Coherent diffractive imaging beyond the projection approximation: waveguiding at extreme ultraviolet wavelengths.

We study extreme-ultraviolet wave propagation within optically thick nanostructures by means of high-resolution coherent diffractive imaging using high-harmonic radiation. Exit waves from different objects are reconstructed by phase retrieval algorithms, and are shown to be dominated by waveguiding within the sample. The experiments provide a direct visualization of extreme-ultraviolet guided modes, and demonstrate that multiple scattering is a generic feature in extruded nanoscale geometries. The observations are successfully reproduced in numerical and semi-analytical simulations.