Art wrote:
"Richard you evoked the phrase Poynting`s vector which is an excellent
place to start---etc,"

I appreciate being credited by Art with evoking the Poynting vector, but
I wasn`t first.

The priginal poster wrote:
"Now I have an incident E field(which happens to be a RHCP, that I can
write as a plane wave: etc."

Art then responded:
"Matt, Gain can mean many things. If you can back up on your vector
approach, a look at Poynting`s theorem would be a good start."

I posted next, recommending Terman and Kraus to the self-proclaimed
"Newbie" I suggested he look at one of Kraus` assigned problems, no.
1-16-2 which asks the student to:
"Show that the average Poynting vector of a circularly polarized wave is
twice that of a linearly polarized wave if the maximum electric field E
is the same in both waves."

Everyone will say that`s obvious as the polarized constituent waves in
CP are at right angles and thus are independent. But, Kraus goes through
all the steps and supplies all the math to enable the student to make
the proof. It`s like a geometry proof of the obvious but it is still
informative to work the problens.

I am lazy and rhought that these great professors do a great job of
explaining everything accurately and succinctly. I could never hope to
do it so well. It is a job for the student himself to follow the
explanation and I merely pointed to those I think are the best.

Best regards, Richard Harrison, KB5WZI