  The evidence that double negative media, with an effective negative
permittivity, and an effective negative permeability, can be manufactured to
operate at frequencies ranging from microwave to optical is ushering in a new
era of metamaterials. They are referred to here as 'left-handed', even though a
variety of names is evident from the literature. In anticipation of a demand
for highly structured integrated practical waveguides, this paper addresses the
impact of this type of medium upon waveguides that can be also nonlinear. After
an interesting historical overview and an exposure of some straightforward
concepts, a planar guide is investigated, in which the waveguide is a slab
consisting of a left-handed medium sandwiched between a substrate and cladding
that are simple dielectrics. The substrate and cladding display a Kerr-type
nonlinear response. Because of the nonlinear properties of the Kerr media, the
power flow direction can be controlled by the intensity of the electric field.
A comprehensive finite-difference-time-domain (FDTD) analysis is presented that
concentrates upon spatial soliton behaviour. An interesting soliton-lens
arrangement is investigated that lends itself to a novel cancellation effect.
