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¹H NMR: Complex Splitting01:13

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A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
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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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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Multiple bound states in the continuum in a grating-slab-coupled structure.

Yuchen Li1, Shou Zhou1, Weihua Wang1

  • 1School of Material Science and Physics, China University of Mining and Technology, Xuzhou 221116, People's Republic of China. wh.wang@outlook.com.

Physical Chemistry Chemical Physics : PCCP
|June 26, 2025
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Summary

This study introduces a novel grating-slab structure capable of supporting multiple bound states in the continuum (BICs), including symmetry-protected, accidental, and Friedrich-Wintgen types. This platform offers enhanced control over light manipulation for advanced photonic applications.

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Area of Science:

  • Photonics and optical physics
  • Condensed matter physics
  • Wave phenomena

Background:

  • Bound states in the continuum (BICs) are localized resonant states within the radiation continuum.
  • BICs are classified into symmetry-protected (SP-BIC), accidental (A-BIC), and Friedrich-Wintgen (FW-BIC) types based on their formation mechanisms.
  • Simultaneously achieving all three BIC types presents a significant design challenge.

Purpose of the Study:

  • To propose and demonstrate a simple grating-slab coupled structure for engineering multiple BIC types.
  • To investigate the tunability and characteristics of different BICs within the proposed structure.
  • To provide a versatile platform for advanced light manipulation.

Main Methods:

  • Utilized a grating-slab coupled structure to engineer BICs.
  • Analyzed the interplay between structural components to control BIC properties.
  • Investigated the quality factors, topological features, and field patterns of the supported BICs.

Main Results:

  • The structure successfully supported two SP-BICs, one A-BIC, and one FW-BIC.
  • SP-BICs exhibited quadratic scaling of quality factors with asymmetry parameters.
  • A-BIC showed tunability with slab thickness, characteristic of topological protection, while FW-BIC displayed coupling-induced avoided crossing.
  • Off-Γ BICs shared topological features like topological charge despite different field patterns.

Conclusions:

  • The proposed grating-slab structure serves as an effective platform for simultaneously achieving and manipulating multiple BIC types.
  • This work offers a new avenue for designing advanced photonic devices with tailored light-matter interactions.
  • The ability to engineer diverse BICs opens possibilities for novel light manipulation strategies.