Some applications of Gaussian beam theory in reflector antenna design

A Gaussian beam propagating in the `z´ direction is described by a 1/e width parameter w(z), and a parameter R(z) which is normally described as the radius of curvature of the wavefront, although the wave is not truly spherical. A reflector antenna can be designed using conic sections as though R(z) is a true spherical wavefront radius. At a beam waist w takes a minimum value w₀ and R is infinite. If the beam is required to have specified values of w and R at some point, then the distance z from the waist is given by R/(1+(Rλ/πw² )²). This shows that the beam waist has a large displacement from the geometrical focus towards the reflector if the latter has a small value of D²/fλ. Two designs using these principles are reviewed