Investigation of self-filtering unstable resonator for soft x-ray lasers

In this paper, it is proposed that the self-filtering unstable resonator (SFUR) is suitable for soft x-ray lasers which have active medium with a short-gain-lifetime. In order to evaluate the idea, we have analyzed the self-filtering unstable resonator in two dimensions with Ne-like Fe soft x-ray active medium for transitions 2p53p→2p53s and 3d94d→3d94p at 25.5 nm. The role of field-limiting aperture in mode propagation has been shown. Moreover, beam quality factor M2 has been calculated and output mode behavior studied and compared with a plane-parallel (PP) resonator of equal length. The calculations indicate that the M2 factor in SFUR resonator is smaller than PP resonator and therefore output beam divergence is lower and the mode quality is much better. It is expected that a high quality beam of soft x-ray laser with brightness of the order 1013W/cm2sr and energy more than 10 nJ may be achievable with a properly designed diffraction-filtered unstable resonator.