Rate equation reformulation including coherent excitation: application to periodic protocols based on spectral hole-burning

A large number of signal-processing protocols are based on recording a spectral pattern via spectral hole-burning in an inhomogeneously broadened absorption profile. We present a simulation method specifically designed for periodic excitation sequences leading to the creation of a spectral pattern. This method is applicable to any multilevel atomic structure. The atomic variables’ coherent dynamics are solved for a single temporal excitation step. The result is expressed as an equivalent population transfer rate. This way, the whole sequence is described as a matrix product and the steady state of the system under periodic excitation is easily derived. The propagation through the atomic medium is fully decoupled from the temporal evolution. We apply this method to the engraving of a spectral grating in a large-absorption Tm:YAG sample for wideband spectral analysis.