Helmholtz solitons at nonlinear interfaces

Abstract

Reflection and refraction of spatial solitons at dielectric interfaces, accommodating arbitrarily angles of incidence, is studied. Analysis is based on Helmholtz soliton theory, which eliminates the angular restriction associated with the paraxial approximation. A novel generalization of Snell's law is discovered that is valid for collimated light beams and the entire angular domain. Our new theoretical predictions are shown to be in excellent agreement with full numerical simulations. New qualitative features of soliton refraction and limitations of previous paraxial analyses are highlighted.

Nonlinear interfaces: intrinsically nonparaxial regimes and effects

“…In absence of discontinuity, ∆ = 0 and α = 1, one recovers the NLH for a homogeneous medium [24] from (3), which can be written as [37] κ ∂ 2 u ∂ζ 2 + i ∂u ∂ζ + 1 2…”

“…By phase-matching of exact soliton solutions [26] for ξ < 0 and ξ ≥ 0, one obtains a generalised Snell's law [37] that governs the evolution of beams at boundary separating two Kerr focusing media γn 01 cos(θ i ) = n 02 cos(θ t ).…”

“…Parameter δ alone can be used to predict how the soliton refracts at the interface: θ t > θ i (external refraction) for δ < 0, θ t < θ i (internal refraction) for δ > 0 and θ t = θ i for δ = 0. This last case is a total transparency condition [37], obtained when the linear and nonlinear refractive index mismatches cancel each other. Under this condition, the soliton crosses the interface at a constant angle.…”

“…The results presented in this paper extend the analysis of this generalised Snell's law (Section 2). Moreover, we also explore highly nonparaxial contexts, not previously addressed in [37] and found at interfaces exhibiting nonlinear and linear external refraction. Nonlinear external refraction is demonstrated to exist at interfaces where internal refraction would be found for linear plane waves (Section 3).…”

“…In a previous work [37] a generalised Snell's law was introduced and its validity was assessed for interfaces exhibiting linear internal refraction, where beams crossing an interface undergo small angular deviations. The results presented in this paper extend the analysis of this generalised Snell's law (Section 2).…”