From fast to slow light in a resonantly driven absorbing medium

TL;DR

This paper provides an analytical and numerical study of how a resonantly driven absorbing medium affects the propagation of amplitude-modulated signals, revealing conditions for fast and slow light effects based on intensity and relaxation times.

Contribution

It derives an exact analytical transfer function for amplitude modulation in a two-level medium, elucidating the transition from fast to slow light regimes.

Findings

Group delay can be negative (fast light) at low cw intensities.

Group delay becomes positive (slow light) at higher cw intensities.

Maximum group delay is limited by the population relaxation time.

Abstract

We theoretically study the propagation through a resonant absorbing medium of a time-dependent perturbation modulating the amplitude of a continuous wave (cw). Modeling the medium as a system of two-level atoms and linearizing the Maxwell-Bloch equations for the perturbation, we establish an exact analytical expression of the transfer function relating the Fourier transforms of the incident and transmitted perturbations. It directly gives the gain and the phase shift undergone in the medium by a harmonic modulation. For the case of a pulse modulation, it enables us to determine the transmission time of the pulse center-of-mass (group delay), evidencing the relative contributions of the coherent and incoherent (population) relaxation. We show that the group delay has a negative value (fast light) fixed by the coherent effects when the cw intensity is small compared to the saturation intensity and becomes positive (slow light) when this intensity increases, before attaining a maximum that cannot exceed the population relaxation time. The analytical results are completed by numerical determinations of the shape of the transmitted pulses in the different regimes.