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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

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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,...
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Gauss's Law: Spherical Symmetry01:26

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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...
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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.
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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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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...
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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Super-Gaussian conical refraction beam.

A Turpin, Yu V Loiko, T K Kalkandkiev

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    |August 1, 2014
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    Summary
    This summary is machine-generated.

    Researchers transformed Gaussian beams into super-Gaussian beams using conical refraction. This novel method creates flat-top beams with enhanced propagation characteristics, verified experimentally in a biaxial crystal.

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    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Materials Science

    Background:

    • Gaussian beams are fundamental in optics but lack a flat-top profile.
    • Controlling beam profiles is crucial for applications like laser machining and microscopy.
    • Conical refraction offers a unique phenomenon for light manipulation in anisotropic media.

    Purpose of the Study:

    • To demonstrate the transformation of Gaussian beams into super-Gaussian beams using conical refraction.
    • To investigate the beam propagation characteristics of the generated super-Gaussian beams.
    • To experimentally validate the theoretical predictions using a specific biaxial crystal.

    Main Methods:

    • Utilizing the phenomenon of conical refraction in a biaxial crystal.
    • Adjusting the ratio between the ring radius and waist radius of the input Gaussian beam to 0.445.
    • Analyzing the transverse profile and propagation parameters of the resulting beams.

    Main Results:

    • Successfully transformed Gaussian input beams into super-Gaussian beams with a quasi flat-top transverse profile.
    • Observed that the super-Gaussian beam possesses a confocal parameter three times larger than that of a standard Gaussian beam.
    • Experimental results using a KGd(WO4)2 biaxial crystal showed excellent agreement with theoretical predictions.

    Conclusions:

    • Conical refraction provides an effective method for generating super-Gaussian beams with desirable flat-top profiles.
    • The generated super-Gaussian beams exhibit significantly improved propagation characteristics, indicated by a larger confocal parameter.
    • The experimental validation confirms the feasibility and accuracy of this optical transformation technique.