Vector modulation instability in birefringent graded-index multimode fibers

Abstract

We study vectorial modulation instability occurring inside a birefringent graded-index (GRIN) fiber when the two polarization components of the optical field are coupled nonlinearly through cross-phase modulation. In the scalar case in which only modes of one polarization are excited, the geometric parametric instability is known to produce an infinite number of sidebands around the wavelength of the input optical beam. We show that the birefringence of a GRIN fiber splits each of these sidebands into a triplet, whose frequency spacing depends on the differential group delay between the orthogonally polarized components. We verify the predictions of the linear stability analysis numerically by solving two coupled nonlinear Schrödinger equations that include spatial self-imaging effects through an effective nonlinear parameter. We present results for both continuous and pulsed optical beams experiencing normal or anomalous group-velocity dispersion inside a GRIN fiber.