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$Interference and Diffraction$ 02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

Deflection of a Beam

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...

Beams

Beams

Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...

Design of Prismatic Beams for Bending

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...

Prismatic Beams: Problem Solving

Prismatic Beams: Problem Solving

In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the designer...

Distribution of Stresses in a Narrow Rectangular Beam

Distribution of Stresses in a Narrow Rectangular Beam

In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these areas.

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Related Experiment Video

Updated: Jun 13, 2026

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

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

Published on: January 28, 2019

Shaped nondiffracting beams.

Carlos López-Mariscal¹, Kristian Helmerson

¹National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8424, USA. clopez@nist.gov

|April 23, 2010

Summary

This summary is machine-generated.

Researchers can now create nondiffracting beams with any desired transverse shape. This is achieved by controlling the angular spectra of Helmholtz-Gauss wave fields, allowing for tailored beam intensity patterns.

More Related Videos

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

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

Published on: August 12, 2013

Related Experiment Videos

Last Updated: Jun 13, 2026

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

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

Published on: January 28, 2019

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

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

Published on: August 12, 2013

Area of Science:

Optics and Photonics
Wave Phenomena
Beam Shaping

Background:

Nondiffracting beams maintain their transverse shape during propagation.
Controlling beam characteristics is crucial for applications in imaging and optical manipulation.
Helmholtz-Gauss beams are a type of wave field with specific propagation properties.

Purpose of the Study:

To demonstrate the generation of nondiffracting beams with arbitrary transverse shapes.
To explore the use of azimuthal complex modulation for beam tailoring.
To establish a method for controlling the intensity pattern of nondiffracting beams.

Main Methods:

Utilizing the angular spectra of Helmholtz-Gauss wave fields.
Applying azimuthal complex modulation to the wave field's angular spectrum.
Analyzing the resulting beam's propagation characteristics and intensity profile.

Main Results:

Successfully generated nondiffracting beams with user-defined transverse intensity patterns.
Confirmed that azimuthal complex modulation is a sufficient degree of freedom for shape control.
Demonstrated precise tailoring of beam intensity profiles.

Conclusions:

Arbitrary transverse shaping of nondiffracting beams is achievable.
Azimuthal complex modulation of angular spectra offers a powerful tool for beam engineering.
This technique enables the creation of specialized beams for advanced optical applications.