A comprehensive theory is developed for describing the nonlinear propagation of optical pulses through silicon waveguides with nanoscale dimensions. Our theory includes not only the vectorial nature of optical modes but also the coupling between the transverse electric and magnetic modes occurring for arbitrarily polarized optical fields. We have studied the dependence of relevant nonlinear parameters on waveguide dimensions and found a class of waveguide geometries for which self-phase modulation can have a dramatic impact on the polarization state of the optical field. Self-induced polarization changes are studied for both the continuous and pulsed optical fields propagating in silicon waveguides. We also discuss the possibility of using these effects for intensity discrimination and pulse compression.
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