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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...
Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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 stress...
Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

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 first...
Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

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...
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments. Initially, this...

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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

Two-dimensional nonlinear beam shaping.

Asia Shapira1, Roy Shiloh, Irit Juwiler

  • 1Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel. asiasapi@post.tau.ac.il

Optics Letters
|June 5, 2012
PubMed
Summary
This summary is machine-generated.

Researchers created a new method for shaping light waves in nonlinear crystals using computer-generated holograms. This technique successfully converted a single light beam into multiple complex beams, advancing nonlinear optics.

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Area of Science:

  • Nonlinear Optics
  • Photonics
  • Wavefront Shaping

Background:

  • Quadratic nonlinear crystals are crucial for light manipulation.
  • Controlling light wavefronts in nonlinear media presents significant challenges.
  • Existing methods for arbitrary wavefront shaping are limited.

Purpose of the Study:

  • To develop a novel technique for two-dimensional arbitrary wavefront shaping.
  • To utilize binary nonlinear computer-generated holograms for this purpose.
  • To explore nonlinear beam shaping and mode conversion in photonic crystals.

Main Methods:

  • Employing transverse illumination of a binary modulated nonlinear photonic crystal.
  • Leveraging the nonlinear Raman-Nath process for phase matching.
  • Utilizing binary nonlinear computer-generated holograms for wavefront control.

Main Results:

  • Demonstrated experimental conversion of a Gaussian beam pump light.
  • Successfully generated three Hermite-Gaussian and three Laguerre-Gaussian beams at the second harmonic.
  • Validated the technique for arbitrary wavefront shaping in nonlinear crystals.

Conclusions:

  • The developed technique enables precise two-dimensional wavefront shaping.
  • Binary nonlinear computer-generated holograms offer versatile applications in nonlinear optics.
  • This method significantly expands possibilities in nonlinear beam shaping and mode conversion.