wrote:
Here is the transient state of the system an instant
after the first internal reflection from point B arrives
back at point A.

1st medium 2nd medium 3rd medium
A B
1000mW----| |
|----888.9mW----|
111.1mW----| |----790.1mW
|----98.76mW----|
87.79mW----| |
|----10.97mW


You are correct that in this system (1/4-wave matching layer), the
total reflectance goes to zero.

However, your understanding of superposition is wrong.

Powers obey the equation P1 + P2 + 2*(P1*P2)cos(theta)
when the fields are superposed. 2*(P1*P2)cos(theta) is
known as the "interference" term. That interference term
automatically adjusts the power equation IN ORDER TO AVOID
SUPERPOSITION OF POWERS. That's what I did.

You CANNOT superimpose POWERS,

I would not even dream of superposing powers. Perhaps you
don't understand the role of the interference term in the
power equation which is to AVOID the superposition of
powers.

P1 + P2 would be superposing powers. I didn't do that.

P1 + P2 + 2*sqrt(P1*P2)cos(theta) is NOT superposing powers.

or even talk about the "power" of various
reflections in the same media. You can only add the wave amplitudes
(electric fields). THEN you take the total amplitude and square that
to get the power.

Eugene Hecht would be surprised to hear you say such since he
talked about the powers (irradiance) of various reflections in
the same media.

I did not superpose powers. I used Hecht's equations for powers
(irradiance). When E-field1 is superposed with E-field2, powers
obey the equation:

Ptotal = P1 + P2 + 2*sqrt(P1*P2)cos(theta)

where (theta) is the angle between the E-fields, P1 is the power
associated with E-field1, and P2 is the power associated with
E-field2. Reference: _Optics_, by Hecht, equation 9.14

Since the above is a steady-state matched situation, the forward
power in second medium involves total constructive interference:

So Ptotal = P1 + P2 + 2*sqrt(P1*P2)

where P1 = Pfor1*T and P2 = Pref2*R
T is the Transmittance and R is the reflectance
These are very similar to the S-parameter power equations.

Reference "total constructive interference" in _Optics_, by Hecht
equation 9.15. The only difference in irradiance and power is
the unit-area which, for our example, is arbitrary.
--
73, Cecil http://www.qsl.net/w5dxp

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