The creation of electromagnetic metamaterials is an important activity. The latter should anticipate the kind of
applications in which unique metamaterial behaviour can appear. This paper addresses nonlinear wave phenomena in
both the strongly and the weakly nonlinear regimes. It inevitably involves novel nonlinear guided waves and solitonic
beam activities. In this context, some magnetooptic control is introduced. In addition, the kind of structural complexity
that can lead to trapped rainbows will be briefly examined. Finally, some aspects are made of vortex control in a
diffraction-managed metamaterial is presented.
The literature is alive with papers devoted to the design of metamaterials and there appears to be a particular desire to create photonic applications that will operate at THz frequencies and above. At one level the modelling of suitable artificial molecules is straightforward but nevertheless the approximations involved need to be able to inspire confidence for optical frequency operation. This presentation will set out a modelling activity that is known to be satisfactory only over certain frequency ranges. Split-ring and omega particles will be specifically investigated and the possibilities discovered will be related to the current experimental expertise. The detailed manner in which the constitutive relations can be controlled and the novel way in which an envelope equation emerges for even the most complex structure is exposed. The transmission and reflection properties of nano-structured materials will be discussed within a magneto-optic environment. Simulations of sub-wavelength transmission through holes in metallic and magneto-optic screens will be discussed using finite-difference time-domain (FDTD) methods. Modelling the interaction of light beams with metamaterials is developed, again using FDTD techniques, and it is shown that special care needs to be taken with structures that have sharp external edges. Finally, a summary of the problems surrounding efficient computations will be shown and some discussion of the role of genetic algorithms in metamaterial design will be featured.
A study of optical vortices solitons propagation under the influence of an inhomogeneous external magnetic field is presented. The external magnetic field is applied on the z-axis, which is also the direction of propagation, so that a Faraday configuration is created. This study of magnetooptic vortices in a bulk, nonlinear, gyrotropic media leads to an investigation of the coupling of the electric field components, E<sub>x</sub> and E<sub>y</sub>, in the (x,y) plane. An optical beam propagating in the bulk is modelled by coupled equations in which the nonlinear refractive index is Kerr-like bulk optical nonlinearity. A transformation to rotating coordinates enables circularly polarised waves to be selected and a peak in the magnetisation over the centre of the beam is used. An important spatial dependence of the magnetisation parameter, defined as Q(x), stimulates novel singular behaviour. To demonstrate this kind of gyrotropy experimentally the usual Kerr nonlinearity may be too weak for comfortable observations but semi-magnetic semiconductors and atomic gases are shown to be possible candidates for which Faraday rotations are impressive.
A description of the fascinating coupling between gyrotropic media and negative refracting media will be presented. The article will address negative phase velocity media and particular types of dielectric-gyrotropic film-dielectric systems in which the applied magnetic field may result in a magneto-optic, or gyromagnetic, influence. The control features use a diverse family of dispersion
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. A planar guide is investigated first, in which the waveguide
is a slab consisting of a double negative medium, sandwiched between a substrate and cladding that are simple
dielectrics. The TE modes are addressed because they lend themselves to accurate analysis when 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. The rest of the paper addresses a comprehensive finite difference-
time-domain analysis. It uses spatial soliton behaviour in the advanced example section. An interesting
soliton-lens arrangement is presented that deploys positive and negative slabs to create a novel cancellation effect.
A brief review is developed of the manner in which forced gyrotropic effects can be exploited through the application of a magnetic field to special classes of materials. Magnetooptics brings controlled complexity into important two- and threedimensional phenomena. These are addressed through the introduction of dissipative-external energy input effects and optical singularities. The latter create edge and screw dislocations with latter being identified with optical vortices. The way in which magnetization distributions control vortex dynamics is discussed.