Surface trapped x-rays: Whispering-gallery modes at lambda=0.7 angstrom

X-ray bound states trapped on a curved surface are realized by coupling subangstrom photons at grazing angles into a bent silicon wafer with adjustable radius. At small radii of curvature the usual ray approximation breaks down and new phenomena associated with wave optical behavior of x-ray surface eigenmodes are revealed. For such samples, tunneling is shown to extinguish all but the ground state surface eigenmode, whose presence may be detected after extremely long distances of propagation along the surface.