what does "1/e^2" mean?

[ixfd64]

I'm sorry for asking such a dumb question, but does anyone know what does "1/e[sup]2[/sup]" mean? I know that it has something to do with a laser's beam diameter (it's often written next to the beam diameter on spec sheets), but I have no idea on what it means.

 

[knimrod]

The diameter of a Gaussian beam is measured between points near the outer edge of the beam where its intensity is about 86% (1-1/e2) less than the intensity at the center of the beam.

 

[ixfd64]

I see. Thanks.

 

[pseudonomen137]

Yep, to expand a little bit, 1/e^2 is basically just a way to classify beam diameter. A TEM00 laser output's beam is not a perfect circle, but a circular spot with highest intensity in the center, where the intensity tapers off as you get further and further from the center. Therefore you can't say there's a definite diameter to that circle, and we have the 1/e^2 definition. There are others, some places use 1/e and other types, but 1/e^2 is the most common. Basically, the spot radius is the distance away from the center where the intensity is 1/e^2 what it was at the center (roughly .135x)

knimrod, at the 1/e^2 radius, roughly 86% of the beams power will be within that circle, but the intensity is less than 86%.

 

[knimrod]

I could have worded that better... I fixed it so as not to cause any confusion.

To furthur expand a bit:  The reason you see beam diameter usually specified as 1/e2 points is because the diameter is measured along a line that is perpendicular to, and intersecting the beam axis.    The diameter is defined at the points along this line where the optical intensity drops to 1/e2 (~13.5%) of the optical intensity at the peak.