Nonlinear light localization around the core of a `holey' fiber

We examine localized surface modes in the core of a photonic crystal fiber composed of a finite nonlinear (Kerr) hexagonal waveguide array with a central defect. Using a discrete approach, we find the fundamental surface mode and its stability window. We also examine an unstaggered, ring-shaped surface mode and find that it is always unstable, decaying to the single-site fundamental surface mode. A continuous model computation reveals that an initial vortex excitation (S=1) of small amplitude around the central hole can survive for a relatively long evolution distance. At high amplitudes, however, it decays to a ring configuration with no well-defined phase structure.