Perturbative approach to continuum generation in a fiber Bragg grating

Area of Science:

• Nonlinear optics
• Wave propagation in optical fibers

Background:

• Nonlinear Schrödinger equation describes pulse propagation in optical fibers.
• Fiber Bragg gratings (FBGs) introduce spectral filtering effects.
• Simulating FBG effects in nonlinear regimes is computationally intensive.

Purpose of the Study:

• To develop a perturbative method for analyzing FBG effects on nonlinear pulse propagation.
• To enable rapid estimation of FBG-induced continuum enhancement.
• To validate the method against full nonlinear simulations and experimental data.

Main Methods:

• Derivation of a perturbative solution to the nonlinear Schrödinger equation.
• Incorporation of a fiber Bragg grating with a narrow bandgap.
• Computation of dispersive waves via integration over the unperturbed solution.
• Application to uniform and sampled gratings.

Main Results:

• The perturbative approach accurately estimates continuum enhancement peaks.
• The method requires only a single nonlinear simulation without the grating.
• Good agreement was found with full nonlinear simulations for various grating types.
• Qualitative reproduction of experimental results was achieved.

Conclusions:

• The derived perturbative solution offers an efficient way to model FBG effects in nonlinear fiber optics.
• This approach significantly reduces computational cost for analyzing continuum generation.
• The method is applicable to different FBG designs and provides reliable predictions.