previously unknown features of propagation. Notably, it was found that in a micro - sphere optical resonator that supports a suitable combination of WGM modes, the group velocity for a train of light pulses could be positive, zero, or negative. A positive group velocity could be so small that the delay could be much longer than the ring-down time of the resonator; a delay of such great length is impossible for a single pulse interacting with either a linearly responding lossless resonator or a coupled- resonator optical waveguide.
The optical ring-down time in a silica microsphere resonator is measured using phase-shift cavity ring-down spectroscopy. When detecting Rayleigh backscattered light that is coupled into the input waveguide it is found that the shift of the modulation phase angle, $\ensuremath{\Delta}\ensuremath{\phi}$, is approximately linearly dependent on the amplitude modulation frequency. The microresonator therefore behaves as if it was a delay line. A model involving two different time scales for the buildup of the Rayleigh backscattered light and the decay of the whispering gallery modes is used to explain the observations.
We theoretically study propagation of light in a vertically coupled whispering gallery mode resonator (WGMR) waveguide consisting of a chain of disc WGMRs etched on the surface of a cylinder made of an optically transparent material. The waveguide is capable of reducing the group velocity of light by as much as a factor of a billion, is much more efficient than usual coupled resonator optical waveguides, and compete with slow light atomic systems. We discuss practical as well as fundamental advantages and disadvantages of the resonator and atomic delay lines.
The propagation of light pulses through negative group velocity media is known to give rise to a number of paradoxical situations that seem to violate causality. The solution of these paradoxes has triggered the investigation of a number of interesting and unexpected features of light propagation. Here, we report a combined theoretical and experimental study of the ring-down oscillations in optical cavities filled with a medium with a sufficiently negative frequency dispersion to give a negative round-trip group delay time. We theoretically anticipate that causality imposes the existence of additional resonance peaks in the cavity transmission, resulting in a non-exponential decay of the cavity field and in a breakdown of the cavity decay rate concept. Our predictions are validated by simulations and by an experiment using a room-temperature gas of metastable helium atoms in the detuned electromagnetically induced transparency regime as the cavity medium.