Optics: momentum in an uncertain light.
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Ulf Leonhardt
Publications and source records attributed to Ulf Leonhardt.
Ambiguities in the scattering tomography for central potentials.
Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering ambiguities that arise in central potentials. We show that scattering is a tomographic projection: The integrated scattering angle is a projection of a scattering function onto the impact parameter. This function depends on the potential but may be multivalued, allowing for ambiguities where several potentials share the same scattering data. In addition, multivalued scattering angles also lead to ambiguities. We apply our theory to show that it is, in principle, possible to construct an invisibility device without infinite phase velocity of light.
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Optical conformal mapping.
An invisibility device should guide light around an object as if nothing were there, regardless of where the light comes from. Ideal invisibility devices are impossible, owing to the wave nature of light. This study develops a general recipe for the design of media that create perfect invisibility within the accuracy of geometrical optics. The imperfections of invisibility can be made arbitrarily small to hide objects that are much larger than the wavelength. With the use of modern metamaterials, practical demonstrations of such devices may be possible. The method developed here can also be applied to escape detection by other electromagnetic waves or sound.
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A laboratory analogue of the event horizon using slow light in an atomic medium.
Singularities underlie many optical phenomena. The rainbow, for example, involves a particular type of singularity-a ray catastrophe-in which light rays become infinitely intense. In practice, the wave nature of light resolves these infinities, producing interference patterns. At the event horizon of a black hole, time stands still and waves oscillate with infinitely small wavelengths. However, the quantum nature of light results in evasion of the catastrophe and the emission of Hawking radiation. Here I report a theoretical laboratory analogue of an event horizon: a parabolic profile of the group velocity of light brought to a standstill in an atomic medium can cause a wave singularity similar to that associated with black holes. In turn, the quantum vacuum is forced to create photon pairs with a characteristic spectrum, a phenomenon related to Hawking radiation. The idea may initiate a theory of 'quantum' catastrophes, extending classical catastrophe theory.
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