Some perpendicular arrays for arbitrarily large t

AbstractWe show that perpendicular arrays exist for arbitrarily large t and with λ = 1. In particular, if d devides (t+1) then there is a PA1(t, t+1, t+(f(t+1)d)). If υ ≡ 1 or 2 (mod 3) then there is a PAλ(3, 4, υ) for any λ. If 3 divides λ then there is a PAλ(3, 4, υ) for any v. If n⩾2 there is a PA1(4, 5, 2n+1). Using recursive constructions we exhibit several infinite families of perpendicular arrays with t⩾3 and relatively small λ. We finally discuss methods of constructing perpendicular arrays based on automorphism groups. These methods allow the construction of PA's with (k−t)>1

Full transmission through perfect-conductor subwavelength hole arrays

Light transmission through 2D subwavelength hole arrays in perfect-conductor films is shown to be complete (100%) at some resonant wavelengths even for arbitrarily narrow holes. Conversely, the reflection on a 2D planar array of non-absorbing scatterers is shown to be complete at some wavelengths regardless how weak the scatterers are. These results are proven analytically and corroborated by rigorous numerical solution of Maxwell's equations. This work supports the central role played by dynamical diffraction during light transmission through subwavelength hole arrays and it provides a systematics to analyze more complex geometries and many of the features observed in connection with transmission through hole arrays.Comment: 5 pages, 4 figure

Synthetic three-dimensional atomic structures assembled atom by atom

We demonstrate the realization of large, fully loaded, arbitrarily-shaped three-dimensional arrays of single atoms. Using holographic methods and real-time, atom-by-atom, plane-by-plane assembly, we engineer atomic structures with up to 72 atoms separated by distances of a few micrometres. Our method allows for high average filling fractions and the unique possibility to obtain defect-free arrays with high repetition rates. These results find immediate application for the quantum simulation of spin Hamiltonians using Rydberg atoms in state-of-the-art platforms, and are very promising for quantum-information processing with neutral atoms.Comment: 5 pages, 3 figure

Critical Currents of Josephson-Coupled Wire Arrays

We calculate the current-voltage characteristics and critical current I_c^{array} of an array of Josephson-coupled superconducting wires. The array has two layers, each consisting of a set of parallel wires, arranged at right angles, such that an overdamped resistively-shunted junction forms wherever two wires cross. A uniform magnetic field equal to f flux quanta per plaquette is applied perpendicular to the layers. If f = p/q, where p and q are mutually prime integers, I_c^{array}(f) is found to have sharp peaks when q is a small integer. To an excellent approximation, it is found in a square array of n^2 plaquettes, that I_c^{array}(f) \propto (n/q)^{1/2} for sufficiently large n. This result is interpreted in terms of the commensurability between the array and the assumed q \times q unit cell of the ground state vortex lattice.Comment: 4 pages, 4 figure

Diacritical study of light, electrons, and sound scattering by particles and holes

We discuss the differences and similarities in the interaction of scalar and vector wave-fields with particles and holes. Analytical results are provided for the transmission of isolated and arrayed small holes as well as surface modes in hole arrays for light, electrons, and sound. In contrast to the optical case, small-hole arrays in perforated perfect screens cannot produce acoustic or electronic surface-bound states. However, unlike electrons and light, sound is transmitted through individual holes approximately in proportion to their area, regardless their size. We discuss these issues with a systematic analysis that allows exploring both common properties and unique behavior in wave phenomena for different material realizations.Comment: 3 figure

Collective oscillations in optical matter

Atom and nanoparticle arrays trapped in optical lattices are shown to be capable of sustaining collective oscillations of frequency proportional to the strength of the external light field. The spectrum of these oscillations determines the mechanical stability of the arrays. This phenomenon is studied for dimers, strings, and two-dimensional planar arrays. Laterally confined particles free to move along an optical channel are also considered as an example of collective motion in partially-confined systems. The fundamental concepts of dynamical response in optical matter introduced here constitute the basis for potential applications to quantum information technology and signal processing. Experimental realizations of these systems are proposed.Comment: 4 figures. Optics Express (in press

Bound whispering gallery modes in circular arrays of dielectric spherical particles

Low-dimensional ordered arrays of optical elements can possess bound modes having an extremely high quality factor. Typically, these arrays consist of metal elements which have significantly high light absorption thus restricting performance. In this paper we address the following question: can bound modes be formed in dielectric systems where the absorption of light is negligible? Our investigation of circular arrays of spherical particles shows that (1) high quality modes in an array of 10 or more particles can be attained at least for a refractive index $n_{r}>2$, so optical materials like TiO$_{2}$ or GaAs can be used; (2) the most bound modes have nearly transverse polarization perpendicular to the circular plane; (3) in a particularly interesting case of TiO$_{2}$ particles (rutile phase, $n_{r}=2.7$), the quality factor of the most bound mode increases almost by an order of magnitude with the addition of 10 extra particles, while for particles made of GaAs the quality factor increases by almost two orders of magnitude with the addition of ten extra particles. We hope that this preliminary study will stimulate experimental investigations of bound modes in low-dimensional arrays of dielectric particles.Comment: Submitted to Physical Review

Station-Keeping Requirements for Constellations of Free-Flying Collectors Used for Astronomical Imaging in Space

The accuracy requirements on station-keeping for constellations of free-flying collectors coupled as (future) imaging arrays in space for astrophysics applications are examined. The basic imaging element of these arrays is the two-element interferometer. Accurate knowledge of two quantities is required: the \textit{projected baseline length}, which is the distance between the two interferometer elements projected on the plane tranverse to the line of sight to the target; and the \textit{optical path difference}, which is the difference in the distances from that transverse plane to the beam combiner. ``Rules-of-thumb'' are determined for the typical accuracy required on these parameters. The requirement on the projected baseline length is a \textit{knowledge} requirement and depends on the angular size of the targets of interest; it is generally at a level of half a meter for typical stellar targets, decreasing to perhaps a few centimeters only for the widest attainable fields of view. The requirement on the optical path difference is a \textit{control} requirement and is much tighter, depending on the bandwidth of the signal; it is at a level of half a wavelength for narrow (few %) signal bands, decreasing to $\approx 0.2 \lambda$ for the broadest bandwidths expected to be useful. Translation of these requirements into engineering requirements on station-keeping accuracy depends on the specific details of the collector constellation geometry. Several examples are provided to guide future application of the criteria presented here. Some implications for the design of such collector constellations and for the methods used to transform the information acquired into images are discussed.Comment: 13 pages, 6 figures, accepted 6/29/07 for the August 2007 issue of PAS