Nonlinear surface modes and Tamm states in periodic photonic structures

We study the formation of nonlinear localized modes and discrete surface solitons near the edges or interfaces of weakly coupled nonlinear optical waveguides, one-dimensional photonic crystals. We draw an analogy between the staggered nonlinear surface optical modes and the surface Tamm states known in the electronic theory. We discuss the crossover between discrete solitons inside the array and surface solitons at the edge of the array by analyzing the families of even and odd nonlinear localized modes located at finite distances from the edge of a waveguide array. Then, we study the formation of guided modes localized at an interface separating two different periodic photonic lattices. Employing the effective discrete model, we analyze linear and nonlinear interface modes and also predict the existence of stable interface solitons including the hybrid staggered/unstaggered lattice solitons with the tails belonging to the spectral gaps of different types. Finally, we discuss briefly the recent experimental observation of discrete surface solitons and nonlinear Tamm states.