Complete bandgaps in one-dimensional left-handed periodic structures

Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic bandgap. It is believed that modulation of the refractive index in all three spatial dimensions is required to open a complete bandgap and prevent the propagation of electromagnetic waves in all directions. Here we reveal that, in a sharp contrast to what was known before and contrary to the accepted physical intuition, a one-dimensional periodic structure containing the layers of transparent left-handed (or negative-index) metamaterial can trap light in three-dimensional space due to the existence of a complete bandgap.Comment: 4 pages, 5 figure

Propagation of the surface plasmon polaritons through gradient index and periodic structures

We study the propagation of surface electromagnetic waves along the metallic surface covered by various layered dielectric structures. We show that strong radiative losses typical for the scattering of the surface wave can be considerably suppressed when single dielectric step is substituted by gradient index or periodic layered structure

Frozen light in photonic crystals with degenerate band edge

Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmitted wave can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux. The field amplitude in the transmitted wave can exceed that of the incident wave by several orders of magnitude. There are two qualitatively different kinds of frozen mode regime. The first one is associated with a stationary inflection point of electromagnetic dispersion relation. This phenomenon has been analyzed in our previous publications. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this new phenomenon is that it can occur in much simpler periodic structures. This spectacular effect is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in a variety practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc

Frozen light in periodic metamaterials

Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the primitive translation of the periodic structure. In such a case, the periodic medium cannot be assigned any meaningful refractive index. Still, such features as negative refraction and/or opposite phase and group velocities for certain directions of light propagation can be found in almost any photonic crystal. The only reservation is that unlike hypothetical uniform left-handed media, photonic crystals are essentially anisotropic at frequency range of interest. Consider now a plane wave incident on a semi-infinite photonic crystal. One can assume, for instance, that in the case of positive refraction, the normal components of the group and the phase velocities of the transmitted Bloch wave have the same sign, while in the case of negative refraction, those components have opposite signs. What happens if the normal component of the transmitted wave group velocity vanishes? Let us call it a "zero-refraction" case. At first sight, zero normal component of the transmitted wave group velocity implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possibility. Instead, the transmitted wave can appear in the form of an abnormal grazing mode with huge amplitude and nearly tangential group velocity. This spectacular phenomenon is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in numerous applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc

Abnormal phenomena in a one-dimensional periodic structure containing left-handed materials

The explicit dispersion equation for a one-dimensional periodic structure with alternative layers of left-handed material (LHM) and right-handed material (RHM) is given and analyzed. Some abnormal phenomena such as spurious modes with complex frequencies, discrete modes and photon tunnelling modes are observed in the band structure. The existence of spurious modes with complex frequencies is a common problem in the calculation of the band structure for such a photonic crystal. Physical explanation and significance are given for the discrete modes (with real values of wave number) and photon tunnelling propagation modes (with imaginary wave numbers in a limited region).Comment: 10 pages, 4 figure

MHD wave propagation from the sub-photosphere to the corona in an arcade-shaped magnetic field with a null point

The aim of this work is to study the energy transport by means of MHD waves propagating in quiet Sun magnetic topology from layers below the surface to the corona. Upward propagating waves find obstacles, such as the equipartition layer with plasma b=1 and the transition region, and get converted, reflected and refracted. Understanding the mechanisms by which MHD waves can reach the corona can give us information about the solar atmosphere and the magnetic structures. We carry out two-dimensional numerical simulations of wave propagation in a magnetic field structure that consists of two vertical flux tubes separated by an arcade shaped magnetic field. This configuration contains a null point in the corona, that significantly modifies the behaviour of the waves. We describe in detail the wave propagation through the atmosphere under different driving conditions. We also present the spatial distribution of the mean acoustic and magnetic energy fluxes and the spatial distribution of the dominant frequencies in the whole domain. We conclude that the energy reaches the corona preferably along vertical magnetic fields, inside the flux tubes, and it has an acoustic nature. Most of the magnetic energy keeps concentrated below the transition region due to the refraction of the magnetic waves and the continuous conversion of acoustic-like waves into fast magnetic waves in the equipartition layer located in the photosphere. However, part of the magnetic energy reaches the low corona when propagating in the region where the arcades are located, but waves are sent back downwards to the lower atmosphere at the null point surroundings. This phenomenon, together with the reflection and refraction of waves in the TR and the lower turning point, act as a re-feeding of the atmosphere. In the frequency distribution, we find that high frequency waves can reach the corona outside the vertical flux tubes.Comment: 13 pages, 13 figure

Effective elastic properties of planar SOFCs: A non-local dynamic homogenization approach

The focus of the article is on the analysis of effective elastic properties of planar Solid Oxide Fuell Cell (SOFC) devices. An ideal periodic multi-layered composite (SOFC-like) reproducing the overall properties of multi-layer SOFC devices is defined. Adopting a non-local dynamic homogenization method, explicit expressions for overall elastic moduli and inertial terms of this material are derived in terms of micro-fluctuation functions. These micro-fluctuation function are then obtained solving the cell problems by means of finite element techniques. The effects of the temperature variation on overall elastic and inertial properties of the fuel cells are studied. Dispersion relations for acoustic waves in SOFC-like multilayered materials are derived as functions of the overall constants, and the results obtained by the proposed computational homogenization approach are compared with those provided by rigorous Floquet-Boch theory. Finally, the influence of the temperature and of the elastic properties variation on the Bloch spectrum is investigated