Surface lattice solitons: Analytical solutions

A novel phase-space method is employed for the construction of analytical stationary solitary waves located at the interface between a periodic nonlinear lattice of the Kronig-Penney type and a linear (or nonlinear) homogeneous medium. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having a zero background or nonzero semi-infinite background. For all cases. the method provides conditions for the values of the propagation constant of the stationary solutions and the linear refractive index in each part in order to assure existence of solutions with specific profile characteristics. The evolution of the analytical solutions under propagation is investigated for cases of realistic configurations and interesting features are presented while their remarkable robustness is shown to facilitate their experimental observation.