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Related Concept Videos

Relation Between Moment of a Force and Angular Momentum01:21

Relation Between Moment of a Force and Angular Momentum

In the realm of spinning tops, the application of force at a distance from the center produces torque, a pivotal factor that alters the angular momentum of the top, thereby inducing its rotation. The concept of moment, akin to linear force in rotation, quantifies how a force acting upon an object initiates rotational motion. Angular momentum serves as the rotational counterpart to linear momentum, representing an object's inherent tendency to persist in its rotational state.
The temporal change...
Angular Momentum01:21

Angular Momentum

Angular momentum characterizes an object's rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its...
Angular Momentum: Single Particle01:10

Angular Momentum: Single Particle

Angular momentum is directed perpendicular to the plane of the rotation, and its magnitude depends on the choice of the origin. The perpendicular vector joining the linear momentum vector of an object to the origin is called the “lever arm.” If the lever arm and linear momentum are collinear, then the magnitude of the angular momentum is zero. Therefore, in this case, the object rotates about the origin such that it lies on the rim of the circumference defined by the lever arm magnitude.
The...
Angular Momentum about an Arbitrary Axis01:11

Angular Momentum about an Arbitrary Axis

Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into the angular...
Conservation of Angular Momentum: Application01:18

Conservation of Angular Momentum: Application

A system's total angular momentum remains constant if the net external torque acting on the system is zero. Examples of such systems include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth's rotation over millions of years due to frictional forces exerted on tidal deformations. However in the absence of a net external torque, the angular momentum remains conserved. The conservation of angular momentum principle requires a change...
Conservation of Angular Momentum01:09

Conservation of Angular Momentum

A system's total angular momentum remains constant if the net external torque acting on the system is zero. Considering a system that consists of n tiny particles, the angular momentum of any tiny particle may change, but the system's total angular momentum would remain constant. The principle of conservation of angular momentum only considers the net external torque acting on the system. While there are internal forces exerted by different particles within the system that also produce internal...

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Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures
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Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Published on: November 21, 2019

Fourier relationship between angular position and optical orbital angular momentum.

Eric Yao, Sonja Franke-Arnold, Johannes Courtial

    Optics Express
    |June 17, 2009
    PubMed
    Summary
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    We show that light

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    Area of Science:

    • Quantum optics
    • Classical optics

    Background:

    • Orbital angular momentum (OAM) is a fundamental property of light.
    • Understanding the relationship between OAM and spatial properties is crucial for optical applications.

    Purpose of the Study:

    • To demonstrate the Fourier relationship between angular position and orbital angular momentum (OAM) of light.
    • To experimentally verify that the OAM distribution is the Fourier transform of an aperture function.

    Main Methods:

    • Utilizing spatial light modulators (SLMs) as diffractive optical elements.
    • Defining initial OAM states and aperture functions with SLMs.
    • Measuring the OAM distribution of light after passing through the aperture.

    Main Results:

    • Confirmed the Fourier relationship between angular position and OAM.
    • The OAM distribution precisely matched the complex Fourier transform of the aperture function.
    • The relationship holds even at the single-photon level.

    Conclusions:

    • The study experimentally validates the theoretical Fourier relationship between light's spatial properties and its orbital angular momentum.
    • This fundamental connection is demonstrated robustly, even under low light conditions, paving the way for advanced optical technologies.