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arXiv:physics/9803015 · Physical Review A

Superluminal optical phase conjugation: Pulse reshaping and instability

M. Blaauboer, Abraham G. Kofman, Alexander E. Kozhekin, Gershon Kurizki, Daan Lenstra, A. Lodder

Published Jun 1, 1998• 38 citations
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Abstract

We theoretically investigate the response of optical phase conjugators to incident probe pulses. In the stable (subthreshold) operating regime of an optical phase conjugator it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability.

DOI
10.1103/physreva.57.4905

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We theoretically investigate the response of optical phase conjugators to incident probe pulses. In the stable (subthreshold) operating regime of an optical phase conjugator it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability.
We theoretically analyze wave packet transmission through a phase-conjugating mirror and show that the transmission of a suitably chosen input pulse is superluminal, i.e. the peak of the pulse emerges from the mirror before the time it takes to travel the same distance in vacuum. This pulse reshaping effect can be attributed directly to the dispersion relation in the nonlinear medium constituting the mirror. Thus, for the first time a connection is laid between optical phase conjugation and superluminal behavior. In view of its additional amplifying ability, a phase-conjugating mirror is a most promising candidate for an experimental observation of tachyonic signatures.
We show that optical tachyonic dispersion corresponding to superluminal (faster than-light) group velocities characterizes parametrically amplifying media. The turn-on of parametric amplification in finite media, followed by illumination by spectrally narrow probe wavepackets, can give rise to transient tachyonic wavepackets. In the stable (sub-threshold) operating regime of an optical phase conjugator it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability. Remarkably, the quantum information transmitted by probe or conjugate pulses, albeit causal, is confined to times corresponding to superluminal velocities. These phenomena are explicitly analyzed for four-wave mixing, stimulated Raman scattering and parametric downconversion.
Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.
In an open / type system with the spontaneously generated coherence (SGC), when the probe and driving fields have different frequencies, the switching of the group velocity of the probe pulse from subluminal to superluminal is realized not only by adjusting values of the relative phase between the probe and driving fields but also by varying values of the incoherent pumping rate. For the subluminal propagation, the system always exhibits the probe absorption, however, the superluminal propagation is always companied with gain of the probe field.
Pulse propagation through 1-dimensional stratified media is studied. The general features of pulse propagation in relation to the delay or advancement of the pulse are discussed. It is shown that in a lossless system with spatial symmetry the reflected and the transmitted pulses have the same delay or advancement. The phase times and the explicit output pulse profiles for an input Gaussian pulse are calculated. While recalling recent results for a variety of systems (resonant absorbers or heterogeneous medium in a Fabry-Perot cavity, a slab of negative index medium, a left-handed/right-handed periodic structure, etc.), new results involving coupled waveguides and a high finesse cavity containing an electromagnetically induced transparency (EIT) medium are presented. Calculations clearly show that for pulses with a carrier tuned at the resonance of the stratified media, one generally has subluminal propagation. Alternatively, in stop gaps or away from the resonances one ends up with superluminal transit. In the case of the EIT cavity it is shown that the large dispersion offered by the intracavity medium can lead to substantial superluminality (ng≃−106) with peak transmission as high as 20%. This is in sharp contrast to large signal attenuation for usual superluminal transit. Note also that EIT, to the best of the authors knowledge, has so far been used to achieve only slow light.