Helmholtz solitons in diffusive Kerr-type media

Abstract

6Soliton evolution at diffusive Kerr-type media is analyzed within the framework of the Helmholtz theory. The angular limitations of previous paraxial studies are overcome when both soliton propagation and diffusion of carriers are allowed to occur along any arbitrary direction. A model including two-dimensional carrier diffusion is proposed and its exact soliton solutions within the weakly nonlocal regime are presented. The restriction of carrier diffusion to a single transverse coordinate leads to the breakdown of the rotational symmetry of the Helmholtz framework and soliton behavior becomes angular dependent. We study the impact of this limitation in an intrinsic angular scenario, such as a nonlinear interface.

Reply to “Comment on ‘Spatial optical solitons in highly nonlocal media”'

“…For light propagation in the presence of a highly nonlocal response, the latter smooths out the longitudinal variations in the light-induced index well, thus minimizing back reflections. The inclusion of longitudinal nonlocality improves the agreement between the mathematical model and the physical system [47,48]. In essence, our overall model (i.e., including light evolution and lightmatter interaction) satisfies the paraxial approximation better than standard ones (i.e., when longitudinal nonlocality is neglected).…”

Soliton refraction and Goos–Hänchen shifts at diffusion step nonlocal interfaces

“…In all these works, the properties of Helmholtz solitons have been properly addressed and essential corrections to their paraxial counterparts have been highlighted. More recently, this Helmholtz treatment has been applied to the study of nonlocal media where nonlocality arises from the diffusion of carriers [36].…”

“…H(ξ) is the Heaviside function that addresses the first (H(ξ)=0 if ξ<0) or the second (H(ξ)=1 if ξ0) medium. As regards the nonlocal contribution, d 01 and d 02 are the normalized diffusion coefficients in each medium [36,44], while f nl is the nonlocal contribution to the refractive index [36]:…”

“…The analysis we perform in this work is based on the formalism presented in [44], which, in turn, builds upon previous results of [36]. In [44], however, this general formalism is used exclusively for studying the dual switching behavior that arises under a specific combination of changes in the local and nonlocal contributions to the refractive index across the interface.…”

“…The analysis of the system response to small changes of the interface parameters must first consider the limitations inherent to working within the framework of the Helmholtz theory [25,26] where a weakly nonlocal regime [36,48] This regime would correspond to the one described in the upper right corner of table 1.…”