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Self-seeding is a promising approach to significantly narrow the self-amplified spontaneous emission bandwidth of X-ray free-electron lasers (FELs) and hence to produce nearly transform-limited pulses. We study the radiation propagation through a grating monochromator installed at the Linac Coherent Light Source (LCLS). The monochromator design is based on a toroidal VLS grating working at a fixed incidence angle mounting without an entrance slit. It covers the spectral range from 500 eV to 1000 eV. The optical system was studied using a wave optics method to evaluate the performance of the self-seeding scheme. Our wave optics analysis takes into account the finite size of the coherent source, third-order aberrations and height error of the optical elements. Two propagation approaches are studied with time-dependent FEL simulations. In addition, the pulse-front tilt phenomenon effect is illustrated

Soft x-ray self-seeding simulation methods and their application for the Linac Coherent Light Source