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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure around a central atom from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding...
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Updated: Jul 3, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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Published on: May 27, 2020

Generalized Geometric Phase for Coupled Meta-Atoms.

Yue Wang1, Shengjie Wu1, Chen Chen1

  • 1National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China.

Nano Letters
|July 2, 2026
PubMed
Summary
This summary is machine-generated.

This study reveals that meta-atom coupling significantly impacts the Pancharatnam-Berry (PB) phase in metasurfaces, challenging linear dependence assumptions. Quasi-normal mode analysis shows PB phase is determined by meta-atom coupling and orientation, enabling precise meta-optical device characterization.

Keywords:
Coupling effectsMetasurfacesPB phaseQuasi-normal modes

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Last Updated: Jul 3, 2026

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Area of Science:

  • Metasurfaces
  • Geometric Phase Optics
  • Nanophotonics

Background:

  • Geometric phase, including Pancharatnam-Berry (PB) phase, is crucial for metasurface functionalities.
  • Conventional metasurface design assumes a linear relationship between PB phase and meta-atom orientation.
  • Previous observations of non-linear PB phase behavior lacked a clear mechanistic explanation.

Purpose of the Study:

  • To analyze the evolution of PB phases in metasurfaces.
  • To investigate the underlying mechanisms responsible for the breakdown of linear PB phase dependence.
  • To establish a systematic framework for accurate PB phase analysis in meta-optical devices.

Main Methods:

  • Detailed theoretical analysis of PB phase evolution.
  • Investigation using quasi-normal modes (QNMs) to understand phase determination.
  • Experimental validation using a specifically designed grating structure.

Main Results:

  • Identified meta-atom mutual coupling as a critical factor influencing PB phase.
  • Demonstrated that PB phase is determined by far-field radiation polarizations of excited QNMs.
  • Showcased the combined influence of meta-atom orientation and mutual coupling on PB phase.

Conclusions:

  • Meta-atom coupling plays a non-negligible role in determining the PB phase.
  • QNMs provide a framework to link meta-atom properties to far-field polarization and PB phase.
  • This work enables high-precision characterization and design of meta-optical devices.