The Raman effect and solitons in an elliptical optical fiber

We derive a general system of coupled nonlinear Schrödinger equations, describing light in a bimodal optical fiber, taking into account the quasi-instantaneous Raman effect, group-velocity birefringence, phase-velocity birefringence, and optical activity, and for light with general ellipticity. The Raman coefficients prove to obey a relation which depends on the ellipticity. When group-velocity birefringence and optical activity are both non-zero, polarization couples to the changing frequency, so soliton polarization cannot be held constant in this case. Without optical activity, there are solitons with constant polarization either entirely in one polarization ("simple") or equally divided between the two polarizations ("vector"). At ellipticity angle 0° to 35.3°, the simple solitons are stable and the vector solitons are unstable, and vice versa for ellipticity angle 35.3° to 90°. With optical activity, the polarization can be constant, but with a rather more complex form. Stability is also examined, and bistability is found in some circumstances.