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IEEE PhotonicsGlobal

Pulse Transmission across a Single Optical Ring-Resonator with Negative Group Velocity: Theory and Experiment

Henri P. Uranus, Leimeng Zhuang, Chris G. H. Roeloffzen, H.J.W.M. Hoekstra

Published Dec 1, 2008• 1 citation
Publisher

Abstract

We study pulse transmission across a single optical ring-resonator circuit theoretically. The theory is supported by experimental measurements. From the study, we discuss intuitively the fulfillment of the causality rules in negative delay phenomenon, which occurs when the circuit possesses a negative group velocity.
DOI
10.1109/ipgc.2008.4781334

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The possibility to engineer the group velocity $(v_g)$ of light has attracted much attention in the last couple of years. One of the most exotic phenomena in this research field is the negative $v_g$phenomenon. Negative $v_g$ implies that if we send light pulse into the optical medium, the peak of the output will leave the output before the peak of the input pulse entering the medium, i.e. a pulse 'advancement' or negative delay. This paper will discuss such counter-intuitive 'back-to-the-future' phenomenon and its direct time-domain experimental observations on a real photonic chip using measurement equipments available in a typical optical telecommunication laboratory. Comments on the consistency of the phenomenon with the causality principles as well as possible application will also be briefly discussed.

•Sep 1, 2008•1 citation
Abstract: We report a direct experimental observation of pulse temporal behavior in an integrated optical two-port ring-resonator circuit as a function of coupling strength, including the transition across the critical coupling point. We demonstrate the observation of pulse ‘advancement’ in the negative vg regime and pulse delay in the positive vg regime. We also observed a smooth transition of the pulse shape from highly negative to highly positive vg (or vice versa) through a pulse splitting phenomenon. The observed phenomena agree well to theoretical simulations.
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.
Transfer matrix method (TMM) was used to study the phenomena of ‘slow’- and ‘fast’-light in a single two-port ring-resonator (TPRR) circuit theoretically. Their classifications into ‘slow’- and ‘fast’-light with negative and positive group velocity (v_g), where ‘slow’ means |v_g|<c and ‘fast’ means |v_g|>c, will be introduced. The role of such phenomena in controlling light-matter interaction and pulse delay/’advancement’ will be discussed. Direct experimental observations on pulse temporal behaviors in the regimes of ‘slow’- and ‘fast’-light with negative and positive v_g will be demonstrated, showing large and small pulse ‘advancement’ and delay, respectively. Pulse splitting phenomenon as a transition from a highly delayed to a highly ‘advanced’ pulse and vice versa, will also be experimentally demonstrated. Theoretical simulations on the pulse delay and ‘advancement’ based on the TMM and Fourier transform, which show a good qualitative agreement to the experimental results, will also be presented. The exploitation of ‘slow’-light, either with positive or negative v_g for enhancing light-matter interaction will be discussed through evaluating their effects to the performance of integrated-optical refractometric sensor. It will be shown that when the light is ‘slow’, either with negative or positive v_g, there is enhancement of the sensor sensitivity. An integrated-optical sensor which exploits such properties and exhibits sensitivity of one order better than the present day state-of-the-art commercial Mach-Zehnder interferometer refractometric sensor, will be presented.
A two-port ring-resonator circuit is studied theoretically. It is shown that superluminal and negative group velocity (vg) phenomena can occur in both a passive two-port ring-resonator circuit with loss and an active one with gain. We present numerical observations of temporal behavior of a Gaussian pulse passing through circuits having such properties. We also show that when the negative vg is ‘slow’ (|vg|<<c), there is enhanced sensitivity of the phase shift to the ring effective index changes, which suggests its potential for highly sensitive optical sensing applications.
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 possibility to engineer the group velocity (vg)(v_g)(vg​) of light has attracted much attention in the last couple of years. One of the most exotic phenomena in this research field is the negative vgv_gvg​phenomenon. Negative vgv_gvg​ implies that if we send light pulse into the optical medium, the peak of the output will leave the output before the peak of the input pulse entering the medium, i.e. a pulse 'advancement' or negative delay. This paper will discuss such counter-intuitive 'back-to-the-future' phenomenon and its direct time-domain experimental observations on a real photonic chip using measurement equipments available in a typical optical telecommunication laboratory. Comments on the consistency of the phenomenon with the causality principles as well as possible application will also be briefly discussed.