Deflection and diffraction of x rays bound to curved surfaces.

We present two new x-ray optical effects observed on a whispering-gallery waveguide. The first is a gradual in-surface deflection of guided waves caused by the non-Euclidean intrinsic curvature of the waveguide surface. The second is the excitation of in-surface dynamical diffraction modes that reflects the strong influence of the surface photonic band structure of a crystalline waveguide. Both phenomena portend a rich array of basic and applied x-ray optical potentialities.