# Slow light in saturable absorbers : Progress in the resolution of a controversy

## TL;DR

This paper resolves a controversy in slow light transmission through saturable absorbers by showing that the incoherent bleaching and CPO models are fundamentally equivalent, with experimental validation supporting the incoherent model.

## Contribution

It clarifies the relationship between two competing models of slow light in saturable absorbers and provides experimental evidence favoring the incoherent bleaching model.

## Key findings

- The two models are fundamentally equivalent under corrected assumptions.
- Experimental results on ruby pulses support the incoherent bleaching model.
- The shape of transmitted pulses matches analytical predictions of the incoherent model.

## Abstract

There are two opposing models in the analysis of the slow transmission of light pulses through saturable absorbers. The canonical incoherent bleaching model simply explains the slow transmission by combined effects of saturation and of non-instantaneous response of the medium resulting in absorption of the front part of the incident pulse larger than that of its rear. The second model, referred to as the coherent-population-oscillations (CPO) model, considers light beams whose intensity is slightly pulse modulated and attributes the time delay of the transmitted pulse to a reduction of the group velocity. We point out some inconsistencies in the CPO model and show that the two models lie in reality on the same hypotheses, the equations derived in the duly rectified CPO model being local expressions of the integral equations obtained in the incoherent bleaching model. For large modulation index, the CPO model, based on linearized equations, breaks down. The incoherent bleaching model then predicts that the transmitted light should vanish when the intensity of the incident light is strictly zero. This point is confirmed by the experiments that we have performed on ruby with square-wave incident pulses and we show that the whole shape of the observed pulses agrees with that derived analytically by means of the incoherent bleaching model. We also determine in this model the corresponding evolution of the fluorescence light, which seems to have been evidenced in other experiments.