The field of complex photonic media encompasses many leading-edge areas in physics, chemistry, nanotechnology, materials science, and engineering. In Tutorials in Complex Photonic Media, leading experts have brought together 19 tutorials on breakthroughs in modern optics, such as negative refraction, chiral media, plasmonics, photonic crystals, and organic photonics.
This text will help students, engineers, and scientists entering the field to become familiar with the interrelated aspects of the subject. It also serves well as a supplemental text in introductory and advanced courses on optical materials, nanotechnology, physical optics, or photonic metamaterials.
We have measured the microwave transmission between 12 and 18 GHz through wire arrays formed into two
dimensional square lattices. One array made of copper wire 0.14 mm in radius consisted of five rows by
21 columns having a lattice constant of 5.2 mm. This array exhibited a pass band above 15 GHz, in good
agreement with the calculated plasma frequency found from an expression for the permittivity derived in the
long wavelength limit. A second array was made with Nichrome wire of radius 18 μm and lattice constant
1.1 mm. This array was filled with dielectric loaded with powdered magnetite. A sample of this metamaterial
5.8 mm thick and with no externally applied magnetic field exhibited a pass band above 17 GHz. Implications
for creating metamaterials with a negative index of refraction from wire arrays embedded in a magnetic host
Metamaterials demonstrating a negative phase velocity for light usually consist of arrays of wires and cut-ring structures. Such media are characterized by both the permittivity and permeability being negative. Calculations of the Ohmic loss associated with the wires alone indicate that dissipation can be minimized by making them of metal of the highest possible conductivity and by having the largest possible wire radius. Replacement of the cut-ring structures with a ferrite further reduces losses since ferrites can be less lossy than typical conductors. The upper limit to the wire radius is ultimately set by the requirement that the permittivity be negative. The calculations take into account the skin depth within the wires. Although bigger wires lead to more volume in which Ohmic losses are present, these wires are more effective in shorting out the electric field and thereby decreasing the Ohmic loss. An array made of large diameter and high conductivity wires leads to a strong electromagnetic response and a well defined plasma frequency for the wire array.
A metamaterial exhibiting a negative index of refraction can be
fabricated from an array of conducting wires cladded with non-magnetic dielectric and embedded in a magnetic host medium. The wires are responsible for the ε < 0 property and the magnetic medium for the μ < 0 property. A near exact calculation of the electromagnetic response of this metamaterial indicated that the bandwidth over which n < 0 depends primarily on the magnetization of the magnetic host and on the radius of the wire, the outer radius of the cladding, and the lattice constant of the wire array. For readily available materials the dissipation within the medium is mainly due to Ohmic losses within the wire and not magnetic dissipation within the magnetic host. The losses can be minimized by choosing an high conductivity metal for the wire and by having the radius of the wire and outer radius of the cladding as large as
practical consistent with maintaining ε < 0.
Periodic two-dimensional arrays of straight, conducting wires have been
used to create structures with negative permittivity and have been
incorporated into structures exhibiting a negative index of refraction or
phase velocity. In these cases the electromagnetic wave propagating
through the structure has its electric field parallel to the wires.
Solutions to Maxwell's equations for transverse electromagnetic waves in
these structures have been found previously using either an approximate
permittivity appropriate to the long wavelength limit or been determined
numerically using a finite element analysis. The calculation presented
here is an exact solution of Maxwell's equations for a square wire array
valid for wavelengths larger that the wire diameter. The permittivity
calculated in the long wavelength limit predicts propagation constants
which agree remarkably well with the exact solution down to wavelengths
comparable to the lattice constant of the wire array, with the first
serious discrepancy occurring at the first Bragg reflection. The exact
solution shows that the gaps in the frequency versus propagation constant
relation in the  direction decrease in size as the order of the Bragg
reflection increases. Also the second, fourth, sixth, etc., Bragg
reflections are complicated by the emergence of higher order grating modes
which result in dispersion relation crossings near the Bragg reflection.
Materials having both a negative permittivity and a negative permeability allow the free propagation of electromagnetic waves with a negative phase velocity (NPV), i.e., the phase velocity is opposite the direction of energy propagation. An NPV material can be made with a lattice of fine wires cladded in nonmagnetoc insulation and embedded in a magnetic host. The wires give rise to the negative permittivity, the magnetic host supplies the negative permeability, and the nonmagnetic cladding minimizes the coupling between the wires and the magnetic host. This structure is so simple that it has the potential to be made small enough for NPV materials to operate in the far infrared. This presentation describes calculations developed to compare to experiments at microwave frequencies with cladded wires in ferrimagnetic hosts.
There has been considerable interest generated by the demonstration of (epsilon) < 0, (mu) < 0 composite materials. These negative index of refraction materials, a subset of the class of materials labeled 'left-handed', possess two different arrays of resonant structures which separately give rise to negative (epsilon) and (mu) over the appropriate microwave frequency interval. Any attempt to significantly increase the operating frequency will require shrinking the resonant elements to a nanostructure. Replacing the array of elements responsible for (mu) < 0 with a nonconducting ferrimagnet significantly reduces the complexity of the resulting nanostructured material. This presentation includes a brief overview of the behavior of negative index of refraction materials and an enumeration of the advantages and disadvantages of using a ferrimagnet to produce (mu) < 0. In addition, calculations of the transmission of electromagnetic waves through a ferrimagnet based negative index of refraction material are presented. In particular, the prospects for operating in the far IR and microwave regimes, pro9blems with the interaction between the (epsilon) < 0 structures and the ferrimagnet, and tunability with externally applied magnetic fields are discussed.
Magnetoelasticity encompasses a wide range of phenomena including, but not limited to, volume and Joule magnetostriction, the Villari effect, direct and inverse Wiedemann effects, the (Delta) E effect, and a magnetoelastic contribution to the apparent magnetic anisotropy. These effects are conveniently codified in a magnetoelastic energy density which, together with the magnetic (including exchange) and elastic energy densities, provides a consistent thermodynamic description of magnetoelasticity. In this review I shall briefly examine each of these effects and the corresponding terms of the energy density. This energy density is described by a collection of material constants which, in principle, are derivable from theory. The physical coordinates which are maintained constant in any experiment dictate the relevant combination of these material constants which is ultimately observed. Static and dynamic measurements are generally carried out with different constraints and, not surprisingly, these experiments measure different combinations of material parameters. For example, the highly magnetostrictive smart material Terfenol-D (Dy0.73Tb0.27Fe1.95) has a static magnetic anisotropy which is markedly different from the anisotropy exhibited in a dynamic measurement.
In this talk, which is tutorial in nature, I present a review of the phenomenon of magmetostriction in magnetic materials. Magnetostriction has its origin in the spin-orbit coupling of the electrons responsible for the magnetization. Terfenol-D (Dy0.73Tb0.27Fe1.95) has such an enormous magnetostriction parameter that is has acquired smart material status. Suitably oriented crystals have strain changes of approximately equals 0.2% when the magnetization direction is rotated by 90 degree(s). Devices based on t his material include microphones, inch-worm motors, actuators, etc. On a fundamental level, magnetostriction provides an interation mechanism between photons and phonons. Calculations and experimental data for 17 GHz microwave reflection and transmission measurements are presented. Finally, possible experiments at optical frequencies are suggested.