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This chapter presents a theoretical analysis of electromagnetic field propagation in planar waveguides and experimental results obtained with synchrotron and laboratory sources. The basic equations of electromagnetic modes in a front-coupling planar WG are presented in section 2, and section 3 reports a comparison between computer simulation and experimental results in the general case of tapered waveguides. Then an original algorithm to retrieve the amplitude and phase of the electromagnetic field at the exit of the planar WG using an iterative method is presented (section 4). A theoretical analysis and computer simulation for WG with an additional periodic structure on the side reflecting walls of the WG are described in section 5, and experimental results are discussed in chapter 6 proving that spatial resolutions of few hundred nanometres in phase contrast imaging can be obtained with a laboratory source. Conclusions are drawn in section 7.

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