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Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates hasrevealed significant spatial inhomogeneity on the nanoscale. Regions on theorder of a coherence length in size show variations of the magnitude of thesuperconducting gap of order $\pm20%$ or more. An important unresolved questionis whether or not these variations are also present in the bulk, and how theyinfluence superconducting properties. As many theories and data analyses forhigh-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude,this is a pressing question. We consider the far-infrared optical conductivityand evaluate, within an effective medium approximation, what signatures ofspatial variations in gap magnitude are present in various optical quantities.In addition to the case of d-wave superconductivity, relevant to the high-$T_c$cuprates, we have also considered s-wave gap symmetry in order to provideexpected signatures of inhomogeneities for superconductors in general. Whilesignatures of gap inhomogeneities can be strongly manifested in s-wavesuperconductors, we find that the far-infrared optical conductivity in d-waveis robust against such inhomogeneity.

Signatures of superconducting gap inhomogeneities in optical properties