Abstract
We develop a full theoretical analysis of the nonlinear interactions of the two polarizations of a waveguide by means of a vectorial model of pulse propagation which applies to high index subwavelength waveguides. In such waveguides there is an anisotropy in the nonlinear behavior of the two polarizations that originates entirely from the waveguide structure, and leads to switching properties. We determine the stability properties of the steady state solutions by means of a Lagrangian formulation. We find all static solutions of the nonlinear system, including those that are periodic with respect to the optical fiber length as well as nonperiodic soliton solutions, and analyze these solutions by means of a Hamiltonian formulation. We discuss in particular the switching solutions which lie near the unstable steady states, since they lead to self-polarization flipping which can in principle be employed to construct fast optical switches and optical logic gates.
Highlights
The Kerr nonlinear interaction of the two polarizations of the propagating modes of a waveguide leads to a host of physical effects that are significant from both fundamental and application points of view
We develop a model of nonlinear interactions of the two polarizations using full vectorial nonlinear pulse propagation equations, with which we analyze the nonlinear interactions in the emerging class of subwavelength and high index optical waveguides
As defined and demonstrated here through simulation by means of a full vectorial model, are attractive for practical applications, since they allow nonlinear self-flipping of the polarization states of light propagating in an optical waveguide
Summary
The Kerr nonlinear interaction of the two polarizations of the propagating modes of a waveguide leads to a host of physical effects that are significant from both fundamental and application points of view. Important features of this model are: (1) the propagating modes of the waveguide are not, in general, transverse and have large z components and, (2) the orthogonality condition of different polarizations over the cross section of the waveguide is given by e1(x, y) × h∗2(x, y) zdA = 0, rather than e1(x, y) e2(x, y) = 0 as in the scalar models These aspects lead to an improved understanding of many nonlinear effects in HIS-WGs; it was predicted in [33], for example, that within the vectorial model the Kerr effective nonlinear coefficients of HIS-WGs have higher values than those predicted by the scalar models due to the contribution of the zcomponent of the electric field, as later confirmed experimentally [46].
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