On Bright and Dark Breathers in Lattices with Saturable Nonlinearity

Abstract

In the past two decades the special attention is devoted to the strongly localized modes [1] which are promising candidates for guiding, steering, and switching of light beams in the nonlinear optical lattices. The effect of energy localization through discreteness and nonlinearity is universal and relevant for many non-optical systems, such as DNA-promoter dynamics [2], discrete breathers in a Josephson ladder [3], localized modes in the anharmonic crystals [4], or localization of matter waves in the Bose–Einstein condensates using optically-induced periodic potentials [5]. Bright discrete solitons have been studied in detail in photonic lattices exhibiting cubic, quadratic, saturable, and nonlocal nonlinearity [1, 6–9]. Because of various experimental difficulties and demand for higher input power dark solitons are investigated discernible rarely when compared to their bright analog [10, 11]. Very recently, stable propagation of on-site and inter-site dark solitons were experimentally observed in the self-defocusing lithium niobate waveguide arrays with saturable nonlinearity at microwatt power level [12, 13]. In this paper the comparative study of the moving localized bright and dark modes in lattices with saturable nonlinearity [14] is presented. This study is based on the grand canonical free energy concept [15] and analysis of the eigenvalue spectra of the localized configurations.