Art wrote:
"When you refer it to a "mucked up Yagi" you must understand that the
Yagi is primarily set up to focus available radiation by redistribution,
where as with a Gaussian there is no focusing or relaying of energy by
coupling."

Words fail me. Without redistribution, there is only a point source.
More than one source is necessary for the radiant energy to produce
gain. It is immaterial whether the energy gets to a second source by
conduction or radiation. Interaction between the energies of more than
one source is essential for gain.

Focus is convergence of energy and is the stuff gain comes from.

Best regards, Richard Harrison, KB5WZI