The theoretical analysis on photon echoes is reported in a resonant multi-level system with level degeneracy, by a general consideration. With respect to the system possessing more than three-fold degeneracy, the intensity of photon echoes depends not only on the areas of the exciting optical pulses, but also on their polarization characteristics. In particular, it was found that some anomalous echoes change their intensities with the polarization directions of exciting optical pulses which have different frequencies from those of the echoes because of the coherent coupling of resonant transitions with common energy level and the interference effect of transitions through the degenerate sublevels. In the first half of this paper the general formulation on the multi-level system with arbitrary degeneracy is performed, and in the second half, the application of the general theory to some typical examples is also given.
The three-level photon echo has been described in different works[1,2] by using rotating wave approximation but none of them didnt get re-sults which show the effects of detuning frequencies on frequency of ground level of system; also the effect distance between two generated levels on signal resonance is being neglected. In this work, we stud-ied a-type system theoretically and numerically. By considering the Dopplers effect in environment, we get different equation for polariza-tion of echo signal and its intensity. 1