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Nowadays, unique characteristics of surface electromagnetic waves, particularly, surface plasmons supported by a specially designed photonic crystal find numerous applications. We propose to exploit an evident analogy between such a photonic crystal and a structure with a sine-modulated refractive index. The light propagation inside the latter is described by the famous Mathieu’s differential equation. This application of the Mathieu’s equation can be useful for a design of multilayer structures, and also for fundamental understanding of electromagnetic phenomena in inhomogeneous media.
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