Optimization of Periodic Composite Structures for Sub-Wavelength Focusing
Recently, there has been plenty of work in designing and fabricating materials with an effective negative refractive index. Veselago realized that a slab of material with a refractive index of -1 would act as a lens. Pendry suggested that the Veselago lens would act as a superlens, providing a perfect image of an object in contrast to conventional lenses which are only able to focus a point source to an image having a diameter of the order of the wavelength of the incident field.Recent work has shown that similar focusing effects can be obtained with certain slabs of 'conventional' periodic composite materials: photonic crystals. The present work seeks to answer the question of what periodic dielectric composite medium (described by dielectric coefficient with positive real part) gives an optimal image of a point source. An optimization problem is formulated and it is shown that a solution exists provided the medium has small absorption. Solutions are characterized by an adjoint-state gradient condition, and several numerical examples illustrate both the plausibility of this design approach, and the possibility of obtaining smaller image spot sizes than with typical photonic crystals.
- OSTI ID:
- 21241852
- Journal Information:
- Applied Mathematics and Optimization, Vol. 60, Issue 1; Other Information: DOI: 10.1007/s00245-008-9063-8; Copyright (c) 2009 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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