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

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

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...

Gauss's Law: Cylindrical Symmetry

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...

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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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Updated: Oct 13, 2025

Setting a Successful Sorting for Extracellular Vesicle Isolation

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Published on: October 11, 2024

Cylindrical vector beam sorter with spin-dependent spiral transformation.

Ziang Lin, Zhiqiang Xie, Yanliang He

|November 15, 2021

Summary

We developed a novel cylindrical vector beam (CVB) sorter using spin-dependent spiral transformations. This method effectively sorts CVB modes, enabling high-resolution separation and demonstrating potential for optical communication and interconnection applications.

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Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

Optics and Photonics
Quantum Optics
Information Optics

Background:

Cylindrical vector beams (CVBs) possess unique polarization properties.
Efficient sorting and demultiplexing of CVBs are crucial for advanced optical systems.
Existing methods for CVB manipulation face limitations in resolution and efficiency.

Purpose of the Study:

To propose and experimentally demonstrate a novel cylindrical vector beam (CVB) sorter.
To exploit spin-orbital interaction for high-resolution CVB mode sorting.
To showcase the application of CVB sorting in optical communication.

Main Methods:

Utilizing a spin-dependent spiral transformation based on geometric phase.
Modulating orthogonal circularly polarized components of CVBs.
Employing a convex lens for spatial separation of sorted CVB modes.

Main Results:

Successfully sorted five CVB modes (from -2 to +2) with high resolution.
Achieved a separation efficiency of 3.65 for the sorted CVB modes.
Demonstrated a two-channel CVB multiplexing communication with a bit error rate near 10^-6.

Conclusions:

The proposed CVB sorter offers an effective method for CVB demultiplexing.
The technique shows promise for applications in mode filtering and routing in all-optical interconnections.
The spin-dependent spiral transformation provides a pathway for high-resolution optical beam manipulation.