Influence of statistical errors in refractive index on fibre Bragg grating reflection

Solitons in a Box-Shaped Wave Field with Noise: Perturbation Theory and Statistics

We investigate the fundamental problem of the nonlinear wave field scattering data corrections in response to a perturbation of initial condition using inverse scattering transform theory. We present a complete theoretical linear perturbation framework to evaluate first-order corrections of the full set of the scattering data within the integrable one-dimensional focusing nonlinear Schrödinger equation (NLSE). The general scattering data portrait reveals nonlinear coherent structures-solitons-playing the key role in the wave field evolution. Applying the developed theory to a classic box-shaped wave field, we solve the derived equations analytically for a single Fourier mode acting as a perturbation to the initial condition, thus, leading to the sensitivity closed-form expressions for basic soliton characteristics, i.e., the amplitude, velocity, phase, and its position. With the appropriate statistical averaging, we model the soliton noise-induced effects resulting in compact relations for standard deviations of soliton parameters. Relying on a concept of a virtual soliton eigenvalue, we derive the probability of a soliton emergence or the opposite due to noise and illustrate these theoretical predictions with direct numerical simulations of the NLSE evolution. The presented framework can be generalized to other integrable systems and wave field patterns.

Femtosecond point-by-point inscription of Bragg gratings by drawing a coated fiber through ferrule

A ferrule-based method of direct fs FBG inscription through protective plastic coating is demonstrated. Fluctuations of fiber core position relative to the writing fs beam are compensated by the developed auto-alignment system. As a result, high-quality FBGs with length from 0.1 to 50 mm are fabricated in polyimide-coated fibers, whose spectra are well described by the theory. The fabricated FBGs have great potential in sensor applications at high temperature and harsh environments both point-action and distributed ones.