The mechanism of the polarizational mode instability in birefringent fiberoptics

We show that the soliton solutions of the integrable Manakov equation exhib it an instability under arbitrarily small Hamiltonian perturbations. The in stability arises from eigenvalues embedded in the essential spectrum of the associated linearized operators; these eigenvalues are dislodged by smooth perturbations. Specifically we consider perturbations which arise in ber o ptics as a result of birefringence, including the so-called four-wave mixin g term. Employing the Evans function and a Dirichlet expansion on the stabl e manifold of the linearized system, we obtain rigorous perturbation result s and compute the stability diagram of the fast wave for all physical value s of the birefringent parameters, using a novel numerical scheme derived fr om the Dirichlet expansion.