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, IeN(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: IeN(tπ) = 2 exp [- t π/T1] - 1, when tπ/T1<1n 2 and IeN (tπ) = 0 for longer times. (T 1 is the population relaxation time.) In this limit the echo decay is independent of the coherence relaxation time T2, illustrating the profound effect intermolecular coupling may have on any nonlinear optical measurement. We show that at low temperatures, when T2 = 2T 1, the echo decay rate increases as the optical density increases. However, for higher temperatures, when T2 is sufficiently shorter than 2T1, the opposite behavior results, that is, the echo decay rate decreases as the optical density increases. © 1990 American Institute of Physics.
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