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Related Concept Videos

Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
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: 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: 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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...

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Translational, rotational, and vibrational coupling into phase in diffractively coupled optical cavities.

B W Barr1, M P Edgar, J Nelson

  • 1School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK. bryan.barr@glasgow.ac.uk

Optics Letters
|July 19, 2011
PubMed
Summary

Future gravitational wave detectors using all-reflective optics face challenges. Translational and vibrational motion of diffractive input gratings introduce unwanted phase shifts, detectable by standard cavity length sensors.

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Area of Science:

  • Optics and Gravitational Wave Detection
  • Advanced Interferometry Techniques

Background:

  • All-reflective optical systems are proposed for next-generation gravitational wave detectors.
  • Fabry-Perot cavities with diffraction gratings as input couplers are a key component.
  • Grating surface translation can introduce unwanted phase shifts in optical systems.

Purpose of the Study:

  • To investigate the sensitivity of cavity length-sensing techniques to diffractive input coupler motion.
  • To demonstrate that standard sensors detect translational, rotational, and vibrational noise.
  • To experimentally verify theoretical predictions of noise coupling in suspended cavities.

Main Methods:

  • Utilized a prototype-scale suspended cavity with a diffractive input coupler.
  • Employed conventional cavity length-sensing techniques to monitor system response.
  • Experimentally measured amplitude response and frequency dependency of induced noise.

Main Results:

  • Cavity length-sensing techniques are sensitive to translational motion of the diffractive input coupler.
  • Sensors also detect rotational (yaw) and vibrational motion of the optical element.
  • Experimental results align with theoretical predictions regarding noise coupling amplitude and frequency.

Conclusions:

  • Standard cavity length-sensing methods are not immune to input coupler motion in all-reflective systems.
  • Translational, rotational, and vibrational noise from diffractive couplers impacts detector sensitivity.
  • Understanding and mitigating this noise coupling is crucial for future gravitational wave detector designs.