Parametric resonance in periodically tapered optical fibres: Scalar and vectorial modulational instability bands

Parametric resonance (PR) is a well-known instability phenomenon which occurs in systems the parameters of which are varied periodically during evolution. It is natural that such a general phenomenon was associated to the equally important instability process that is ubiquitous in nonlinear optics: modulational instability (MI). The link between PR and MI has been established in relation to the periodic re-amplification of signals in long-haul telecommunication optical cables. However photonic crystal fibres (PCFs), owing to their group velocity dispersion (GVD) landscape and improved confinement properties, permit to observe this phenomenon on a much shorter length scale (metres instead of kilometres). Moreover a smooth sinusoidal variation of parameters can be achieved. In this work we report on the existence of MI bands in the normal dispersion regime which are accurately explained as a PR phenomenon. They occur both in the scalar nonlinear Schrödinger (NLS) and in the vectorial NLS [e.g. for highly birefringent fibres (HBF)] propagation equations.