Generalized metric for broadband flat lens performance comparison

A plethora of metalenses and diffractive lenses ("flat lenses") have been demonstrated over the years. Recently, attempts have been made to stretch their performance envelope, particularly in the direction of wide-band achromatic performance. While achromatic behavior has been demonstrated, showing an actual improvement in imaging performance relative to conventional (non-chromatically corrected) flat lenses has remained a major challenge. The reasons for this are use of inappropriate performance metrics, lack of comparison to a baseline conventional design, and lack of a performance metric that combines signal-to-noise ratio and resolution. An additional problem is that different published flat lens designs use different first order parameters, so they cannot be compared. In this work we present an overall performance metric that will allow comparison of different types of flat lenses, even if their first order optical parameters are not the same. We apply this metric to several published achromatic flat lens designs and compare them to the equivalent conventional flat lens, which we consider as the lower bound for achromatic flat lens performance. We found that the performance of the achromatic flat lenses studied does not surpass that of a conventional diffractive lens. Use of this metric paves the way for future developments in the field of achromatic flat lenses, which will display proven progress.