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Angular Momentum01:21

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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...
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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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The angular impulse and momentum principle provides insights into how forces applied at a distance from an object's rotational axis influence its angular velocity. It builds upon the crucial relationship between the moment of force and angular momentum. By integrating this equation, substituting the limits for the initial and final times, a comprehensive expression representing the angular impulse and momentum principle is derived.
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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.
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Related Experiment Video

Updated: Feb 15, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Astigmatic laser beams with a large orbital angular momentum.

Victor V Kotlyar, Alexey A Kovalev, Alexey P Porfirev

    Optics Express
    |January 13, 2018
    PubMed
    Summary

    Researchers demonstrate how to generate high orbital angular momentum (OAM) laser beams using a simple cylindrical lens. This method avoids complex optical elements and allows for adjustable OAM values in astigmatic Gaussian beams.

    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Quantum Optics

    Background:

    • Orbital angular momentum (OAM) in light beams enables advanced applications.
    • Generating beams with high OAM often requires complex optical setups.

    Purpose of the Study:

    • To investigate the representation of focused elliptic Gaussian beams.
    • To derive an exact expression for the OAM of astigmatic Gaussian beams.
    • To demonstrate a method for generating and controlling high OAM laser beams.

    Main Methods:

    • Representing an elliptic Gaussian beam as a series of even angular harmonics.
    • Deriving an exact expression for OAM using Legendre functions.
    • Employing a hybrid numeric-experimental approach to measure OAM.

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    Main Results:

    • An astigmatic Gaussian beam can be expressed as a sum of even angular harmonics with varying topological charges.
    • An exact OAM expression was derived, showing selective retention of positive or negative topological charge terms.
    • A hybrid approach yielded a normalized OAM of 109, a 6% difference from the calculated value of 116.

    Conclusions:

    • High OAM laser beams can be generated without specialized optical elements like spiral phase plates.
    • OAM values are adjustable by modifying the Gaussian beam's waist radius and the cylindrical lens's focal length.
    • The presented method allows for the generation of laser beams with significantly large OAM.