Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Gauss's Law

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

Intensity Of Electromagnetic Waves

Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a plane electromagnetic wave with E0 and B0 as the peak electric and magnetic fields and traveling along the x-axis, the time-varying energy flux can be given by the following equation:

Principal Stresses in a Beam

Principal Stresses in a Beam

In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
Analyzing principal stresses is crucial, especially in...

Beams with Symmetric Loadings

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

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.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Maréchal intensity criteria modified for gaussian beams: errata.

Applied optics·2010

Same author

A photographic recording medium for 10.6-micro laser radiation.

Applied optics·2010

Same author

Efficient high-power UV generation by use of a resonant ring driven by a cw mode-locked IR laser.

Optics letters·2009

Same author

Efficient, 15-W output power, diode-end-pumped Nd:YAG laser.

Optics letters·2009

Same author

Single-longitudinal-mode, tunable, pulsed Ti:sapphire laser oscillator.

Optics letters·2009

Same author

2.0 J Ti:sapphire laser oscillator.

Optics letters·2009

Search research articles

Related Experiment Video

Updated: Jun 16, 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

Maréchal intensity criteria modified for gaussian beams.

|February 6, 2010

Summary

This study reexamines the Maréchal evaluation for Gaussian beams, considering primary and spherical aberrations. It provides a new method for assessing peak intensity degradation in optical systems with Gaussian illumination.

Area of Science:

Optical Engineering
Wave Optics
Aberration Theory

Background:

The Maréchal definition is crucial for evaluating optical system performance.
Gaussian beams are prevalent in modern optical systems.
Aberrations significantly degrade far-field intensity.

Purpose of the Study:

To reexamine the Maréchal evaluation for Gaussian apertures.
To develop a method for assessing peak intensity degradation in aberrated Gaussian beams.
To identify the impact of Gaussian illumination on Strehl ratio.

Main Methods:

Mathematical analysis of the Maréchal evaluation for Gaussian beams.
Inclusion of primary and all orders of spherical aberration.
Comparison with Maréchal's equations for uniform beams.

More Related Videos

Irradiator Commissioning and Dosimetry for Assessment of LQ α and β Parameters, Radiation Dosing Schema, and in vivo Dose Deposition

Irradiator Commissioning and Dosimetry for Assessment of LQ α and β Parameters, Radiation Dosing Schema, and in vivo Dose Deposition

Published on: March 11, 2021

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Published on: June 7, 2019

Related Experiment Videos

Last Updated: Jun 16, 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

Irradiator Commissioning and Dosimetry for Assessment of LQ α and β Parameters, Radiation Dosing Schema, and in vivo Dose Deposition

Irradiator Commissioning and Dosimetry for Assessment of LQ α and β Parameters, Radiation Dosing Schema, and in vivo Dose Deposition

Published on: March 11, 2021

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Published on: June 7, 2019

Main Results:

Derived equations for Maréchal evaluation in Gaussian beams, incorporating aberration effects.
Identified additional factors due to Gaussian illumination.
Demonstrated the approach of these factors to unity for uniform beams.

Conclusions:

The modified Maréchal evaluation accurately predicts peak intensity degradation for Gaussian beams.
Aberration balancing strategies can optimize peak intensity under Gaussian illumination.
The study provides insights into the unique effects of Gaussian illumination on optical performance.