| Summary: | Developments in nanotechnology and material science have produced optical materials with astonishing properties. Theory and experimentation have demonstrated that, among other properties, the law of refraction is reversed at an interface between a naturally occurring material and these so-called metamaterials. As the technology advances metamaterials have the potential to vastly impact the field of optical science.In this study we provide a foundation for future work in the area of geometric optics and lens design with metamaterials. The concept of negative refraction is extended to derive a comprehensive set of first-order imaging principles as well as an exhaustive aberration theory to 4th order. Results demonstrate congruence with the classical theory; however, negative refraction introduces a host of novel properties. In terms of aberration theory, metamaterials present the lens designer with increased flexibility. A singlet can be bent to produce either positive or negative spherical aberration (regardless of its focal length), its contribution to coma can become independent of its conjugate factor, and its field curvature takes on the opposite sign of its focal power. This is shown to be advantageous in some designs such as a finite conjugate relay lens; however, in a wider field of view landscape lens we demonstrate a metamaterial's aberration properties may be detrimental.This study presents the first comprehensive investigation of metamaterial lenses using industry standard lens design software. A formal design study evaluates the performance of doublet and triplet lenses operating at F/5 with a 100 mm focal length, a 20° half field of view, and specific geometric constraints. Computer aided optimization and performance evaluation provide experimental controls to remove designer-induced bias from the results. Positive-index lenses provide benchmarks for comparison to metamaterial systems subjected to identical design constraints. We find that idiosyncrasies in a metamaterial lens' aberration content can be exploited to produce imaging systems that are superior to their conventional counterparts. However, in some circumstances the reduced low-order aberration content in a metamaterial lens reduces the effectiveness of aberration balancing and stop shifting. Through a series of design experiments the relative advantages and challenges of using metamaterials in lens design are revealed.
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