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How To Convert FWHM Measurements to 1/e-Squared Halfwidths


Sometimes, manufacturers provide Gaussian beam data as Full Width Half Maximum (FWHM) measurements.  This article describes how to convert FWHM measurements to 1/e^2 halfwidth measurements, which are used by Zemax.

Authored By: Dan Hill

Published On: April 4, 2007


The Relationship Between the FWHM and 1/e-Squared Halfwidth of a Gaussian Beam

This article is also available in Japanese.

For Gaussian beam size measurements, Zemax uses the 1/e2 half-width point, which means the intensity has fallen to about 13.5% of the peak.  However, often times manufacturer’s data sheets provide only Full Width Half Maximum (FWHM) measurements and not 1/e2 half-widths. 

For a truly TEM00, rotationally symmetric & normalized Gaussian beam, there is a linear relationship between these two values. 

Gaussian Beam Characteristics

The intensity of a Gaussian beam goes as:

where w is the half width of the beam to the 1/e2 intensity point at some distance from the waist along the propagation axis, and r is the radial distance from the center of the beam.  The width, w, at some z position is given by:

where w0 is the waist radius at the 1/e2 point.

For a normalized Gaussian beam, we know that the FWHM is the point at which the beam reaches half of the peak intensity.  As a result, our equation simplifies to:

The FWHM is the “full-width of the beam at half of the maximum intensity,” so we need to divide this value by 2 so that we can replace it with r, the radial size.

Simplifying, we get:

Taking the natural log of both sides, and bringing the constant to the other side of the equation yields:

 or,



Solving for w, the relationship between the FWHM and the 1/e2 intensity point becomes:


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