Gaussian Laser Modes

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration considers the intensity distribution of Hermite-Gaussian transverse electromagnetic (TEM) modes produced by a laser. These modes are solutions of the paraxial wave equation in Cartesian coordinates. They represent the transverse (-) intensity distribution of a laser beam propagating in the direction.

Contributed by: Antoine Weis (November 2008)
(Université de Fribourg)
Open content licensed under CC BY-NC-SA



The Hermite-Gaussian modes

are an important family of solutions of the paraxial wave equation

that describes the optical field, that is, the amplitude of the electric field in a laser beam propagating along . The transverse (-) intensity distribution of the beam is given by


In the above, is the phase of the beam, which is irrelevant when discussing the intensity and is called the beam radius. As the beam propagates changes in a characteristic manner. However, as seen from the expressions above, acts as a scaling parameter, so that the transverse beam pattern does not change along the propagation direction; it merely changes its scale, shown in this Demonstration for .

By setting


the integrated intensity is normalized to yield unit power


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.