TABLE OF CONTENTS When a Gaussian beam encounters a circular aperture, the fraction of the power passing through is equal to
| where | a | = radius of the aperture |
| w | = radial distance from the beam's center to the point where the beam intensity is 0.135 of the intensity at the center of the beam |
The beam intensity as a function of radius is
| where | w | = as defined as above |
| r | = radius at some point in the beam |
The power as a function of size of the aperture is computed from
The 0.135 comes from fact that at the 1/ e 2 point of the beam, the intensity is down to 0.135 of the intensity in the center of the beam. Thus, we see that an aperture of 3 w transmits 99 percent of the beam.
This rule applies to beams that are characterized as Gaussian in radial intensity pattern. While this is nearly true of aberration-free beams produced by lasers, there are some minor approximations that must be accommodated for real beams.
Of course, as in any system in which an electromagnetic wave encounters an aperture, diffraction will occur. The result is that, in the far field of the aperture, one can expect to see fringes, rings, and other artifacts of diffraction superimposed on the geometric optics result of a Gaussian beam with the edges clipped off.
H. Weichel, Laser System Design, SPIE Course Notes, SPIE Press, Bellingham, WA,...
