Three-dimensional Self-similar Fractal Light in Canonical Resonators

Unstable canonical resonators can possess eigenmodes with a fractal intensity structure [Karman et al., Nature 402, 138(1999)]. In one particular transverse plane, the intensity is not merely statistically fractal, but self-similar [Courtial and Padgett, PRL 85, 5320 (2000)]. This can be explained using a combination of diffraction and imaging with magnification greater than one. Here we show that the same mechanism also shapes the intensity cross-section in the longitudinal direction into a self-similar fractal, but with a different magnification. This results in three-dimensional, self-similar, fractal intensity structure in the eigenmodes

A combinatorial identity for studying Sato-Tate type problems

We derive a combinatorial identity which is useful in studying the distribution of Fourier coefficients of L-functions by allowing us to pass from knowledge of moments of the coefficients to the distribution of the coefficients.Comment: This paper contains the proof of a combinatorial identity used to study effective equidistribution laws for the Fourier coefficients of elliptic curve L-functions investigated by the first two authors in http://arxiv.org/abs/1004.275

The effectiveness of thin films in lieu of hyperbolic metamaterials in the near field

We show that the near-field functionality of hyperbolic metamaterials (HMM), typically proposed for increasing the photonic local density of states (LDOS), can be achieved with thin metal films. Although HMMs have an infinite density of internally-propagating plane-wave states, the external coupling to nearby emitters is severely restricted. We show analytically that properly designed thin films, of thicknesses comparable to the metal size of a hyperbolic metamaterial, yield a LDOS as high as (if not higher than) that of HMMs. We illustrate these ideas by performing exact numerical computations of the LDOS of multilayer HMMs, along with their application to the problem of maximizing near-field heat transfer, to show that thin films are suitable replacements in both cases.Comment: 5 pages, 3 figure

Zero field splitting, field-dependent magnetization of mixed-valent S = 3/2 Diruthenium(II,III) tetracarboxylates

Journal ArticleThe 2 K field-dependent magnetization, M(H), of S = 3/2 [RunII/III2(OAc)4]+ was studied. [RuII/III 2(OAc)4]+ exhibits an unusually low magnetization with respect to that predicted by the classical Brillouin function. This reduced value is a consequence of the large anisotropy arising from the large zero-field splitting (ZFS), D (+63 ± 11 cm-1), of the [RuII/III2(OAc)4]+ cation, which alters the energy levels with respect to the isotropic energy levels used to derive the Brillouin function. Analytical expressions for the parallel and perpendicular components of M(H) that include zero-field splitting (ZFS), D, and interdimer coupling, 0, are presented for S=3/2. The expression was derived from second-order perturbation theory for \D\>> gUBH. The experimental data fit very well with g = 2.24 ± 0.01, D = +69.5 cm-1 (D/kB = +100 K), and 0 > 0 > -0.6 K indicative of very weak interdimer interactions for both [RuII/III2(OAc)4]Cl and [RuII/III2(OAc)4]3[CoIII(CN)6]

Evidence for solitons in conducting organic charge-transfer crystals

Journal ArticleMagnetic susceptibility of (N-methylphenazinium)x(phenazine)(1-x (tetracyanoquinodimethanide) [(NMP)x(Phen)1-x(TCNQ)] shows the formation of defect states for 0.5<x<0.54. Diffuse x-ray scattering and g-value studies indicate that these defects are solitons formed in the highly correlated quasi-one-dimensional system that occurs near the quarter-filled-band limit. A model for the decrease in the energy gap in the presence of large numbers of solitons is proposed to explain the excess conductivity

Structural and magnetic characterization of a- and B-2,4-hexadiyne-1,6-diyl Bis(2,2,5,5-tetramethyl-1-oxyl-3-pyrroline-3-carboxylate) and its thermal degradation product

Journal ArticleThe search for ferromagnetic organic compounds and polymers is the focus of contemporary research.1 - 5 Polymerization of di-iminoxyl diacetylene monomers has been suggested as a means to prepare a high spin potentially ferromagnetically coupled polymers3 and the thermal, photochemical, and glow discharge treatment of 4,4'-(butadiynel, 1,4-diyl)-bis-(2,2,6,6-tetramethyl-4-hydroxypiperidin-l-oxyl) (1-oxyl) (1) was reported to form a black polymer of which some samples exhibit field dependent magnetization corresponding to an 'insignificant' amount (0.1%) of a ferromagnet.3,4 Later, Cao and co-workers reported 0.7% for thermally treated (1).

Magnetization and dynamics of reentrant ferrimagnetic spin-glass [MnTPP]::+[TCNE].-.2PhMe

Journal ArticleWe present direct current (dc) magnetization M(T,H) and alternating current (ac) susceptibility Xac(T,H,f) data for the quasi-one-dimensional molecule-based ferrimagnet [MnTPP]::+[TCNE].-.•2PhMe (TPP=meso-tetraphenylporphyrinato, TCNE=tetracyanoethylene). Static scaling of the real part X' of the ac susceptibility and data collapse of M(T,H) over a limited reduced temperature range above Tc=13 K lead to the critical exponents y=1.6, B=0.5, and 8=4.2. Below Tc , Xac depends sensitively on frequency and exhibits a striking double-peak structure similar to that found in reentrant spin glasses. Possible models for the frequency dependence of the peaks observed in Xac are discussed