Compact surface Fano states embedded in the continuum of waveguide arrays.

We describe theoretically and observe experimentally the formation of a surface state in a semi-infinite waveguide array with a side-coupled waveguide, designed to simultaneously achieve Fano and Fabry-Perot resonances. We demonstrate that the surface mode is compact, with all energy concentrated in a few waveguides at the edge and no field penetration beyond the side-coupled waveguide position. Furthermore, we show that by broadening the spectral band in the rest of the waveguide array it is possible to suppress exponentially localized modes, while the Fano state having the eigenvalue embedded in the continuum is preserved.