We present an analytical approach to describe field propagation along a planar x-ray waveguide (WG) in the presence of absorption losses. The method utilizes the complete expression for the complex index of refraction in solving the Helmholtz equation describing the guided modes. In this way, the propagation modes for the WG are no longer imposed to be standing waves and the energy flow from the core to the cladding, a consequence of the absorption in the cladding, can be calculated. In addition, the method accurately describes the field coupling between a plane wave and the WG, reproducing the self-imaging phenomenon. The case of partially coherent illumination has also been calculated for a realistic laboratory x-ray source.
© 2013 Optical Society of America
Original Manuscript: February 25, 2013
Revised Manuscript: April 17, 2013
Manuscript Accepted: April 22, 2013
Published: May 21, 2013
K. J. Tsanaktsidis, D. M. Paganin, and D. Pelliccia, "Analytical description of partially coherent propagation and absorption losses in x-ray planar waveguides," Opt. Lett. 38, 1808-1810 (2013)