Calculation of material properties and ray tracing in transformation media

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability

Focussing Light Using Negative Refraction

A slab of negatively refracting material, thickness d, can focus an image at a distance 2d from the object. The negative slab cancels an equal thickness of positive space. This result is a special case of a much wider class of focussing: any medium can be optically cancelled by an equal thickness of material constructed to be an inverted mirror image of the medium, with, $\epsilon$ and $\mu$ reversed in sign. We introduce the powerful technique of coordinate transformation, mapping a known system into an equivalent system, to extend the result to a much wider class of structures including cylinders, spheres, and intersecting planes and hence show how to produce magnified images. All the images are perfect in the sense that both the near and far fields are brought to a focus and hence reveal sub wavelength details.Comment: pdf file onl

Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients

We analyze the reflection and transmission coefficients calculated from transfer matrix simulations on finite lenghts of electromagnetic metamaterials, to determine the effective permittivity and permeability. We perform this analysis on structures composed of periodic arrangements of wires, split ring resonators (SRRs) and both wires and SRRs. We find the recovered frequency-dependent permittivity and permeability are entirely consistent with analytic expressions predicted by effective medium arguments. Of particular relevance are that a wire medium exhibits a frequency region in which the real part of permittivity is negative, and SRRs produce a frequency region in which the real part of permeability is negative. In the combination structure, at frequencies where both the recovered real part of permittivity and permeability are simultaneously negative, the real part of the index-of-refraction is found also to be unambigously negative.Comment: *.pdf file, 5 figure

Ray-optical refraction with confocal lenslet arrays

Two parallel lenslet arrays with focal lengths f1 and f2 that share a common focal plane (that is, which are separated by a distance f1+f2) can refract transmitted light rays according to Snell's law, but with the 'sin's replaced with 'tan's. This is the case for a limited range of input angles and other conditions. Such confocal lenslet arrays can therefore simulate the interface between optical media with different refractive indices, n1 and n2, whereby the ratio η=-f2/f1 plays the role of the refractive-index ratio n2/n1. Suitable choices of focal lengths enable positive and negative refraction. In contrast to Snell's law, which leads to nontrivial geometric imaging by a planar refractive-index interface only for the special case of n1=±n2, the modified refraction law leads to geometric imaging by planar confocal lenslet arrays for any value of η. We illustrate some of the properties of confocal lenslet arrays with images rendered using ray-tracing software

Anisotropy and oblique total transmission at a planar negative-index interface

We show that a class of negative index (n) materials has interesting anisotropic optical properties, manifest in the effective refraction index that can be positive, negative, or purely imaginary under different incidence conditions. With dispersion taken into account, reflection at a planar negative-index interface exhibits frequency selective total oblique transmission that is distinct from the Brewster effect. Finite-difference-time-domain simulation of realistic negative-n structures confirms the analytic results based on effective indices.Comment: to appear in Phys. Rev.

Impact of the inherent periodic structure on the effective medium description of left-handed and related meta-materials

We study the frequency dependence of the effective electromagnetic parameters of left-handed and related meta-materials of the split ring resonator and wire type. We show that the reduced translational symmetry (periodic structure) inherent to these meta-materials influences their effective electromagnetic response. To anticipate this periodicity, we formulate a periodic effective medium model which enables us to distinguish the resonant behavior of electromagnetic parameters from effects of the periodicity of the structure. We use this model for the analysis of numerical data for the transmission and reflection of periodic arrays of split ring resonators, thin metallic wires, cut wires as well as the left-handed structures. The present method enables us to identify the origin of the previously observed resonance/anti-resonance coupling as well as the occurrence of negative imaginary parts in the effective permittivities and permeabilities of those materials. Our analysis shows that the periodicity of the structure can be neglected only for the wavelength of the electromagnetic wave larger than 30 space periods of the investigated structure.Comment: 23 pages, 14 figure

Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab

Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus the nonpropagating near-fields, thereby achieving a subdiffraction image. In this work we discuss the sensitivity of the subwavelength focus to various slab parameters, pointing out the connection to slab plasmon modes. We also note and resolve a paradox associated with the perfect imaging of a point source. We conclude that subwavelength resolution is achievable with available technology, but only by implementation of a critical set of design parameters.Comment: pdf fil

Negative refraction and left-handed behavior in two-dimensional photonic crystals

We systematically examine the conditions of obtaining left-handed (LH) behavior in photonic crystals. Detailed studies of the phase and group velocities as well as the phase np and group ng refractive index are given. The existence of negative refraction does not guarantee the existence of negative index of refraction and so LH behavior. A wedge type of experiment is suggested that can unambiguously distiguinsh between cases of negative refraction that occur when left-handed behavior is present, from cases that show negative refraction without LH behavior.Comment: 4 pages 4 figures, submitted to Phys. Rev. B Rapid Communication

Optomagnetic composite medium with conducting nanoelements

A new type of metal-dielectric composites has been proposed that is characterised by a resonance-like behaviour of the effective permeability in the infrared and visible spectral ranges. This material can be referred to as optomagnetic medium. The analytical formalism developed is based on solving the scattering problem for considered inclusions with impedance boundary condition, which yields the current and charge distributions within the inclusions. The presence of the effective magnetic permeability and its resonant properties lead to novel optical effects and open new possible applications.Comment: 48 pages, 13 figures. accepted to Phys. Rev. B; to appear vol. 66, 200

The Quantum-Mechanical Position Operator in Extended Systems

The position operator (defined within the Schroedinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wavefunction, as usual in condensed matter physics. We show how to define the position expectation value by means of a simple many-body operator acting on the wavefunction of the extended system. The relationships of the present findings to the Berry-phase theory of polarization are discussed.Comment: Four pages in RevTe