The modal fields within x-ray lithographic masks are analyzed using standard optical waveguide theory and a ‘‘beam propagation method (BPM).’’ From the properties of the guided modes, it is shown that for small feature sizes the field no longer resembles the geometrical shape of the absorber structure, but strongly the shape of the modes. TE and TM modes behave almost identically and, thus, scalar diffraction calculations are generally valid in the domain of soft x rays. Mode cut-off of the fundamental mode never occurs. Using such guiding properties it is possible to generate spatially concentrated (16 nm) x-ray fields with much larger absorber openings (40 nm). A BPM with fast Fourier transforms is employed to efficiently calculate the accurate wave front propagation inside the mask, to determine the physical boundary condition downstream of the absorber structure and to calculate the diffracted image in the wafer plane. The BPM in free space is equivalent with the Rayleigh–Sommerfeld diffraction formula. The method turns out to be very useful in field image calculations of x-ray lithographic systems using phase and absorption mask patterns of arbitrary shapes and surface roughnesses.