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

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.