Abstract

There is currently quite a lot of interest in spatial solitions^1-3 planar optical wave guides. The first calculations, involving bright and dark solitons propagating in magneto-optic materials, will be reported. They follow up recent work of the authors, based on Lagrangian formalism. It will be shown that magneto-optic problems divide, roughly, into polar, longitudinal, and transverse configurations, according to the orientation of the magnetic field to the soliton propagation direction. The system consists of a thin nonlinear film, sandwiched between a linear, nonmagnetic, semi-infinite, cladding, and a semi-infinite, magnetic, linear substrate. It is assumed that the power levels are only sufficient to drive the film into a nonlinear state. The discussion will show that this is reasonable and that the longitudinal and polar cases are of maximum, strategic interest. Technically, both cases are controlled off-diagonal elements in the dielectric tensor, which are proportional to a parameter Q, which, when unsealed, lies between 10^-2 and 10^-4. Although these values seem to be quite small, in absolute terms they compete vigorously with the nonlinearity. The starting point is a derivation of a new family of coupled envelope equations; all within the familiar, slowly varying amplitude, weakly nonlinear, weakly guiding formalism. We then demonstrate, by a scaling technique, that there exists an important, magneto-optic, cross-coupling term, which can sometimes be dominant. New parameters will be introduced that will be used mathematically, and numerically, to show that, with readily available materials, an external magnetic field is a powerful control parameter. The weakness of the nonlinearity is in accord with experiment and means that the modal fields are unchanged during the accumulation of nonlinear phase and magnetic Kerr phase shifts. Both are represented, mathematically, within a Lagrangian model. In the simplest case, when the magnetisation is a constant, very simple mathematical results for bright and dark solitons flow from this novel theory. They are vindicated by the numerical experiments. Beams that are attractive to each other in the absence of a magnetic field can be turned against each other. Dark beam channels can be significantly modified and multiple beam interactions are shown to imply a new range of devices. In particular, polarisation-dependent gating devices with small beam control will be used as illustrations. A really interesting possibility is the use of a magnetisation distribution. It is possible to laser anneal doped YIG, for example, and freeze the magnetisation into different directions at different points along the boundary, thus yielding various forms of Q = Q(x).

© 1994 IEEE