Asymmetric imaging: Reciprocity bounds and manifestations
Abstract
Recent demonstrations of unidirectional imaging using diffractive multilayers have brought a concept akin to optical isolation to imaging, yet the fundamental limits of such asymmetry have remained unknown. 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 ≤ 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 μm 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.
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BibTeX
@misc{audhkhasi2026asymmetric,
title = {{Asymmetric imaging: Reciprocity bounds and manifestations}},
author = {Romil Audhkhasi and Anna Wirth-Singh and Rose Johnson and Maksym Zhelyeznyakov and Vladimir Yarmolik and Rafael Piestun and Andrea Alù and Arka Majumdar and Owen Miller},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36350},
eprint = {2609.36350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36350},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Asymmetric imaging: Reciprocity bounds and manifestations
AU - Romil Audhkhasi
AU - Anna Wirth-Singh
AU - Rose Johnson
AU - Maksym Zhelyeznyakov
AU - Vladimir Yarmolik
AU - Rafael Piestun
AU - Andrea Alù
AU - Arka Majumdar
AU - Owen Miller
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36350
UR - https://arxiv.org/abs/2609.36350
AB - Recent demonstrations of unidirectional imaging using diffractive multilayers have brought a concept akin to optical isolation to imaging, yet the fundamental limits of such asymmetry have remained unknown. 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 ≤ 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 μm 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.
ER -