Coupled solitons in rare-earth doped two-mode fiber

We present first ever analytical solutions for shape-preserving pulses in a Kerr nonlinear two-mode fiber doped with 3-level ? atoms. The two modes are near-resonant with the two transitions of the atomic system. We show the existence of quasi-stable coupled bright-dark pairs if the group velocity dispersion has opposite signs at the two mode frequencies. We demonstrate the remarkable possibility allowed by the fiber dispersion for the existence of a new class of solutions for unequal coupling constants for the two modes. We present the conditions for existence and the analytical form of these solutions in presence of atomic detuning. We confirm numerically the analytical solutions for the spatio-temporal evolution of coupled solitary waves.