Control of the nonlinear polarisation dynamics in a semiconductor waveguide with a periodic magnetic field

Nonlinear polarisation dynamics in semiconductor waveguides is a topic of current interest with applications in vectorial spatial solitons and all-optical switching schemes. It is generally found that as the change in refractive index induced by the Kerr nonlinearity becomes comparable to the birefringence of the waveguide, the single-polarised (TE and TM) stable stationary eigenmode becomes unstable and there is an emergence of a pair of mixed-polarised stable stationary eigenmodes (i.e. bifurcation). The bifurcation in the mode with the lower propagation constant is attributable to the anisotropy in the nonlinear refraction between the TE and TM polarisations. These phenomena have been scrutinised both in the plane-wave and spatial soliton cases obtaining analytic results for the bifurcation threshold. Of interest is the additional degree of control obtained with a longitudinal magnetic field through the magneto-optic effect which may, for example, allow the polarisation state to be switched from one stationary state to another. The polarisation dynamics are analysed in terms of the Stokes parameters allowing the evolution trajectories to be mapped on a Poincare sphere for the non-dissipative case. We derive the Hamiltonian for the system consisting of terms for the anisotropic Kerr nonlinearity, waveguide birefringence and longitudinal magneto-optic effect. From the Hamiltonian the evolution equations in terms of the Stokes parameters can be subsequently obtained.