Joint Summer Research Conference in the Mathematical Sciences
Mathematical Modeling of Novel Optical Materials and Devices
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Graeme Milton's Abstract

Anomalous localized resonance, a proof of superlensing in the quasistatic regime, and limitations of superlenses

Enlarging upon work of Nicorovici, McPhedran and Milton (1994) we have a rigorous proof that in the quasistatic regime a cylindrical superlens can successfully image a dipolar line source in the limit as the loss in the lens tends to zero. In this limit it is proved that the field blows up to infinity in two sometimes overlapping annular anomalously locally resonant regions, one of which extends inside the lens and the other of which extends outside the lens. If the object being imaged responds to an applied field it is argued that it must lie outside the resonant regions to be sucessfully imaged. If the image is being probed it is argued that the resonant regions created by the probe should not interfere with either the probe itself or the object being imaged, if that object responds to an applied field. Perfect imaging in a cylindical superlens is shown to extend to the static equations of magnetoelectricity or thermoelectricity provided they have a special structure which makes these equations equivalent to the quasistatic equations, as follows from previous work of Cherkaev and Gibiansky (1994) and Milton (2002).

Snowbird, Utah     June 11 - 17, 2005