Richard Clark wrote:
Returning again with a new example, described in text as:

1w | 1/4WL | |/
laser-----air-----|---Si Crystal---|---Al contact--- |/
1st medium | 2nd medium | 3rd medium |/
n = 1.0 n = 5.8275 n 6

As I've offered in other posts, the "total" cancellation is entirely
driven by very simple optics which resolve to obvious ratios in the
expression of conservation of energy.

Uhhhhhhh Richard, that is not a matched example so, of course,
there is no total cancellation of reflections. Why do you
think a mis-matched system would ever have total cancellation?

What can we do to make it a matched example?
Make n3 = 5.8275^2 = 33.93. I have no idea what medium 3 is
made out of but it also has to reflect 1/2 the energy incident
upon its surface. Now the reflectance (power reflection coefficient)
equals 0.5 and is the same at discontinuity A as it is at
discontinuity B. The 3rd medium will be considered to be infinite
for purposes of simplicity.

1w 1st medium | 1/4WL |
laser-----air-----|---2nd medium---|---3rd medium---...
n = 1.0 | n = 5.8275 | n=33.93
A B

Now it is matched and reflections are totally canceled. The
forward power in medium 1 is 1W. The reflected power in medium 1
is zero. The forward power in medium 2 is 2W. The reflected
power in medium 2 is 1W. The forward power in medium 3 is
1W. The reflected power in medium 3 is zero.

The above example is akin to the following transmission line
example with identical forward and reflected powers.

1/4WL
1W XMTR---50 ohm line---+---291.4 ohm line---+---1698 ohm load
A B
Pfor1=1W-- Pfor2=2W-- PL=1W
--Pref1=0W --Pref2=1W

This is a Z0-matched system with no reflections on the 50 ohm
line. The fact that half the power is reflected at each discontinuity
makes it easy to calculate and recognize.

************************************************** *********************
In a lossless matched system where half the power is reflected at each
discontinuity, the forward power in medium 2 will be exactly double
the forward power in medium 1.
************************************************** *********************

Please read that over until you understand it and then try to figure
out why. Hint: it is not a violation of the conservation of energy
principle. Soon the hole you have dug for yourself will be so deep,
you won't be able to reach your keyboard. :-)
--
73, Cecil http://www.qsl.net/w5dxp


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