Cecil Moore wrote:
Jim Kelley wrote:
Correction. The Z matching device functions to increase the energy
flow toward the load and decreases the energy flow toward the source.
Interference is just the mathematical description of the resulting
spacial distribution.

The decrease to zero in reflected energy flow toward the source
is known as "total destructive interference" in the noun version
of the word as used by Hecht. The increase in energy flow
toward the load is known as constructive interference. One need
not refer to superposition as the cause of interference since
the interference *event* implies superposition of two (or more)
coherent waves as the *cause* of the interference *process*.

I am using "interference" as a noun synonymous
with an "interference process" event, not as in "interference
rings". The Z0-matching event cannot occur without an interference
process (event). "Total destructive interference" as defined
by Hecht is *necessary and sufficient* for a Z0-match to occur,
i.e. if total destructive interference exists toward the source,
a Z0-match has been achieved.

From Websters: "interference - n. the *process* in which
two coherent EM waves combine to reinforce or cancel each
other." The reinforcing or canceling can be partial or total.
Thus, I am using Hecht's noun definition of "interference"
which "yields a resultant irradiance that deviates from the
sum of the component irradiances". Reinforcement or cancellation
is the *result* of that *process*. Superposition is the *cause*
of that *process*.

The *result* of the interference *process* is sometimes wave
cancellation if the appropriate conditions exist. That's
what happens at a Z0-match.

The interference pattern of an antenna is the *result*
of the interference *process*. Hecht says interference
"corresponds" to the "interaction" of two or more
coherent EM waves "yielding a result ...". He clearly
considers interference to be in the cause and effect
chain of events, as do I.

Cecil,

You are waaay too concerned with philosophical words like *cause*,
*process*, *result*, and *event*.

There is no justification for saying that interference causes
superposition or that superposition causes interference or any such
combinations. Causality is a very important concept in physics, but it
has no useful meaning in this situation.

The way a physicist solves problems like this is to set up the equations
in terms of generic sinusoidal functions with variable parameters. Then
the boundary conditions of the problem are applied to determine
precisely what the parameters must be. That's it. No worries about *why*
something is happening or what is causing what. Those items are
impossible to define in any case.

If you were to read Born and Wolf you would find that they deal with the
multiple interference problem (antireflective glass) in exactly the same
manner. They never even mention constructive or destructive interference.

There is a reason physicists use this type of problem solving method. It
works for a entire range of boundary conditions. Try using your
constructive/destructive interference technique when the problem is not
quite so simple. For example, 3D problems when the incidence angles are
not so tidy, materials with absorption, or multiple films such as those
used in *real* AR coatings. You might muddle through with some generic
concept of constructive/destructive interference, but you won't be able
to get a quantitatively useful answer.

By the way, Born and Wolf must have been pretty well connected. It
appears that they copied the multiple reflection lattice diagram from
your web page. 8-)

73,
Gene
W4SZ