Fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains

TL;DR

This paper theoretically investigates the fundamental wave modes of a probe photon in optical fibers with periodic pulse trains, revealing shape-preserving solitons and their dependence on nonlinear effects and walk-off phenomena.

Contribution

It provides exact solutions for probe wave modes in dispersion-managed fibers, highlighting the formation of orthogonal solitons and their characteristics under cross-phase modulation.

Findings

Identifies shape-preserving probe modes robust against dispersion.

Predicts degenerate bright and dark soliton trains.

Shows modes have finite momentum and are not fully transparent with walk-off.

Abstract

Wave modes induced by cross-phase reshaping of a probe photon in the guiding structure of a periodic train of temporal pulses are investigated theoretically with emphasis on exact solutions to the wave equation for the probe. The study has direct connection with recent advances on the issue of light control by light, the focus being on the trapping of a low-power probe by a temporal sequence of periodically matched high-power pulses of a dispersion-managed optical fiber. The problem is formulated in terms of the nonlinear optical fiber equation with averaged dispersion, coupled to a linear equation for the probe including a cross-phase modulation term. Shape-preserving modes which are robust against the dispersion are shown to be induced in the probe, they form a family of mutually orthogonal solitons the characteristic features of which are determined by the competition between the self-phase and cross-phase effects. Considering a specific context of this competition, the theory predicts two degenerate modes representing a train of bright signals and one mode which describes a train of dark signals. When the walk-off between the pump and probe is taken into consideration, these modes have finite-momentum envelopes and none of them is totally transparent vis-\`a-vis the optical pump soliton.