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A mathematical and numerical framework for near-field optics.

Habib Ammari1, Doo Sung Choi2, Sanghyeon Yu1

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Summary

This study reconstructs surface perturbations using plasmonic particle interactions. It achieves super-resolved imaging by analyzing frequency shifts, offering a direct method for analyzing nanoscale surface features.

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Möbius transformationgeneralized polarization tensorsnear-field opticsplasmonic resonancesplasmonic sensingsuper-resolution

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Area of Science:

  • Plasmonics
  • Nanophotonics
  • Inverse Problems

Background:

  • Reconstructing nanoscale surface features is crucial for material science and device fabrication.
  • Existing methods often lack the resolution required for detailed analysis of small perturbations.

Purpose of the Study:

  • To develop a super-resolved reconstruction method for small, local perturbations on a planar surface.
  • To utilize the field interaction between a plasmonic particle and a surface for this reconstruction.

Main Methods:

  • Employing a conformal mapping to transform the particle-surface system into a coated structure.
  • Relating even Fourier coefficients of the transformed domain to plasmonic frequency shifts.
  • Proposing a direct reconstruction algorithm for surface perturbations.

Main Results:

  • Demonstrated a direct method for reconstructing surface perturbations.
  • Established a link between plasmonic frequency shifts and surface topography.
  • Numerical examples validate the proposed reconstruction technique's viability and limitations.

Conclusions:

  • The proposed method enables super-resolved reconstruction of planar surface perturbations.
  • Conformal mapping and analysis of plasmonic resonances are effective tools for inverse problems.
  • The technique offers a promising approach for nanoscale surface metrology.