Non - Focusing Instabilities in Coupled ,

The nonlinear coupling of two scalar nonlinear Schrr odinger (NLS) elds results in non-focusing instabilities that exist independently of the well-known modulational instability of the focusing NLS equation. The focusing versus defocusing behavior of scalar NLS elds is a well-known model for the corresponding behavior of pulse transmission in optical bers in the anomalous (focusing) versus normal (defocusing) dispersion regime 19, 20]. For bers with birefringence (induced by an asymmetry in the cross-section,) the scalar NLS elds for two orthogonal polarization modes couple nonlinearly 26]. Experiments by Rothenberg 32, 33] have demonstrated a new type of modulational instability in a birefringent normal dispersion ber, and he proposes this cross-phase coupling instability as a mechanism for the generation of ultra-fast, terahertz optical oscillations. In this paper the non-focusing plane wave instability in an integrable coupled nonlinear Schrr odinger (CNLS) partial diierential equation system is contrasted with the focusing instability from two perspectives: traditional linearized stability analysis and integrable methods based on periodic inverse spectral theory. The latter approach is a crucial rst step toward a nonlinear, nonlocal understanding of this new optical instability analogous to that developed