Surface plasmons on a quasiperiodic grating

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A method is presented for calculating the frequencies of non-retarded surface plasmons propagating on a semi-infinite medium with a surface profile described by a one-dimension quasiperiodic function. The profiles are generated, in analogy with previous work on quasiperiodic superlattices, by repeating unitary cells constructed according to an inflation rule. Dispersion relations are obtained for a semi-infinite free-electron metal as the active medium, with surface profiles obeying the Fibonacci and Thue-Morse sequences.