Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit

Volumes of sub-wavelength electromagnetic elements can act like homogeneous materials: metamaterials. In analogy, sheets of optical elements such as prisms can act ray-optically like homogeneous sheet materials. In this sense, such sheets can be considered to be metamaterials for light rays (METATOYs). METATOYs realize new and unusual transformations of the directions of transmitted light rays. We study here, in the ray-optics and scalar-wave limits, the wave-optical analog of such transformations, and we show that such an analog does not always exist. Perhaps, this is the reason why many of the ray-optical possibilities offered by METATOYs have never before been considered.Comment: 10 pages, 3 figures, references update

Ray-optical refraction with confocal lenslet arrays

Two parallel lenslet arrays with focal lengths f1 and f2 that share a common focal plane (that is, which are separated by a distance f1+f2) can refract transmitted light rays according to Snell's law, but with the 'sin's replaced with 'tan's. This is the case for a limited range of input angles and other conditions. Such confocal lenslet arrays can therefore simulate the interface between optical media with different refractive indices, n1 and n2, whereby the ratio η=-f2/f1 plays the role of the refractive-index ratio n2/n1. Suitable choices of focal lengths enable positive and negative refraction. In contrast to Snell's law, which leads to nontrivial geometric imaging by a planar refractive-index interface only for the special case of n1=±n2, the modified refraction law leads to geometric imaging by planar confocal lenslet arrays for any value of η. We illustrate some of the properties of confocal lenslet arrays with images rendered using ray-tracing software

Local light-ray rotation

We present a sheet structure that rotates the local ray direction through an arbitrary angle around the sheet normal. The sheet structure consists of two parallel Dove-prism sheets, each of which flips one component of the local direction of transmitted light rays. Together, the two sheets rotate transmitted light rays around the sheet normal. We show that the direction under which a point light source is seen is given by a Mobius transform. We illustrate some of the properties with movies calculated by ray-tracing software.Comment: 9 pages, 6 figure

Thermodynamic and rheological properties of rhyolite and andesite melts

The heat capacities of a rhyolite and an andesite glass and liquid have been investigated from relative-enthalpy measurements made between 400 and 1800 K. For the glass phases, the experimental data agree with empirical models of calculation of the heat capacity. For the liquid phases, the agreement is less good owing to strong interactions between alkali metals and aluminum, which are not currently accounted for by empirical heat capacity models. The viscosity of both liquids has been measured from the glass transition to 1800 K. The temperature dependence of the viscosity is quantitatively related to the configurational heat capacity (determined calorimetrically) through the configurational entropy theory of relaxation processes. For both rhyolite and andesite melts, the heat capacity and viscosity do not differ markedly from those obtained by additive modeling from components with mineral compositions

Ray-optical negative refraction and pseudoscopic imaging with Dove-prism arrays

A sheet consisting of an array of small, aligned Dove prisms can locally (on the scale of the width of the prisms) invert one component of the ray direction. A sandwich of two such Dove-prism sheets that inverts both transverse components of the ray direction is a ray-optical approximation to the interface between two media with refractive indices +n and –n. We demonstrate the simulated imaging properties of such a Dove-prism-sheet sandwich, including a demonstration of pseudoscopic imaging

Superoscillation in speckle patterns

Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability density function of intensity and phase gradient for isotropic gaussian random wave superpositions. Strikingly, this fraction is 1/3 when all the waves in the two-dimensional superposition have the same wavenumber. The fraction is 1/5 for a disk spectrum. Although these superoscillations are weak compared with optical fields with designed superoscillations, they are more stable on paraxial propagation.Comment: 3 pages, two figures, Optics Letters styl

Thermodynamic and rheological properties of rhyolite and andesite melts

The heat capacities of a rhyolite and an andesite glass and liquid have been investigated from relative-enthalpy measurements made between 400 and 1800 K. For the glass phases, the experimental data agree with empirical models of calculation of the heat capacity. For the liquid phases, the agreement is less good owing to strong interactions between alkali metals and aluminum, which are not currently accounted for by empirical heat capacity models. The viscosity of both liquids has been measured from the glass transition to 1800 K. The temperature dependence of the viscosity is quantitatively related to the configurational heat capacity (determined calorimetrically) through the configurational entropy theory of relaxation processes. For both rhyolite and andesite melts, the heat capacity and viscosity do not differ markedly from those obtained by additive modeling from components with mineral compositions

Simulation of superresolution holography for optical tweezers

Optical tweezers manipulate microscopic particles using foci of light beams. Their performance is therefore limited by diffraction. Using computer simulations of a model system, we investigate the application of superresolution holography for two-dimensional (2D) light shaping in optical tweezers, which can beat the diffraction limit. We use the direct-search and Gerchberg algorithms to shape the center of a light beam into one or two bright spots; we do not constrain the remainder of the beam. We demonstrate that superresolution algorithms can significantly improve the normalized stiffness of an optical trap and the minimum separation at which neighboring traps can be resolved. We also test if such algorithms can be used interactively, as is desirable in optical tweezers