Interplay between multiple scattering, emission, and absorption of light in the phosphor of a white light-emitting diode

We study light transport in phosphor plates of white light-emitting diodes (LEDs). We measure the broadband diffuse transmission through phosphor plates of varying YAG:Ce$^{3+}$ density. We distinguish the spectral ranges where absorption, scattering, and re-emission dominate. Using diffusion theory, we derive the transport and absorption mean free paths from first principles. We find that both transport and absorption mean free paths are on the order of the plate thickness. This means that phosphors in commercial LEDs operate well within an intriguing albedo range around 0.7. We discuss how salient parameters that can be derived from first principles control the optical properties of a white LED.Comment: 14 pages, 9 figure

Absolute dimensions of solar-type eclipsing binaries. EF Aquarii: a G0 test for stellar evolution models

Recent studies have shown that stellar chromospheric activity, and its effect on convective energy transport in the envelope, is most likely the cause of significant radius and temperature discrepancies between theoretical evolution models and observations. We aim to determine absolute dimensions and abundances for the solar-type detached eclipsing binary EF Aqr, and to perform a detailed comparison with results from recent stellar evolutionary models. uvby-beta standard photometry was obtained with the Stromgren Automatic Telescope. The broadening function formalism was applied on spectra observed with HERMES at the Mercator telescope in La Palma, to obtain radial velocity curves. Masses and radii with a precision of 0.6% and 1.0% respectively have been established for both components of EF Aqr. The active 0.956 M_sol secondary shows star spots and strong Ca II H and K emission lines. The 1.224 M_sol primary shows signs of activity as well, but at a lower level. An [Fe/H] abundance of 0.00+-0.10 is derived with similar abundances for Si, Ca, Sc, Ti, V, Cr, Co, and Ni. Solar calibrated evolutionary models such as Yonsei-Yale, Victoria-Regina and BaSTI isochrones and evolutionary tracks are unable to reproduce EF Aqr, especially for the secondary, which is 9% larger and 400 K cooler than predicted. Models adopting significantly lower mixing length parameters l/H_p remove these discrepancies, as seen in other solar type binaries. For the observed metallicity, Granada models with a mixing length of l/H_p=1.30 (primary) and 1.05 (secondary) reproduce both components at a common age of 1.5+-0.6 Gyr. Observations of EF Aqr suggests that magnetic activity, and its effect on envelope convection, is likely to be the cause of discrepancies in both radius and temperature, which can be removed by adjusting the mixing length parameter of the models downwards.Comment: 11 pages, 8 figures, accepted for publication by A&

Signature of a three-dimensional photonic band gap observed on silicon inverse woodpile photonic crystals

We have studied the reflectivity of CMOS-compatible three-dimensional silicon inverse woodpile photonic crystals at near-infrared frequencies. Polarization-resolved reflectivity spectra were obtained from two orthogonal crystal surfaces corresponding to 1.88 pi sr solid angle. The spectra reveal broad peaks with high reflectivity up to 67 % that are independent of the spatial position on the crystals. The spectrally overlapping reflectivity peaks for all directions and polarizations form the signature of a broad photonic band gap with a relative bandwidth up to 16 %. This signature is supported with stopgaps in plane wave bandstructure calculations and with the frequency region of the expected band gap.Comment: 9 pages, 5 figure

The Kazhdan-Lusztig conjecture for W-algebras

The main result in this paper is the character formula for arbitrary irreducible highest weight modules of W algebras. The key ingredient is the functor provided by quantum Hamiltonian reduction, that constructs the W algebras from affine Kac-Moody algebras and in a similar fashion W modules from KM modules. Assuming certain properties of this functor, the W characters are subsequently derived from the Kazhdan-Lusztig conjecture for KM algebras. The result can be formulated in terms of a double coset of the Weyl group of the KM algebra: the Hasse diagrams give the embedding diagrams of the Verma modules and the Kazhdan-Lusztig polynomials give the multiplicities in the characters.Comment: uuencoded file, 29 pages latex, 5 figure

Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices

We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant $\epsilon_s$ of spheres is lower than the dielectric constant $\epsilon_b$ of the background medium. If $\epsilon_s> \epsilon_b$, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast $\epsilon_b/\epsilon_s$ for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two figures, and a few references adde

Cross-talk between signaling pathways leading to defense against pathogens and insects

In nature, plants interact with a wide range of organisms, some of which are harmful (e.g. pathogens, herbivorous insects), while others are beneficial (e.g. growth-promoting rhizobacteria, mycorrhizal fungi, and predatory enemies of herbivores). During the evolutionary arms race between plants and their attackers, primary and secondary immune responses evolved to recognize common or highly specialized features of microbial pathogens (Chisholm et al., 2006), resulting in sophisticated mechanisms of defense

A simple formula for the L-gap width of a face-centered-cubic photonic crystal

The width $\triangle_L$ of the first Bragg's scattering peak in the (111) direction of a face-centered-cubic lattice of air spheres can be well approximated by a simple formula which only involves the volume averaged $\epsilon$ and $\epsilon^2$ over the lattice unit cell, $\epsilon$ being the (position dependent) dielectric constant of the medium, and the effective dielectric constant $\epsilon_{eff}$ in the long-wavelength limit approximated by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic behaviour of the absolute gap width $\triangle_L$ for high dielectric contrast $\delta$ exactly. The standard deviation $\sigma$ steadily decreases well below 1% as $\delta$ increases. For example $\sigma< 0.1$ for the sphere filling fraction $f=0.2$ and $\delta\geq 20$. On the interval $\delta\in(1,100)$, our formula still approximates the absolute gap width $\triangle_L$ (the relative gap width $\triangle_L^r$) with a reasonable precision, namely with a standard deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the close-packed case. Differences between the case of air spheres in a dielectric and dielectric spheres in air are briefly discussed.Comment: 13 pages, 4 figs., RevTex, two references added. For more info see http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm

Observation of sub-Bragg diffraction of waves in crystals

We investigate the diffraction conditions and associated formation of stopgaps for waves in crystals with different Bravais lattices. We identify a prominent stopgap in high-symmetry directions that occurs at a frequency below the ubiquitous first-order Bragg condition. This sub-Bragg diffraction condition is demonstrated by reflectance spectroscopy on two-dimensional photonic crystals with a centred rectangular lattice, revealing prominent diffraction peaks for both the sub-Bragg and first-order Bragg condition. These results have implications for wave propagation in 2 of the 5 two-dimensional Bravais lattices and 7 out of 14 three-dimensional Bravais lattices, such as centred rectangular, triangular, hexagonal and body-centred cubic