Transmission Studies of Left-handed Materials

Left-handed materials are studied numerically using an improved version of the transfer-matrix method. The transmission, reflection, the phase of the reflection and the absorption are calculated and compared with experiments for both single split-ring resonators (SRR) with negative permeability and left-handed materials (LHMs) which have both the permittivity and permeability negative. Our results suggest ways of positively identifying materials that have both permittivity and permeability negative, from materials that have either permeability or permittivity negative

Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.Comment: 7 pages, 3 figure

Broadband Extraordinary Transmission in a Single Sub-wavelength Aperture

Coordinate transformation is applied to design an all-dielectric device for Extraordinary Transmission (ET) in a single sub-wavelength slit. The proposed device has a broadband feature and can be applied from microwave to visible frequency bands. Finite-Difference Time-Domain (FDTD) simulations are used to verify the device's performance. The results show that significantly increased transmission is achieved through the sub-wavelength aperture from 4 GHz to 8 GHz when the device is applied. In contrast with previously reported systems, the frequency sensitivity of the new device is very low.Comment: 9 pages, 8 figure

Propagation of waves in metallic photonic crystals at low frequencies and some theoretical aspects of left-handed materials

An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence of the existence of such waves has been found recently via experiments and computations. We have obtained an exact dispersion equation for omega (k) and studied the cutoff frequency omega_0 = omega(0) as a function of parameters of the photonic crystal. An analytical expression for the permittivity epsilon is calculated. It is shown, that if the crystal is embedded into a medium with negative mu, it has no propagating modes at any frequency. Thus, such a compound system is not a left-handed material (LHM). The recent experimental results on the LHM are discussed.Comment: 8 pages, 3 figure

Singular evanescent wave resonances

Resonators fold the path of light by reflections leading to a phase balance and thus constructive addition of propagating waves. However, amplitude decrease of these waves due to incomplete reflection or material absorption leads to a finite quality factor of all resonances. Here we report on our discovery that evanescent waves can lead to a perfect phase and amplitude balance causing an ideal Fabry-Perot resonance condition in spite of material absorption and non-ideal reflectivities. This counterintuitive resonance occurs if and only if the metallic Fabry-Perot plates are in relative motion to each other separated by a critical distance. We show that the energy needed to approach the resonance arises from the conversion of the mechanical energy of motion to electromagnetic energy. The phenomenon is similar to lasing where the losses in the cavity resonance are exactly compensated by optical gain media instead of mechanical motion. Nonlinearities and non-localities in material response will inevitably curtail any singularities however we show the giant enhancement in non-equilibrium phenomena due to such resonances in moving media.Comment: In this version we show that the predicted singular resonance leads to giant heat transfer between moving plate

Near Field Lenses in Two Dimensions

It has been shown that a slab of materials with refractive index = -1 behaves like a perfect lens focussing all light to an exact electromagnetic copy of an object. The original lens is limited to producing images the same size as the object, but here we generalise the concept so that images can be magnified. For two dimensional systems, over distances much shorter than the free space wavelength, we apply conformal transformations to the original parallel sided slab generating a variety of new lenses. Although the new lenses are not `perfect' they are able to magnify two dimensional objects. The results apply equally to imaging of electric or magnetic sub wavelength objects in two dimensions. The concepts have potential applications ranging from microwave frequencies to the visible.Comment: PDF fil

Fermat's principle with complex refractive indices and local light-ray rotation

We describe local light-ray rotation in terms of complex refractive indices. We show that Fermat's principle holds, and we derive an extended Snell's law. The change in the angle of a light ray with respect to the normal to a refractive-index interface is described by the modulus of the refractive-index ratio, the rotation around the interface normal is described by the argument of the refractive-index ratio.Comment: 3 pages, 2 figure

A spherical perfect lens

It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the sub-wavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with $\epsilon(r) \sim 1/r$ and $\mu(r)\sim 1/r$. We concentrate on lens-like solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of $\mu$ and $\epsilon$ respectively.Comment: Revtex4, 9 pages, 2 figures (eps

A metamaterial frequency-selective super-absorber that has absorbing cross section significantly bigger than the geometric cross section

Using the idea of transformation optics, we propose a metamaterial device that serves as a frequency-selective super-absorber, which consists of an absorbing core material coated with a shell of isotropic double negative metamaterial. For a fixed volume, the absorption cross section of the super-absorber can be made arbitrarily large at one frequency. The double negative shell serves to amplify the evanescent tail of the high order incident cylindrical waves, which induces strong scattering and absorption. Our conclusion is supported by both analytical Mie theory and numerical finite element simulation. Interesting applications of such a device are discussed.Comment: 16 pages, 5 figure