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Scaling law linking field and weight dynamic ranges in superoscillation
Phys. Rev. A 114, 013505 – Published 7 July, 2026
DOI: https://doi.org/10.1103/zrmd-2dxx
Abstract
Superoscillation (SO) offers a theoretical pathway to unlimited far-field superresolution, yet the associated physical costs lack a unified quantitative scaling description. In this work, we investigate the fundamental limits of deep SO by establishing a scaling law that links the field dynamic range (FDR) and the weight dynamic range (WDR) and validate it through numerical synthesis of one-dimensional SO fields. We observe a strong, near-linear correlation between FDR and WDR in the log-log domain, described by . This relation reveals that extreme resolution is governed by two coupled constraints: a focus requires not only a 1661-dB FDR, corresponding to a detection bottleneck, but also a 177-dB WDR, which imposes a comparably stringent requirement on field synthesis and fabrication.
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References (19)
- Y.-H. Ouyang, H.-Y. Luan, Z.-W. Zhao, W.-Z. Mao, and R.-M. Ma, Singular dielectric nanolaser with atomic-scale field localization, Nature (London) 632, 287 (2024).
- N. I. Zheludev and G. Yuan, Optical superoscillation technologies beyond the diffraction limit, Nat. Rev. Phys. 4, 16 (2022).
- G. Chen, Z.-Q. Wen, and C.-W. Qiu, Superoscillation: From physics to optical applications, Light: Sci. Appl. 8, 56 (2019).
- G. H. Yuan, E. T. Rogers, and N. I. Zheludev, Achromatic super-oscillatory lenses with sub-wavelength focusing, Light: Sci. Appl. 6, e17036 (2017).
- Y. Shen, N. Papasimakis, and N. I. Zheludev, Space-time superoscillations, Nat. Commun. 17, 2053 (2026).
- A. M. Wong and G. V. Eleftheriades, Adaptation of Schelkunoff's superdirective antenna theory for the realization of superoscillatory antenna arrays, IEEE Antennas Wireless Propag. Lett. 9, 315 (2010).
- A. M. Wong and G. V. Eleftheriades, An optical super-microscope for far-field, real-time imaging beyond the diffraction limit, Sci. Rep. 3, 1715 (2013).
- H. Yang, E. Y. Lin, K. N. Kutulakos, and G. V. Eleftheriades, Computational nonscanning incoherent superoscillatory imaging, ACS Photonics 9, 290 (2022).
- H. Yang, E. Y. Lin, K. N. Kutulakos, and G. V. Eleftheriades, Sub-wavelength passive single-shot computational super-oscillatory imaging, Optica 9, 1444 (2022).
- X. Ma, H. Zhang, W. Wei, Y. Tai, Y. Qian, X. Li, and Y. Shen, Observation of superoscillation moiré superlattices, Adv. Photonics 8, 026008 (2026).
- M. Berry, Faster than Fourier, in Quantum Coherence and Reality, Celebration of the 60th Birthday of Yakir Aharonov, edited by J. S. Anandan and J. L. Safko (World Scientific, Singapore, 1994), pp. 55–65.
- M. Berry, N. Zheludev, Y. Aharonov, F. Colombo, I. Sabadini, D. C. Struppa, J. Tollaksen, E. T. Rogers, F. Qin, M. Hong, et al., Roadmap on superoscillations, J. Opt. 21, 053002 (2019).
- M. Berry and S. Popescu, Evolution of quantum superoscillations and optical superresolution without evanescent waves, J. Phys. A 39, 6965 (2006).
- G. H. Yuan, S. Vezzoli, C. Altuzarra, E. T. Rogers, C. Couteau, C. Soci, and N. I. Zheludev, Quantum super-oscillation of a single photon, Light: Sci. Appl. 5, e16127 (2016).
- D. G. Lee and P. J. Ferreira, Superoscillations with optimal numerical stability, IEEE Signal Process. Lett. 21, 1443 (2014).
- K. S. Rogers and E. T. Rogers, Realising superoscillations: A review of mathematical tools and their application, J. Phys. Photonics 2, 042004 (2020).
- H. Yang and G. V. Eleftheriades, Synthesis of super-oscillatory point-spread functions with Taylor-like tapered sidelobes for advanced optical super-resolution imaging, Photonics 8, 64 (2021).
- G. Gbur, Using superoscillations for superresolved imaging and subwavelength focusing, Nanophotonics 8, 205 (2018).
- P. J. S. Ferreira and A. Kempf, Superoscillations: Faster than the Nyquist rate, IEEE Trans. Signal Process. 54, 3732 (2006).
