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Imagine an infinite plane uniformly covered with point sources....
But now suppose these point sources emit mutually incoherently.> .... It's no longer a plane wave, is it?
.... Suppose I imagine blinking all of
the sources on for an instant, like one lobe of their sinusoidal
dipole oscillation.... I get a "box" full of photons that becomes less
and less dense as time goes on: some photons are shooting away
perpendicularly away from the surface, while others are skimming the
surface and making essentially no progress in the normal direction.
HOWEVER, the leading edge of this box is a plane front.
It's for just
this reason that part of me strongly wants to say the radiation
pattern is still plane-like in some important way.