Propagation of the ordinary and extraordinary modulated optical pulses in a nonlinear Kerr-type birefringent optical waveguide: Analytical description

The purpose of this work is to describe theoretically the behavior of modulated pulses in nonlinear birefringent optical waveguides and particularly in the optical fibers, by taking into account the anisotropy of the medium as well as the orientation of the optical axis with respect to the propagation direction of an incoming pulse. Firstly, the multiple times scale method is used to describe the behavior of an optical pulse in the waveguide whose optical axis is perpendicular to the direction of propagation of the pulse. It appears that in the nonlinear regime, the optical pulse splits into two different modes in propagation namely an ordinary mode and an extraordinary mode which propagate with different group velocities. These modes are described by the different nonlinear Schrodinger (NLS) equations involving nonlinear Kerr -like responses. Next, we turn attention to the waveguide whose the optical axis is parallel to the direction of propagation of an incoming pulse and found that the two modes continue to exist, and are also described by different NLS equations. In addition, we show that for some parameter regime, the two modes become identical and described by the same NLS equation.