Title:
Optimization of Micro-Composite Lenses


Abstract:
   This decade there has been a lot 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. This statement is based upon the
claim that the evanescent waves, which usually decay in the near field
region, are amplified by the left handed medium. Several groups have
revealed fundamental problems with Pendry's idea.
    The work presented was inspired by the controversial topic of
designing a superlens. It seeks to answer the question what periodic dielectric
medium (described by dielectric coefficient with positive real part) gives
the optimal image of a point source. An optimization problem is formulated and
it is shown that a solution exists provided the periodic dielectric medium
has "small" absorption.