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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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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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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Related Experiment Video

Updated: Aug 14, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Large second-harmonic vortex beam generation with quasi-nonlinear spin-orbit interaction.

Wenchao Zhao1, Kai Wang1, Xuanmiao Hong1

  • 1Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.

Science Bulletin
|January 19, 2023
PubMed
Summary

Researchers generated high-quality second-harmonic (SH) vortex beams using quasi-nonlinear spin-orbit interaction. This advances optical communications and metasurface devices by efficiently creating harmonic optical vortices.

Keywords:
MetalensesMonolayer WS(2)Orbital-angular momentumPlasmonic metasurfaceSecond-harmonic generation

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Area of Science:

  • Optics and Photonics
  • Materials Science
  • Nonlinear Optics

Background:

  • Harmonic vortex beams offer enhanced information capacity due to their helical wavefronts at harmonic frequencies.
  • Conventional methods for generating harmonic vortex beams are complex and inefficient.

Purpose of the Study:

  • To propose and experimentally demonstrate a novel method for generating high-quality second-harmonic (SH) vortex beams.
  • To overcome the limitations of conventional harmonic vortex beam generators.

Main Methods:

  • Utilizing quasi-nonlinear spin-orbit interaction (SOI) for beam generation.
  • Employing a plasmonic spiral phase plate and a WS2 monolayer.
  • Experimentally realizing SH vortex beams with high topological charges.

Main Results:

  • Successfully generated high-quality SH vortex beams with topological charges up to 28.
  • Demonstrated the imprinting of topological charge from the excitation wavelength onto harmonic signals.
  • Established a relationship between the topological charge of the excitation and the harmonic signals (ln=2nq).

Conclusions:

  • The proposed method efficiently generates large second-harmonic vortex beams.
  • This work opens new possibilities for optical communications and the development of multi-functional hybrid metasurface devices for harmonic beam manipulation.