The Mechanism of the Polarizational Mode Instability in Birefringent Fiber Optics
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Bibliographic record
Abstract
We show that the soliton solutions of the integrable Manakov equation exhibit an instability under arbitrarily small Hamiltonian perturbations. The instability 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 fiber optics as a result of birefringence, including the so-called four-wave mixing term. Employing the Evans function and a Dirichlet expansion on the stable manifold of the linearized system, we obtain rigorous perturbation results and compute the stability diagram of the fast wave for all physical values of the birefringent parameters, using a novel numerical scheme derived from the Dirichlet expansion.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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