Finite superposition solutions for surface states in a type of photonic superlattices

TL;DR

This paper introduces an analytical method to derive and understand stable surface states in photonic superlattices by superposing a finite number of unstable Bloch waves, providing exact solutions and insights into their parametric dependence.

Contribution

The authors develop an exact analytical approach to construct stable surface states in photonic superlattices using superpositions of unstable Bloch waves, advancing understanding of surface phenomena in lattice systems.

Findings

Derived a finite class of in-gap surface states in bichromatic superlattices.

Constructed stable surface states analytically near interfaces.

Explored parametric dependence of surface states.

Abstract

We develop an efficient method to derive a class of surface states in photonic superlattices. In a kind of infinite bichromatic superlattices satisfying some specific conditions, we obtain a finite portion of their in-gap states, which are superpositions of finite numbers of their unstable Bloch waves. By using these unstable in-gap states, we construct exactly several stable surface states near various interfaces in photonic superlattices. We analytically explore the parametric dependence of these exact surface states. Our analysis provides an exact demonstration for the existence of surface states and would be also helpful to understand surface states in other lattice systems.