From fast to slow light in a resonantly driven absorbing medium

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 twolevel system 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.

Strong Reverse Saturation and Fast-Light in Ruby

“…This effect has been used to demonstrate a pulse advancement which could indicate a fast-light effect with a very large and negative group index. We showed that this observation can also be explained very well based on the sluggish response of ruby, consistent with the previous theories [17][18][19][20]. Investigating the relative validity of the sluggish time-dependent absorption theory versus the coherent population oscillation theory will require further experimental investigations.…”

“…This phenomenon had been explained earlier based on coherent population oscillation and hole burning [11][12][13]. While this model continues to be debated [11,12,[14][15][16][17][18][19][20], we consider a simple model based on rate-equations that explains the seemingly fast-light effect without the need of hole or anti-hole burning. In the following, first, we confirm that ruby exhibits RSA.…”

Light propagation through atomic vapours

“…Alternatively, the speed may exceed the speed of light in a vacuum, or even be negative [232,233]: a pulse in this regime is termed fast or superluminal light [234,235]. Through manipulation of experimental parameters it is even possible to observe fast and slow light in the same medium [236]. The possibility that light, and therefore information, could travel faster than the universal speed limit of c set by Einstein's theory of relativity has troubling consequences for the principle of causality [231,237].…”