Analysis of the physical origin of surface modes on finite-size photonic crystals

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The physical properties of the surface modes, which can exist on photonic crystals with limited extension in one direction, are investigated. We show that the dispersion relations of the modes present a continuous transition when crossing the edge of the band gap. Using the homogenization limit, we show that the periodic structure perpendicular to the crystal boundaries plays only a limited role in the phenomenon, namely that of confining the field close to the surface. It is also shown that the underlying physics of these surface modes can be understood using a very simple model where the guiding effect is due to a high index dielectric layer.