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