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Related Concept Videos

Deflection of a Beam01:19

Deflection of a Beam

Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Bessel Function of Order Zero01:20

Bessel Function of Order Zero

A common physical example of wave propagation with radial symmetry is the ripple formed when a stone is dropped into a still pond. The disturbance originates at a central point and travels outward as a circular wave. As the radius of the wavefront increases, the same initial energy is distributed along a progressively larger circumference. Consequently, the amplitude, or height, of the wave decreases with distance from the center. This decay behavior cannot be captured by simple sine or cosine...
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Singularity Functions for Bending Moment01:18

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...

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Related Experiment Video

Updated: Jun 9, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Gaussian-to-Bessel beam transformation using a split refracting system.

K M Ftekharuddin, A A Awwal, M A Karim

    Applied Optics
    |September 8, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A novel two-element refracting system efficiently converts Gaussian laser beams into diffraction-free Bessel beams. This system features nearly spherical input and output surfaces for straightforward integration.

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    Related Experiment Videos

    Last Updated: Jun 9, 2026

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

    Published on: August 12, 2013

    High-speed Continuous-wave Stimulated Brillouin Scattering Spectrometer for Material Analysis
    07:55

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    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
    08:39

    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

    Published on: January 28, 2019

    Area of Science:

    • Optics and Photonics
    • Laser Physics

    Background:

    • Gaussian beams are fundamental in laser applications but diverge.
    • Bessel beams offer unique diffraction-free propagation properties.

    Purpose of the Study:

    • To design a compact optical system for generating Bessel beams from Gaussian beams.
    • To achieve a system with simple input and output optical surfaces.

    Main Methods:

    • Utilized a two-element refractive optical design.
    • Simulated beam transformation from Gaussian to Bessel profiles.

    Main Results:

    • Successfully designed a system that transforms a Gaussian laser beam into a diffraction-free Bessel beam.
    • The system's input and output surfaces are nearly spherical, simplifying manufacturing and alignment.

    Conclusions:

    • The proposed two-element system provides an accessible method for generating Bessel beams.
    • The spherical surface design facilitates practical implementation in various optical setups.