METATOY
A METATOY is a sheet, formed by a two-dimensional array of small, telescopic optical components, that switches the path of transmitted light rays.
In the simplest case, the individual optical components are all identical; the METATOY then behaves like a homogeneous, but pixellated, window that can have very unusual optical properties (see the picture of the view through a METATOY).
METATOYs are usually treated within the framework of geometrical optics; the light-ray-direction change performed by a METATOY is described by a mapping of the direction of any incoming light ray onto the corresponding direction of the outgoing ray.
METATOYs can even create pixellated light-ray fields that could not exist in non-pixellated form due to a condition imposed by wave optics.
[1] Much of the work on METATOYs is currently theoretical, backed up by computer simulations.
A small number of experiments have been performed to date; more experimental work is ongoing.
Telescopic optical components that have been used as the unit cell of two-dimensional arrays, and which therefore form homogeneous METATOYs, include a pair of identical lenses (focal length
) that share the same optical axis (perpendicular to the METATOY) and that are separated by
) that share the same optical axis (again perpendicular to the METATOY) and that are separated by
(a generalization of the former case);[4] a prism;[5] and a Dove prism[6][7][8][9] Examples of inhomogeneous METATOYs include the moiré magnifier,[10] which is based on deliberately "mis-aligned" pairs of confocal microlens arrays; Fresnel lenses, which can be seen as non-homogeneous METATOYs made from prisms; and frosted glass, which can be seen as an extreme case of an inhomogeneous, random METATOY made from prisms.
Examples of METATOYs as defined above have existed long before analogies with metamaterials were noted and it was recognized that METATOYs can perform wave-optically forbidden ray-direction mappings (in pixellated form).
In the ray-optics limit (in which the optical wavelength tends towards zero) of scalar optics (in which light is described as a scalar wave, an approximation that works well for paraxial light with uniform polarization), the light-ray field r
This last equation is a condition, derived from wave optics, on light-ray fields.
In addition, metamaterials provided the inspiration for early METATOYs research, as summarized in the following quote:[1] Motivated by the desire to build optical elements that have some of the visual properties of metamaterials on an everyday size scale and across the entire visible wavelength spectrum, we recently started to investigate sheets formed by miniaturized optical elements that change the direction of transmitted light rays.
In a number of ways, METATOYs are analogous to metamaterials:[1] structure: metamaterials are arrays of small (sub-wavelength size) wave-optical components (electro-magnetic circuits resonant with the optical frequency), whereas METATOYs are arrays of small (so that they work well as pixels), telescopic, "ray-optical components"; functionality: both metamaterials and METATOYs can behave like homogeneous materials, in the case of metamaterials a volume of material, in the case of METATOYs a sheet material, in both cases with very unusual optical properties such as negative refraction.
Arguably amongst the most startling properties of metamaterials are some that are fundamentally wave-optical, and therefore not reproduced in METATOYs.
These include amplification of evanescent waves, which can, in principle, lead to perfect lenses ("superlenses") [13] and magnifying superlenses ("hyperlenses");[14][15] reversal of the phase velocity; reversal of the Doppler shift.
