Optimization of periodic composite structures for sub-wavelength focusing

David C. Dobson; Lyubima B. Simeonova

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arXiv · 0803.1474

Optimization of periodic composite structures for sub-wavelength focusing

David C. Dobson·Lyubima B. Simeonova

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Abstract

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.

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BibTeX RIS

David C. Dobson, Lyubima B. Simeonova. 2008-03-10. Optimization of periodic composite structures for sub-wavelength focusing. https://arxiv.org/abs/0803.1474

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