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Related Concept Videos

Interference: Path Lengths01:10

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
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.
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...
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.
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.
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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Related Experiment Video

Updated: Jun 8, 2026

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source
12:19

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

General self-imaging properties in N × N multimode interference couplers including phase relations.

M Bachmann, P A Besse, H Melchior

    Applied Optics
    |October 12, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Generalized N × N multimode interference couplers exhibit self-imaging properties. Their characteristics are analytically derived, offering insights for integrated optics applications.

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    Related Experiment Videos

    Last Updated: Jun 8, 2026

    Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source
    12:19

    Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

    Published on: April 4, 2017

    Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station
    05:57

    Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

    Published on: April 1, 2020

    A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
    07:56

    A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

    Published on: September 5, 2019

    Area of Science:

    • Photonics
    • Optical Engineering
    • Integrated Optics

    Background:

    • Multimode interference (MMI) couplers are fundamental components in integrated optics.
    • Understanding self-imaging phenomena is crucial for designing efficient optical devices.

    Purpose of the Study:

    • To derive the self-imaging properties of generalized N × N multimode interference couplers.
    • To analytically relate self-image characteristics to coupler dimensions.

    Main Methods:

    • Solving the eigenmode superposition equation analytically.
    • Analyzing devices with lengths (M/N) 3L(c) for multiple self-image occurrences.

    Main Results:

    • Direct analytical relationships between self-image positions, amplitudes, phases, and coupler dimensions.
    • Detailed analysis of devices exhibiting N self-images.

    Conclusions:

    • The derived formalism provides a comprehensive understanding of self-imaging in N × N MMI couplers.
    • Simple phase relations are obtained for practical applications in integrated optics.