On-resonance material fast light

TL;DR

This paper provides a theoretical analysis of how coherent light pulses propagate through a linear medium with a narrow transmission dip, focusing on pulse advancement and optimizing fractional advance.

Contribution

It combines temporal and spectral methods to derive analytical expressions for pulse propagation near resonance, improving understanding of fast light phenomena.

Findings

Analytical expressions match numerical solutions

Pulse maximum can be advanced beyond vacuum propagation

Fractional advance can be optimized for given conditions

Abstract

We theoretically revisit the problem of the propagation of coherent light pulses through a linear medium when the carrier frequency of the pulses coincides with the minimum of a narrow dip in the medium transmission. Considering realistic contrasts between the maximum and minimum transmission of the medium and incident pulses of strictly finite duration, we combine temporal and spectral approaches to obtain analytical expressions of the transmitted pulse that reproduce the main features of the exact numerical solutions derived by fast Fourier transform. A special attention is paid to the advance of the pulse maximum over that of a pulse covering the same distance in vacuum and the ratio of this advance to the pulse duration (fractional advance) is optimized.