Incorporating excitation-induced dephasing into the Maxwell–Bloch numerical modeling of photon echoes

We describe the incorporation of excitation-induced dephasing (EID) into the Maxwell–Bloch numerical simulation of photon echoes. At each time step of the usual numerical integration, stochastic frequency jumps of ions—caused by excitation of neighboring ions—is modeled by convolving each Bloch vector with the Bloch vectors of nearby frequency detunings. The width of this convolution kernel follows the instantaneous change in overall population, integrated over the simulated bandwidth. This approach is validated by extensive comparison against published and original experimental results. The enhanced numerical model is then used to investigate the accuracy of experiments designed to extrapolate to the intrinsic dephasing time T2 from data taken in the presence of EID. Such a modeling capability offers improved understanding of experimental results, and should allow quantitative analysis of engineering tradeoffs in realistic optical coherent transient applications.