Abstract
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 as well as at the interface between two dissimilar nonlinear lattices. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having either zero or nonzero semi-infinite backgrounds. For all cases, the method provides conditions involving the values of the propagation constant of the stationary solutions, the linear refractive index and the dimensions of 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 such as their remarkable robustness which could facilitate their experimental observation.
Highlights
Surface waves appear in diverse areas of physics, chemistry, biology, and display properties that have no counterpart in the bulk [1]
In this work we present a phase space method for the construction of analytical solitary wave solutions located at the interface of a nonlinear (Kerr) Kronig-Penney lattice with a homogeneous linear or nonlinear medium as well as at the interface between two dissimilar nonlinear lattices
The method is based on the phase space geometry of the underlying dynamical system describing the profiles of the stationary solutions
Summary
Surface waves appear in diverse areas of physics, chemistry, biology, and display properties that have no counterpart in the bulk [1]. The utilization of periodic layered media in guided wave optical applications has been a subject of theoretical and experimental investigations for a few decades Among these studies of particular interest is the investigation of the wave guiding properties of the interface between such a periodic medium and a homogeneous medium and the formation of the surface waves. In nonlinear optics TE, TM and mixed-polarization surface waves, traveling along the single interface between homogeneous dielectric media, has been theoretically predicted and analyzed in several works [11, 12, 13, 14, 15, 16, 17, 18] and the formation of surface states has been shown for cases where no linear states exist. This novel class of solutions is obtained under quite generic conditions, while the method is applicable to a large variety of systems, including more complex geometries consisting of linear/nonlinear, self-focusing/defocusing and homogeneous/periodic parts, while other
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