Feasibility considerations of a soft-x-ray distributed feedback laser pumped by an x-ray free electron laser

We discuss the feasibility of a soft-x-ray distributed feedback laser (DFL) pumped by an x-ray free electron laser (X-FEL). The DFL under consideration is a Mg/SiC bi-layered Bragg reflector pumped by a single X-FEL bunch at 57.4 eV, stimulating the Mg L2,3 emission at 49 eV corresponding to the 3s-3d -> 2p1/2,3/2 transition. Based on a model developed by Yariv and Yeh and an extended coupled-wave theory, we show that it would be possible to obtain a threshold gain compatible with the pumping provided by available X-FEL facilities.