Sometimes, manufacturers provide Gaussian beam data as FWHM measurements. This article describes how to convert FWHM measurements to 1 over e squared measurements, which are used by ZEMAX.
This article is also available in Japanese.
This article is also available in Japanese.
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:
