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The beam waist (or beam focus) of a laser beam is the location along the propagation direction where the beam radius has a minimum.
The waist radius is the beam radius at this location.
The beam waist is the location where the beam radius is smallest.
A small beam waist (more precisely, a beam waist with small waist radius) can be obtained by focusing a laser beam with a lens which has a high numerical aperture, and making sure that the lens aperture is largely filled by the input beam.
For non-circular beams, the position of the beam waist can be different for different transverse directions.
This phenomenon is called astigmatism, and it may be generated or removed e.g. by using cylindrical optics.