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Related Concept Videos

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: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's first...
Phase Contrast and Differential Interference Contrast Microscopy01:26

Phase Contrast and Differential Interference Contrast Microscopy

Phase-Contrast Microscopes
In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...
Properties of Enantiomers and Optical Activity02:24

Properties of Enantiomers and Optical Activity

It is essential to understand the difference between chiral and achiral interactions and the implications thereof in optical activity and their applications. Just as our feet, which are chiral, interact uniquely with chiral objects, such as a pair of shoes, but identically with achiral socks, enantiomers of a molecule exhibit different properties only when they interact with other chiral media. An example of a significant implication from this facet is the phenomenon known as optical activity,...

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Related Experiment Video

Updated: Jun 16, 2026

High-speed Continuous-wave Stimulated Brillouin Scattering Spectrometer for Material Analysis
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Published on: September 22, 2017

Jones's Matrix Representation of Optical Instruments. I: Beam Splitters.

A L Fymat

    Applied Optics
    |January 30, 2010
    PubMed
    Summary

    This study presents a general method for calculating Jones matrices for any beam splitter, simplifying optical analysis. The research also explores how beam splitter thickness can maintain interferogram symmetry, even in asymmetric setups.

    Area of Science:

    • Optics
    • Photonics
    • Interferometry

    Background:

    • Beam splitters are fundamental optical components in interferometry.
    • Accurate Jones matrices are crucial for modeling light polarization and phase changes.
    • Existing methods for deriving Jones matrices can be complex and configuration-specific.

    Purpose of the Study:

    • To develop a general method for constructing Jones's reflection and transmission matrices for any beam splitter.
    • To analyze the reversibility of beam splitters concerning amplitude and phase.
    • To investigate methods for preserving interferogram symmetry in asymmetric beam splitter configurations.

    Main Methods:

    • Utilizing Abelès's matrices for matrix derivations.
    • Considering different expressions of Jones's matrices for various beams in interferometric arrangements.

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    A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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  • Analyzing the impact of beam splitter properties on light polarization and phase.

    • Main Results:

    • A universal method for deriving Jones matrices for diverse beam splitter configurations is established.
    • The reversibility of beam splitters' effects on light's amplitude and phase is characterized.
    • A technique to preserve interferogram symmetry by adjusting beam splitter thickness is proposed.

    Conclusions:

    • The generalized method simplifies the analysis of beam splitters in optical systems.
    • Understanding beam splitter reversibility is key for precise optical design.
    • Controlled adjustment of beam splitter thickness offers a practical solution for maintaining interferometric symmetry.