Negative index lens aberrations

We examine the Seidel aberrations of thin spherical lenses composed of media with refractive index not restricted to be positive. We find that consideration of this expanded parameter space allows for the reduction or elimination of more aberrations than is possible with only positive index media. In particular, we find that spherical lenses possessing real aplanatic focal points are possible only with a negative index. We perform ray tracing, using a custom code that relies only on Maxwell's equations and conservation of energy, that confirms the results of the aberration calculations.