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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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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.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

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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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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

1.0K
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.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the...
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Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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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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Magnetic Field Due to Two Straight Wires01:18

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Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the magnetic field at a point "P2", midway between the wires. Also, evaluate the magnetic field when the direction of the current is reversed in the second wire.
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Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

232
Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
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Coupling of two helical circular waveguides.

Mingjie Cui, Zhuo Wang, Changyuan Yu

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    |November 1, 2024
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    Summary
    This summary is machine-generated.

    This study explores optical waveguide couplings using the finite element method (FEM). We reveal new insights into helical coupled circular waveguides, including mode intersections and asymmetric distributions with increasing twist rates.

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    Area of Science:

    • Photonics and Waveguide Technology
    • Computational Electromagnetics
    • Optical Communications

    Background:

    • Coupling between optical waveguides is crucial for device performance.
    • Previous studies have not fully explored the complexities of helical waveguide couplings.

    Purpose of the Study:

    • To investigate the coupling characteristics of two helical coupled circular waveguides.
    • To analyze the impact of twist rate on modal behavior and coupling.
    • To uncover novel phenomena in waveguide coupling using advanced numerical methods.

    Main Methods:

    • Utilizing the finite element method (FEM) for numerical analysis.
    • Employing a helicoidal coordinate system for accurate modeling.
    • Simulating various rotational symmetry cases to observe coupling behaviors.

    Main Results:

    • Identified intersections in effective index curves for two-fold rotationally symmetric cases with increasing twist rate.
    • Linked mode intersections to differing increases in helical path length and emergent high-order harmonics.
    • Observed asymmetric modal distributions in one-fold rotationally symmetric structures as twist rate increases, indicating non-equivalent couplings.

    Conclusions:

    • The study provides a detailed understanding of coupling in helical waveguides.
    • New phenomena, such as mode intersections and asymmetric couplings, have been identified.
    • Findings offer valuable insights for the design and optimization of advanced optical waveguide devices.