Localization and Scaling Behavior of Polariton-Gap in Fibonacci and Symmetric Fibonacci-Class Piezomagnetic Superlattices

Abstract

A comparative study is made on the localization and scaling behavior in piezomagnetic Fibonacci and symmetric Fibonacci-class [SFC( n )] superlattices. For this photon–phonon coupled system, the polaritonic band-gap structures and transmission spectra both show a pattern of self-similarity, the fractal pattern in transmission spectra clearly demonstrates the (quasi)localization nature of polaritons. For Fibonacci superlattices self-similarity behavior takes place between the l th and the ( l +3)th generations, the scaling index α' = τ 3 = 4.236 with \(\tau = 0.5(\sqrt{5} + 1)\) denoting the golden mean. While for the generalized symmetric Fibonacci-class [SFC( n )] superlattices, self-similarity behavior occurs between the l th and the ( l +1)th generations and the scaling index \(\alpha'' = 0.5(n + \sqrt{n^{2} + 4})\). We conclude that the internal symmetric structure is responsible for the evolution of such scaling behavior.