Power dependent soliton location and stability in complex photonic structures

Y Kominis,K Hizanidis

doi:10.1364/oe.16.012124

Abstract

The presence of spatial inhomogeneity in a nonlinear medium results in the breaking of the translational invariance of the underlying propagation equation. As a result traveling wave soliton solutions do not exist in general for such systems, while stationary solitons are located in fixed positions with respect to the inhomogeneous spatial structure. In simple photonic structures with monochromatic modulation of the linear refractive index, soliton position and stability do not depend on the characteristics of the soliton such as power, width and propagation constant. In this work, we show that for more complex photonic structures where either one of the refractive indices (linear or nonlinear) is modulated by more than one wavenumbers, or both of them are modulated, soliton position and stability depends strongly on its characteristics. The latter results in additional functionality related to soliton discrimination in such structures. The respective power (or width/propagation constant) dependent bifurcations are studied in terms of a Melnikov-type theory. The latter is used for the determination of the specific positions, with respect to the spatial structure, where solitons can be located. A wide variety of cases are studied, including solitons in periodic and quasiperiodic lattices where both the linear and the nonlinear refractive index are spatially modulated. The investigation of a wide variety of inhomogeneities provides physical insight for the design of a spatial structure and the control of the position and stability of a localized wave.

Highlights

Electromagnetic waves propagating in periodically structured dielectric materials, such as Photonic Crystals (PCs), share many properties with electron waves in ordinary semiconductors [1, 2] and matter-wave realizations of a Bose-Einstein Condensate (BEC) in optical lattices [3, 4]
In this work we study lattice soliton formation and stability in a configuration of planar geometry where both the linear and the nonlinear refractive index are inhomogeneous with respect to the transverse dimension, with their spatial dependence being of a generic form describing either periodic or quasiperiodic structures [40]
The inhomogeneity of the medium and the resulting breaking of the translational invariance have been related to homoclinic bifurcations of the underlying dynamical system describing stationary solutions

Summary

Introduction

Electromagnetic waves propagating in periodically structured dielectric materials, such as Photonic Crystals (PCs), share many properties with electron waves in ordinary semiconductors [1, 2] and matter-wave realizations of a Bose-Einstein Condensate (BEC) in optical lattices [3, 4]. The linear material properties can be controlled either by choosing a suitable configuration for the lattice or dynamically in the sense of optically induced waveguide arrays and lattices [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] Along this direction, lattice solitons in photonic structures with periodically varying linear refractive index have been extensively investigated either by studying the original continuous model, consisting of the NonLinear Schrodinger Equation (NLSE) describing soliton propagation [17], or by utilizing approximate discrete models [17, 18]. In this work we study lattice soliton formation and stability in a configuration of planar geometry where both the linear and the nonlinear refractive index are inhomogeneous with respect to the transverse dimension, with their spatial dependence being of a generic form describing either periodic or quasiperiodic structures [40].

Model and stationary solutions

Findings

Summary and conclusions