Modelling of supercontinuum generation in highly nonlinear photonic crystal fibres

Abstract

We present a detailed explanation of the modelling of supercontinuum generation in highly nonlinear photonic crystal fibers (PCFs) with low-power picosecond pulses. Due to the strong nonlinearity and necessary broad-band description, the model takes into account self-phase-modulation, cross-phase-modulation, four-wave-mixing, stimulated Raman scattering, linear loss, birefringence, and up to 7th order dispersion. Variations in the fibre parameters along the length of the fibre are described as random fluctuations of the dispersion coefficients, whose strength is estimated from experiments. Our numerical results show that in the PCF direct degenerate four-wave-mixing Stokes and anti-Stokes spectral components are efficiently generated, around which the spectrum broadens in the same way as around the pump. It is important not to loose the power in these additional spectral lines. Depending on the frequency shift relative to the pump and on the gain band-width for the parametric process, the Stokes and anti-Stokes lines may finally merge with the pump, resulting in an ultra-broad spectrum. We show how the dispersion profile of the PCF (in particular a cobweb PCF) must be designed to achieve not only merging, but also stability of the ultra-broad supercontinuum spectrum towards fluctuations in the fibre parameters.