Re: wave emission

[John Denker <jsd@AV8N.COM>]

Carl E. Mungan wrote:

> 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?

That's right, it's not.  An incoherent superposition is
necessarily a wave _packet_.

> .... 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.

I think that's another way of saying the wave-packet spreads
out as propagates.

> HOWEVER, the leading edge of this box is a plane front.

I'm not convinced.  At best that requires a definition of
"the leading edge", which may not be super-easy to define
for a wave-packet.

> 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.

It is plane-like in the sense that it exhibits 2D translation
invariance.  Understanding the symmetry of the situation is
always important!