Poles and zeros of the scattering matrix associated to defect modes

We analyze electromagnetic waves propagation in one-dimensional periodic media with single or periodic defects. The study is made both from the point of view of the modes and of the diffraction problem. We provide an explicit dispersion equation for the numerical calculation of the modes, and we establish a connection between modes and poles and zeros of the scattering matrix.Comment: 6 pages (Revtex), no figure

An experimental and theoretical investigation into the perforated zones for nuclear reactor pressure vessels

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Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals

We calculate analytically the spectra of plasma waves and electromagnetic waves (EMW) in metallic photonic crystal consisting of the parallel thin infinite metallic cylinders embedded in the dielectric media. The axes of metallic cylinders form a regular square lattice in a plane perpendicular to them. The metal inside the cylinders is assumed to be in the high frequency regime $\omega \tau >> 1$, where $\tau$ is the relaxation time. The proposed analytical theory is based upon small parameters $f << 1$, where $f$ is the volume fraction of the metal, and $kR << 1$, where $k$ is the wave vector and $R$ is the radius of the cylinder. It is shown that there are five different branches of the EMW that cover all frequency range under consideration except one very small omnidirectional gap in the vicinity of the frequency of the surface plasmon. However, at some directions of propagation and polarizations the gap may be much larger. The reflection and refraction of the EMW is also considered. The general theory of refraction is proposed which is complicated by the spatial dispersion of the dielectric constant, and one particular geometry of the incident EMW is considered.Comment: 14 pages, 8 figure

Coordination Dependence of Hyperfine Fields of 5sp Impurities on Ni Surfaces

We present first-principles calculations of the magnetic hyperfine fields H of 5sp impurities on the (001), (111), and (110) surfaces of Ni. We examine the dependence of H on the coordination number by placing the impurity in the surfaces, on top of them at the adatom positions, and in the bulk. We find a strong coordination dependence of H, different and characteristic for each impurity. The behavior is explained in terms of the on-site s-p hybridization as the symmetry is reduced at the surface. Our results are in agreement with recent experimental findings.Comment: 4 pages, 3 figure

Light scattering from disordered overlayers of metallic nanoparticles

We develop a theory for light scattering from a disordered layer of metal nanoparticles resting on a sample. Averaging over different disorder realizations is done by a coherent potential approximation. The calculational scheme takes into account effects of retardation, multipole excitations, and interactions with the sample. We apply the theory to a system similar to the one studied experimentally by Stuart and Hall [Phys. Rev. Lett. {\bf 80}, 5663 (1998)] who used a layered Si/SiO$_2$/Si sample. The calculated results agree rather well with the experimental ones. In particular we find conspicuous maxima in the scattering intensity at long wavelengths (much longer than those corresponding to plasmon resonances in the particles). We show that these maxima have their origin in interference phenomena in the layered sample.Comment: 19 pages, 12 figure

Manifestation of photonic band structure in small clusters of spherical particles

We study the formation of the photonic band structure in small clusters of dielectric spheres. The first signs of the band structure, an attribute of an infinite crystal, can appear for clusters of 5 particles. Density of resonant states of a cluster of 32 spheres may exhibit a well defined structure similar to the density of electromagnetic states of the infinite photonic crystal. The resonant mode structure of finite-size aggregates is shown to be insensitive to random displacements of particles off the perfect lattice positions as large as half-radius of the particle. The results were obtained by an efficient numerical method, which relates the density of resonant states to the the scattering coefficients of the electromagnetic scattering problem. Generalized multisphere Mie (GMM) solution was used to obtain scattering matrix elements. These results are important to miniature photonic crystal design as well as understanding of light localization in dense random media.Comment: 4 pages, 2 figure

Onset of magnetism in B2 transition metals aluminides

Ab initio calculation results for the electronic structure of disordered bcc Fe(x)Al(1-x) (0.4<x<0.75), Co(x)Al(1-x) and Ni(x)Al(1-x) (x=0.4; 0.5; 0.6) alloys near the 1:1 stoichiometry, as well as of the ordered B2 (FeAl, CoAl, NiAl) phases with point defects are presented. The calculations were performed using the coherent potential approximation within the Korringa-Kohn-Rostoker method (KKR-CPA) for the disordered case and the tight-binding linear muffin-tin orbital (TB-LMTO) method for the intermetallic compounds. We studied in particular the onset of magnetism in Fe-Al and Co-Al systems as a function of the defect structure. We found the appearance of large local magnetic moments associated with the transition metal (TM) antisite defect in FeAl and CoAl compounds, in agreement with the experimental findings. Moreover, we found that any vacancies on both sublattices enhance the magnetic moments via reducing the charge transfer to a TM atom. Disordered Fe-Al alloys are ferromagnetically ordered for the whole range of composition studied, whereas Co-Al becomes magnetic only for Co concentration >0.5.Comment: 11 pages with 9 embedded postscript figures, to be published in Phys.Rev.

Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

Slater-Pauling Behavior of the Half-Ferromagnetic Full-Heusler Alloys

Using the full-potential screened Korringa-Kohn-Rostoker method we study the full-Heusler alloys based on Co, Fe, Rh and Ru. We show that many of these compounds show a half-metallic behavior, however in contrast to the half-Heusler alloys the energy gap in the minority band is extremely small. These full-Heusler compounds show a Slater-Pauling behavior and the total spin-magnetic moment per unit cell (M_t) scales with the total number of valence electrons (Z_t) following the rule: M_t=Z_t-24. We explain why the spin-down band contains exactly 12 electrons using arguments based on the group theory and show that this rule holds also for compounds with less than 24 valence electrons. Finally we discuss the deviations from this rule and the differences compared to the half-Heusler alloys.Comment: 10 pages, 8 figures, revised figure 3, new text adde

A screen for hoxb1-regulated genes identifies ppp1r14al as a regulator of the rhombomere 4 Fgf-signaling center

AbstractSegmentation of the vertebrate hindbrain into multiple rhombomeres is essential for proper formation of the cerebellum, cranial nerves and cranial neural crest. Paralog group 1 (PG1) hox genes are expressed early in the caudal hindbrain and are required for rhombomere formation. Accordingly, loss of PG1 hox function disrupts development of caudal rhombomeres in model organisms and causes brainstem defects, associated with cognitive impairment, in humans. In spite of this important role for PG1 hox genes, transcriptional targets of PG1 proteins are not well characterized. Here we use ectopic expression together with embryonic dissection to identify novel targets of the zebrafish PG1 gene hoxb1b. Of 100 genes up-regulated by hoxb1b, 54 were examined and 25 were found to represent novel hoxb1b regulated hindbrain genes. The ppp1r14al gene was analyzed in greater detail and our results indicate that Hoxb1b is likely to directly regulate ppp1r14al expression in rhombomere 4. Furthermore, ppp1r14al is essential for establishment of the earliest hindbrain signaling-center in rhombomere 4 by regulating expression of fgf3