The spectral transmission properties of a self-similar optical Fabry-Perot resonator are theoretically studied. The structure considered can be realized by alternation of two dielectric layers of different refractive indices such that the highest refractive-index layers belong to a triadic Cantor set. The transmission spectrum exhibits localized peaks inside forbidden frequency band gaps. This feature could be useful in the design of novel filters. Moreover the self-similarity of the structure is reflected in a weak self-similarity in the transmission spectrum. A comparison with a regular periodic structure is also presented.
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Bertolotti et al. (1994) studied this question.
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