Electric field enhancement has been actively studied recently and many metallic structures that are
capable of locally enhancing electric field have been reported. The Babinet's principle can be utilized,
especially in the form of Booker's extension, to transform the known electric field enhancing structures
into magnetic field enhancing structures. The authors explain this transformation process and discuss
the regime in which this principle breaks down. Unless the metals used can be well approximated with
a PEC model, the principle's predictions fails to hold true. Authors confirm this aspect using numerical
simulations based on realistic material parameters for actual metals. There is large discrepancy
especially when the structural dimensions are comparable or less than the skin-depth at the wavelength
of interest. An alternative way to achieve magnetic field enhancement is presented and the design of a
connected bow-tie structure is proposed as an example. FDTD simulation results confirm the operation
of the proposed structure.
Maxwell's equations describe the classical electromagnetic properties of all systems, including metamaterials, which are
periodic and highly inhomogeneous. In studies of metamaterials, however, one typically further assumes that their low-frequency
properties are described by Maxwell's equations in an equivalent homogenous medium. Hence, tremendous
recent efforts have focused on discovering structures with unusual properties in electrical permittivity and magnetic
permeability tensors. Here we offer an alternative viewpoint, by designing three-dimensional metamaterials, which
may be best described by effective uniform media that is non-Maxwellian. In the low-frequency limit, these
metamaterials support multi-component effective fields, with the numbers of field-components designable by geometry.
Our work indicates that the physics of metamaterials is far richer than previously anticipated. In particular, new effective
low-energy theory with high symmetry can emerge from topological complexity alone.
We present a theoretical condition for achieving three-dimensional self-collimation of light in a photonic crystal. Such effects provide a very interesting mechanism for developing integrated circuits in 3D crystals that can be synthesized in a large scale. We also show that in a dielectric waveguide with a photonic crystal core, the modal properties are very unusual. In particular, a single-mode waveguide for the fundamental mode with a large core and a strong confinement can be realized. This is potentially important for suppressing modal competition in laser structures.