- Open Access
Very high and very low Fisher information for small displacements of a plasmonic silver nanowire
Phys. Rev. Research 7, 043227 – Published 1 December, 2025
DOI: https://doi.org/10.1103/m4cm-545j
Abstract
In this paper, we study the effects of plasmonic resonances on the Fisher information in the far field, of the position of a silver nanowire with respect to the center of a focused spot. We study theoretically a nanowire embedded in a high refractive index substrate that is illuminated by a dark-field focused spot. The position of the nanowire is determined from the scattered far-field intensities. The Fisher information is computed for both a lateral and longitudinal displacement of the nanowire, and its dependence on the illumination frequency is analyzed. The resonance frequencies of the nanowires are determined. We find that frequencies near a plasmonic resonance can enhance the Fisher information. However, at the resonance frequency itself and very close to it, the scattered far field corresponds to an information dark state. The phenomenon is demonstrated for silver, and the underlying physical mechanism is explained with an analytical model. As is shown, the dark state can be converted into a state with very high Fisher information about the positions of the nanowire by modifying the focused spot.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (20)
- C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (John Wiley & Sons, Chichester, West Sussex, 2007).
- N. Kumar, P. Petrik, G. K. Ramanandan, O. El Gawhary, S. Roy, S. F. Pereira, W. M. Coene, and H. P. Urbach, Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry, Opt. Express 22, 24678 (2014).
- H. Deschout, F. C. Zanacchi, M. Mlodzianoski, A. Diaspro, J. Bewersdorf, S. T. Hess, and K. Braeckmans, Precisely and accurately localizing single emitters in fluorescence microscopy, Nat. Methods 11, 253 (2014).
- Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, Optimal point spread function design for 3D imaging, Phys. Rev. Lett. 113, 133902 (2014).
- X. Wei, H. P. Urbach, and W. M. Coene, Cramér–Rao lower bound and maximum-likelihood estimation in ptychography with Poisson noise, Phys. Rev. A 102, 043516 (2020).
- J. Seifert, Y. Shao, R. Van Dam, D. Bouchet, T. Van Leeuwen, and A. P. Mosk, Maximum-likelihood estimation in ptychography in the presence of Poisson–Gaussian noise statistics, Opt. Lett. 48, 6027 (2023).
- Z. Xi, S. Konijnenberg, and H. P. Urbach, Information-efficient metagrating for transverse-position metrology, Phys. Rev. Appl. 14, 014026 (2020).
- D. Bouchet, J. Seifert, and A. P. Mosk, Optimizing illumination for precise multi-parameter estimations in coherent diffractive imaging, Opt. Lett. 46, 254 (2021).
- D. Bouchet, S. Rotter, and A. P. Mosk, Maximum information states for coherent scattering measurements, Nat. Phys. 17, 564 (2021).
- M. Horodynski, D. Bouchet, M. Kühmayer, and S. Rotter, Invariance property of the Fisher information in scattering media, Phys. Rev. Lett. 127, 233201 (2021).
- J. Hüpfl, F. Russo, L. M. Rachbauer, D. Bouchet, J. Lu, T. Kuhl, and S. Rotter, Continuity equation for the flow of Fisher information in wave scattering, Nat. Phys. 20, 1294 (2024).
- Z. Xi and H. P. Urbach, Magnetic dipole scattering from metallic nanowire for ultrasensitive deflection sensing, Phys. Rev. Lett. 119, 053902 (2017).
- Z. Xi and H. P. Urbach, Retrieving the size of deep-subwavelength objects via tunable optical spin-orbit coupling, Phys. Rev. Lett. 120, 253901 (2018).
- J. J. Bowman, T. B. Senior, and P. L. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere Publishing Corporation, New York, 1987), revised ed.
- L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, Cambridge, 2012), 2nd ed.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/m4cm-545j for animations of the fields as functions of time, and also as functions of the frequency.
- A. P. Mosk (personal communication).
- A. Zangwill, Modern Electrodynamics (Cambridge University Press, Cambridge, 2013).
- A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, Optical properties of metallic films for vertical-cavity optoelectronic devices, Appl. Opt. 37, 5271 (1998).
- J. B. P. de Graaff, plasmonic-nanowire (GitLab repository). Delft University of Technology (TU Delft), 2025. Available at https://gitlab.tudelft.nl/J.B.P.deGraaff/plasmonic-nanowire. Accessed 12 Nov 2025.
