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

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 scalarwave 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.

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 Möbius transform. We illustrate some of the properties with movies calculated by ray-tracing software.

Abstract. We have recently started to investigate 2D arrays of confocal lens pairs. Miniaturization of the lens pairs can make the array behave ray-optically like a homogeneous medium. Here we generalize the geometry of the lens pairs. These generalisations include a sideways shift of the lens centres and a change in the orientation of both lenses in each pair. We investigate the basic ray optics of the resulting arrays, and illustrate these with movies rendered using ray-tracing software. We suggest that confocal lenslet arrays could be used to realize rayoptically some recent metamaterials concepts such as the coordinate-transform design paradigm.

No abstract

We derive a formal description of local light-ray rotation in terms of complex refractive indices. We show that Fermat's principle holds, and we derive an extended Snell's law. The change in the angle of a light ray with respect to the normal of a refractive index interface is described by the modulus of the refractive index ratio; the rotation around the interface normal is described by the argument of the refractive index ratio.

We show, theoretically and experimentally, that a sheet formed by two confocal lenticular arrays can flip one component of the local light-ray direction. Ray-optically, such a sheet is equivalent to a Dove-prism sheet, an example of a METATOY (metamaterial for rays), a structure that changes the direction of transmitted light rays in a way that cannot be performed perfectly wave-optically.

TIM (The Interactive METATOY) is a ray-tracing program specifically tailored towards our research in METATOYs, which are optical components that appear to be able to create wave-optically forbidden light-ray fields. For this reason, TIM possesses features not found in other ray-tracing programs. TIM can either be used interactively or by modifying the openly available source code; in both cases, it can easily be run as an applet embedded in a web page. Here we describe the basic structure of TIM's source code and how to extend it, and we give examples of how we have used TIM in our own research.