A coupled-mode analysis of modulation instability in optical fibers

A coupled-mode formulation in the frequency domain has been developed and applied to the analysis of the modulation instability (MI) due to the self- and cross-phase modulations (SPM and XPM) in optical fibers. The modulation instability of two copropagating beams with the same polarization at different carrier frequencies is examined in detail. It is demonstrated that, by identifying the phase-matching conditions among different sideband components, the modulation instability due to the SPM and the XPM may be described by a set of reduced coupled-mode equations. Simple analytical expressions for the gain are derived under this condition. The approximate formulas are compared with the full wave solutions and their scopes of validity are discussed