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Bessel Function of Order Zero

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...

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...

Singularity Functions for Bending Moment

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...

Bending of Curved Members - Neutral Surface

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...

Deformations in a Symmetric Member in Bending

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...

Shear on the Horizontal Face of a Beam Element

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...

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Related Experiment Video

Updated: Jun 19, 2026

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

Spiraling zero-order Bessel beam.

Vygandas Jarutis¹, Aidas Matijosius, Paolo Di Trapani

¹Department of Quantum Electronics, Vilnius University, Vilnius, Lithuania. vygandas.jarutis@ff.vu.lt

|October 14, 2009

Summary

Scientists theoretically explored creating a spiraling Bessel-like beam. This novel light field, achievable with an axicon and hologram, shows promise for microfabrication applications.

Area of Science:

Optics and Photonics
Laser Physics

Background:

Bessel beams are known for their non-diffracting properties.
Light fields that spiral around the propagation axis are of significant interest for specialized applications.

Purpose of the Study:

To theoretically investigate the creation of a zeroth-order Bessel-like beam with a helical trajectory.
To analyze the propagation characteristics of this novel light beam.

Main Methods:

Theoretical analysis of beam propagation.
Modeling of light field behavior.

Main Results:

A theoretical framework for a zeroth-order Bessel-like beam spiraling around the propagation axis was established.
The study outlines experimental feasibility using an axicon and hologram.

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

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

Published on: September 22, 2017

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

Related Experiment Videos

Last Updated: Jun 19, 2026

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

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

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

Published on: September 22, 2017

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

Conclusions:

The theoretical creation of a spiraling Bessel-like beam is possible.
This light beam has potential applications in microfabrication and other advanced optical technologies.