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We study discrete surface solitons in semi-infinite, one-dimensional,nonlinear (Kerr), quasiperiodic waveguide arrays of the Fibonacci andAubry-Andr\'e types, and explore different families of localized surface modes,as a function of optical power content (`nonlinearity') and quasiperiodicstrength (`disorder'). We find a strong asymmetry in the power content of themode as a function of the propagation constant, between the cases of focussingand defocussing nonlinearity, in both models. We also examine the dynamicalevolution of a completely-localized initial excitation at the array surface. Wefind that in general, for a given optical power, a smaller quasiperiodicstrength is required to effect localization at the surface than in the bulk.Also, for fixed quasiperiodic strength, a smaller optical power is needed tolocalize the excitation at the edge than inside the bulk.

Surface solitons in quasiperiodic nonlinear photonic lattices