9827
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Laguerre-Gaussian Modes of Paraxial Wave Equation
Laguerre–Gaussian modes are solutions of the paraxial wave equation. They have circular symmetry and can be written in terms of the Laguerre polynomials
, where
is the radial index and
is the azimuthal index.
Contributed by:
Enrique Zeleny
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
The paraxial equation in cylindrical coordinates is given by
.
A simple separable solution can be written in the form
.
RELATED LINKS
Laguerre Polynomial
(
Wolfram
MathWorld
)
PERMANENT CITATION
Enrique Zeleny
"
Laguerre-Gaussian Modes of Paraxial Wave Equation
"
http://demonstrations.wolfram.com/LaguerreGaussianModesOfParaxialWaveEquation/
Wolfram Demonstrations Project
Published: May 6, 2014
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
The Airy Wave Train
Enrique Zeleny
Cnoidal Waves from Korteweg-de Vries Equation
Enrique Zeleny
Travelling Pulses (Wave Packets)
Roger Beresford
Boole Differential Equation with Continued Fractions
Andreas Lauschke
Eigenfunctions and Eigenvalues of the Airy Equation Using Spectral Methods
Housam Binous, Brian G. Higgins, and Ahmed Bellagi
Laplace-Dirichlet Eigenstates of an Ellipse
Braxton Osting
Nodes in Optical Fibers
Enrique Zeleny
Nonlinear Wave Equation Explorer
Stephen Wolfram
Acceleration of Particles in a Wave Obeying the Korteweg-de Vries Equation
Klaus von Bloh
Wave Generator
Mike Parenteau
Related Topics
Differential Equations
Special Functions
Waves
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+