### Photonic Band Structure of Fibonacci Superlattices with Metamaterials. Part 1: The Algebraic Method of Calculation for Lossless Layers

#### Abstract

We study the properties of the photonic band structure (PBS) of infinite and binary Fibonacci superlattices (FS) containing metamaterial lossless layers. The transfer matrix method (TMM) and periodic boundary conditions are applied. The algebraic method of PBS calculations, based on the Bloch theorem, is described and used. The dispersion relations, for both type of light polarization, characterizing peculiarities of PBS are calculated numerically and presented. Fractal properties of a photonic band structure and the existence of so called zero-n gaps are established.

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