Photon echo decays in optically dense media

In this paper we investigate the influence of optical density or superradiance on the photon echo decay using the coupled Maxwell–Bloch equations. Our theory applies to optically thick but dilute media, where the transition dipole–dipole interaction between nearby chromophores is negligible, but the far-field interaction is not. Corrections to the (normalized) echo decay in the optically thin limit, INe(tπ)=exp [−4tπ/T2] (tπ and T2 are the interpulse separation times and the coherence relaxation times, respectively), are found by expanding the polarization, excited state population and pulse electric fields in powers of ζ=αz, where α is the inverse Beer’s absorption length, and z is the coordinate along the pulse propagation axis. Numerical solutions for optically thick samples are also presented, and when ζ≫1 the normalized echo intensity is found to obey the simple analytic form: INe(tπ)=2 exp [−tπ/T1]−1, when tπ/T1