The DOI matches its Crossref record.
Evolution of quantum superoscillations and optical superresolution without evanescent waves
Abstract
A superoscillatory function—that is, a band-limited function f(x) oscillating faster than its fastest Fourier component—is taken to be the initial state of a freely-evolving quantum wavefunction ψ. The superoscillations persist for unexpectedly long times, but eventually disappear through the interaction of contributions to ψ with complex momenta that are exponentially disparate in magnitude; this is established by applying the asymptotics of integrals, supported by numerics. f(x) can alternatively be regarded as the wave generated by a diffraction grating, propagating paraxially and without evanescence as ψ in the space beyond. The persistence of superoscillations is then interpreted as the propagation of sub-wavelength structure farther into the field than the more familiar evanescent waves.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Berry, M. V. (2009) · Journal of Optics A: Pure and Applied Optics · doi:10.1088/1464-4258/11/9/094001 · Cited by 531
Self-citationRoadmap for Optical Metasurfaces
Kuznetsov, A. I., Brongersma, M. L., Yao, J., Chen, M. K., Levy, U., Tsai, D. P., Zheludev, N. I., Faraon, A., Arbabi, A., Yu, N., et al. (2024) · ACS Photonics · doi:10.1021/acsphotonics.3c00457 · Cited by 420
Superresolution imaging via superoscillation focusing of a radially polarized beam
Kozawa, Y., Matsunaga, D., & Sato, S. (2018) · Optica · doi:10.1364/optica.5.000086 · Cited by 323
Super-Resolution without Evanescent Waves
Huang, F. M., & Zheludev, N. I. (2009) · Nano Letters · doi:10.1021/nl9002014 · Cited by 305
Metadata
- Authors
- Berry, M. V., & Popescu, S.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2006-05-16
- Volume
- 39
- Issue
- 22
- Pages
- 6965-6977
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1982928226
- Cited by
- 442
- References
- 0
- FWCI
- 4.30
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Evolution of quantum superoscillations and optical superresolution without evanescent waves. https://app.cochat.ai/papers/10.1088/0305-4470/39/22/011
- The paper
- Berry, M. V., & Popescu, S. (2006). Evolution of quantum superoscillations and optical superresolution without evanescent waves. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/39/22/011
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
