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For Gaussian beam size measurements, ZEMAX uses the 1/e² point, which means the intensity has fallen to about 13.5% of the peak.  However, often times manufacturer’s data sheets include FWHM measurements and not 1/e². 

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

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: