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

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

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

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 involved orbitals. The...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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,...
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...

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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
09:19

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Published on: July 29, 2013

Strong coupling to two-dimensional Anderson localized modes.

A Cazé1, R Pierrat, R Carminati

  • 1Institut Langevin, ESPCI ParisTech, CNRS, 1 rue Jussieu, 75238 Paris Cedex 05, France.

Physical Review Letters
|August 20, 2013
PubMed
Summary
This summary is machine-generated.

We derived a condition for strong coupling between localized light modes and scatterers in 2D. This coupling threshold links transport theory and cavity quantum electrodynamics, aiding experimental design.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Optics
  • Electromagnetism

Background:

  • Anderson localization describes the trapping of waves in disordered media.
  • Strong coupling is crucial for quantum information processing and novel optical devices.
  • Resonant scatterers enhance light-matter interactions.

Purpose of the Study:

  • To derive a theoretical condition for strong coupling between resonant scatterers and Anderson localized modes.
  • To demonstrate this strong coupling regime using numerical simulations.
  • To connect concepts from transport theory and cavity quantum electrodynamics.

Main Methods:

  • Utilized a scattering formalism to derive the strong coupling condition.
  • Performed exact numerical simulations to verify the theoretical predictions.
  • Expressed the strong coupling threshold using established physical parameters.

Main Results:

  • Derived a condition for strong coupling between a resonant scatterer and an Anderson localized mode in 2D.
  • Numerical simulations confirmed the theoretical predictions, demonstrating the strong coupling regime.
  • The strong coupling threshold was found to be dependent on the Thouless conductance and Purcell factor.

Conclusions:

  • The study establishes a theoretical framework and numerical evidence for strong coupling in 2D disordered photonic systems.
  • It bridges the gap between Anderson localization and cavity quantum electrodynamics concepts.
  • Provides a practical tool for designing and analyzing experiments involving light-matter interactions in localized modes.