Asymmetric imaging: Reciprocity bounds and manifestations

Here we develop a general theory of asymmetric imaging in linear, passive, reciprocal optical systems and derive a fundamental bound on the achievable unidirectionality. Reciprocity requires the forward and reverse transmission operators to have identical singular values, a wave-optical analogue of étendue equality, with a simple consequence: perfect asymmetry is attainable only for sets of $M \leq N/2$ orthogonal object patterns, where $N$ is the number of available object/image modes; for $M > N/2$, the average power asymmetry is bounded by $(N-M)/M$.

Guided by this result, we present two complementary realizations: refractive imaging systems formed by bulk lenses and stops that attain the half-occupation limit, and a 1 cm-diameter all-silicon metasurface doublet that exhibits asymmetric focusing at 4 $μ$m while fully complying with Lorentz reciprocity. We fabricate the doublet by direct laser writing and experimentally demonstrate its focusing asymmetry. By establishing mechanism-independent limits, our results provide a benchmark and design principle for asymmetric imaging across platforms, with implications for defense, surveillance and secure communications.