Conical diffraction and the dispersion surface of hyperbolic metamaterials

Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants $\epsilon_1<0$, $0<\epsilon_2\neq\epsilon_3$. In this general case the two sheets of the index surface intersect forming conical singularities. We derive the ray description of conical refraction in these materials, and show that it is topologically and quantitatively distinct from conical refraction in a conventional biaxial material. We also develop a wave optics description, which allows us to obtain the diffraction patterns formed from arbitrary beams incident close to the optic axis. The resulting patterns lack circular symmetry, and hence are qualitatively different from those obtained in conventional, positive index materials.Comment: 10 pages, 7 figure

Comparison of several methods for obtaining the time response of linear systems to either a unit impulse or arbitrary input from frequency-response data

Several methods of obtaining the time response of Linear systems to either a unit impulse or an arbitrary input from frequency-response data are described and compared. Comparisons indicate that all the methods give good accuracy when applied to a second-order system; the main difference is the required computing time. The methods generally classified as inverse Laplace transform methods were found to be most effective in determining the response to a unit impulse from frequency-response data of higher order systems. Some discussion and examples are given of the use of such methods as flight-data-analysis techniques in predicting loads and motions of a flexible aircraft on the basis of simple calculations when the aircraft frequency response is known

There are many ways to spin a photon : half-quantization of a total optical angular momentum

This work was supported by the Higher Education Authority of Ireland under PRTLI (Programme for Research in Third-Level Institutions) funding cycle 5 and by Science Foundation Ireland (09/SIRG/I1592, 12/RC/2278).The angular momentum of light plays an important role in many areas, from optical trapping to quantum information. In the usual three-dimensional setting, the angular momentum quantum numbers of the photon are integers, in units of the Planck constant ħ. We show that, in reduced dimensions, photons can have a half-integer total angular momentum. We identify a new form of total angular momentum, carried by beams of light, comprising an unequal mixture of spin and orbital contributions. We demonstrate the half-integer quantization of this total angular momentum using noise measurements. We conclude that for light, as is known for electrons, reduced dimensionality allows new forms of quantization.Publisher PDFPeer reviewe

What to Do When the F10.7 Goes Out?

The solar radio flux at 10.7 cm, known as F10.7, is a critical operational space weather index. However, without a clear backup, any interruption to the service can result in substantial errors in model outputs. In this paper we show the impact of one such outage in March 2022 on the models TIE-GCM and NeQuick, and present a number of alternative solutions that could be used for future outages. The analysis is extended to the F10.7 time series since 1951 and the approach resulting in the smallest reconstruction error of F10.7 uses the solar radio flux observations at alternative wavelengths (the best giving a percentage error of 3.1%). Alternatively, use of Sunspot Number, a regular, robust alternative observation, results in a mean percentage error of 8.2% and is also a reliable fallback solution. Additionally, analysis of the error on the use of the conversion between the 12-month rolling sunspot number (R12) and its conversion to F10.7 is included