Studies of surface two-dimensional photonic band-gap structures

Two-dimensional (2D) surface photonic band-gap (SPBG) structures can be obtained by providing a shallow corrugation of the inner surface of a waveguide wall. It can be used as a distributed mirror, a cavity, or a filter in integrated optics or microwave electronics. These structures can also be an alternative to conventional 2D PBG or 1D Bragg structures. In this article, we present the results of theoretical and experimental studies of 2D SPBG structures. Data obtained from experiments are compared with theoretical results and good agreement between theory and experiment is demonstrated. Comparison of a coaxial 2D SPBG structure with a conventional 1D Bragg structure is also presented

Cylindrical, periodic surface lattice — theory, dispersion analysis, and experiment

A two-dimensional surface lattice of cylindrical topology obtained via perturbing the inner surface of a cylinder is considered. Periodic perturbations of the surface lead to observation of high-impedance, dielectric-like media and resonant coupling of surface and non-propagating volume fields. This allows synthesis of tailored-for-purpose "coating" material with dispersion suitable, for instance, to mediate a Cherenkov type interaction. An analytical model of the lattice is discussed and coupled-wave equations are derived. Variations of the lattice dispersive properties with variation of parameters are shown, illustrating the tailoring of the structure's electromagnetic properties. Experimental results are presented showing agreement with the theoretical model

On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H2_{2}

A model of the collisional kinetics of energetic hydrogen atoms, molecules, and ions in pure H$_2$ discharges is used to predict H$_\alpha$ emission profiles and spatial distributions of emission from the cathode regions of low-pressure, weakly-ionized discharges for comparison with a wide variety of experiments. Positive and negative ion energy distributions are also predicted. The model developed for spatially uniform electric fields and current densities less than $10^{-3}$ A/m$^2$ is extended to non-uniform electric fields, current densities of $10^{3}$ A/m$^2$, and electric field to gas density ratios $E/N = 1.3$ MTd at 0.002 to 5 Torr pressure. (1 Td = $10^{-21}$ V m$^2$ and 1 Torr = 133 Pa) The observed far-wing Doppler broadening and spatial distribution of the H$_\alpha$ emission is consistent with reactions among H$^+$, H$_2^+$, H$_3^+$, and H$^-H$ ions, fast H atoms, and fast H$_2$ molecules, and with reflection, excitation, and attachment to fast H atoms at surfaces. The H$_\alpha$ excitation and H$^-$ formation occur principally by collisions of fast H, fast H$_2$, and H$^+$ with H$_2$. Simplifications include using a one-dimensional geometry, a multi-beam transport model, and the average cathode-fall electric field. The H$_\alpha$ emission is linear with current density over eight orders of magnitude. The calculated ion energy distributions agree satisfactorily with experiment for H$_2^+$ and H$_3^+$, but are only in qualitative agreement for H$^+$ and H$^-$. The experiments successfully modeled range from short-gap, parallel-plane glow discharges to beam-like, electrostatic-confinement discharges.Comment: Submitted to Plasmas Sources Science and Technology 8/18/201

Free energy density for mean field perturbation of states of a one-dimensional spin chain

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy

Using Remotely Piloted Aircraft and Onboard Processing to Optimize and Expand Data Collection

Remotely piloted aircraft (RPA) have the potential to revolutionize local to regional data collection for geophysicists as platform and payload size decrease while aircraft capabilities increase. In particular, data from RPAs combine high-resolution imagery available from low flight elevations with comprehensive areal coverage, unattainable from ground investigations and difficult to acquire from manned aircraft due to budgetary and logistical costs. Low flight elevations are particularly important for detecting signals that decay exponentially with distance, such as electromagnetic fields. Onboard data processing coupled with high-bandwidth telemetry open up opportunities for real-time and near real-time data processing, producing more efficient flight plans through the use of payload-directed flight, machine learning and autonomous systems. Such applications not only strive to enhance data collection, but also enable novel sensing modalities and temporal resolution. NASAs Airborne Science Program has been refining the capabilities and applications of RPA in support of satellite calibration and data product validation for several decades. In this paper, we describe current platforms, payloads, and onboard data systems available to the research community. Case studies include Fluid Lensing for littoral zone 3D mapping, structure from motion for terrestrial 3D multispectral imaging, and airborne magnetometry on medium and small RPAs

Periodic structure towards the terahertz region manufactured using high resolution 3D printing

Periodic structures used for high power millimetre and sub-millimetre sources that implement relativistic beam - wave interactions have historically involved the implantation of a dielectric layer around the inner wall of the interaction region or a periodic corrugated structure that serves to reduce the velocity of an internal electromagnetic wave. Moving towards the THz regime, the physical dimensions required to manufacture such a cavity become prohibitively difficult. Ongoing attempts to develop manufacturing processes that provide higher resolution have resulted in a number of viable techniques. Additive Manufacturing or 3D printing offers the possibility of producing components on this scale quickly and efficiently. Here 0.1, 0.4 and 1 THz periodic structures are realised using high resolution (16 micron) 3D printing technology

Microwave Gaseous Discharges

Contains reports on two research projects