Zero-velocity solitons in high-index photonic crystal fibers

Abstract

Nonlinear propagation in slow-light states of high-index photonic crystal fibers (PCFs) is studied numerically. To avoid divergencies in dispersion and nonlinear parameters around the zero-velocity mode, a time-propagating generalized nonlinear Schrödinger equation is formulated. Calculated slow-light modes in a solid core chalcogenide PCF are used to parameterize the model, which is shown to support standing and moving spatial solitons. Inclusion of Raman scattering slows down moving solitons exponentially, so that the zero-velocity soliton becomes an attractor state. An analytical expression for the deceleration rate that compares favorably with the numerical results is derived. Collisions of successive solitons due to the Raman deceleration are studied numerically, and it is found that the soliton interaction is mostly repulsive, as expected from the established theory of fiber solitons.

Trapping of slow solitons by longitudinal inhomogeneity in high-index photonic crystal fibers

“…In [6], δP was assumed to include only nonlinear terms, but in this paper it will also include a linear term representing deviations from the ideal structure:…”

“…Using Eq. (10) along with the Maxwell equations and eigenmode expansions discussed above, one may derive the propagation equation [6] ∂A m ðt;…”

“…It has recently been suggested that slow-light states in fibers could conveniently be excited by optical solitons, which would asymptotically approach the zero-velocity state due to Raman scattering [5,6]. It is well-known that solitons are relatively stable against long-wavelength perturbations [7,8] and that sufficiently slow solitons may be trapped or reflected by longitudinal inhomogeneities [9].…”

“…On the other hand, it suggests that unintentional imperfections could make it difficult to control the behavior of slow solitons. The purpose of this paper is to model the propagation of slow solitons in a realistic As 2 Se 3 fiber design [6], to quantify the effect of weak disorder on soliton stability and propagation.…”

“…In a recent paper, a generalized nonlinear Schrödinger equation propagating in the timedomain was developed and used to model soliton propagation in a microstructured As 2 Se 3 fiber supporting slow modes around 2 μm in a small-area solid core [6]. The time-domain propagation formulation is highly advantageous for describing pulses with very slow, and possibly bidirectional, motion in the longitudinal dimension.…”