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Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

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The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
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Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
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Sound Waves: Resonance01:14

Sound Waves: Resonance

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Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
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Resonance and Hybrid Structures02:16

Resonance and Hybrid Structures

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According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
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Toroids01:27

Toroids

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A toroid is a closely wound donut-shaped coil constructed using a single  conducting wire. In general, it is assumed that a toriod consists of  multiple circular loops perpendicular to its axis.
When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb...
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Parallel Resonance01:23

Parallel Resonance

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The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
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Updated: Aug 8, 2025

Fabrication and Characterization of Superconducting Resonators
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Meta-Atoms with Toroidal Topology for Strongly Resonant Responses.

Odysseas Tsilipakos1, Zacharias Viskadourakis2, Anna C Tasolamprou2,3

  • 1Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, GR-11635 Athens, Greece.

Micromachines
|February 25, 2023
PubMed
Summary

This study explores a toroidal meta-atom, revealing a controllable resonance. The research demonstrates how geometric tuning impacts the electromagnetic response, offering a practical, low-loss system for advanced applications.

Keywords:
3D printingbroken symmetrymetasurfacesmicrowavesmultipole expansiontoroidal dipole

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Area of Science:

  • Metamaterials Science
  • Electromagnetism
  • Nanophotonics

Background:

  • Toroidal meta-atoms offer unique electromagnetic properties.
  • Controllable resonance is crucial for advanced photonic devices.
  • Understanding multipole contributions is key to meta-atom design.

Purpose of the Study:

  • To theoretically and experimentally investigate a conductive meta-atom with toroidal topology.
  • To demonstrate a sharp and controllable resonant response.
  • To analyze the influence of geometric parameters on resonance characteristics.

Main Methods:

  • Theoretical simulations of free-space periodic metasurfaces and waveguide-integrated meta-atoms.
  • Rigorous multipole analysis to determine dominant electromagnetic moments.
  • Fabrication using 3D printing and silver paste coating.
  • Experimental measurements using a vector network analyzer in the 5 GHz regime.

Main Results:

  • A quasi-dark state with tunable radiative coupling was identified.
  • Linewidth (quality factor) and lineshape of resonance are controllable via geometric parameters.
  • The residual electric dipole moment, not the toroidal dipole, primarily dictates the electromagnetic response.
  • Experimental results show good agreement with simulations.

Conclusions:

  • The studied toroidal meta-atom exhibits a highly controllable resonant response.
  • The planar, single-layer, substrate-free design is practical and potentially low-loss.
  • This work provides insights into meta-atom design for tailored electromagnetic behavior.