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Hi Rick,
I think that I'm finally beginning to get a handle on some of these=20
"time-reversed" and "phase conjugation" concepts, so I'll start by =
trying to
answer some of your questions. This topic can be very confusing, since =
the
word
"conjugate" is used to represent different kinds of "conjugation". To
determine
if time reversal is involved, I find it helpful to ask: "What is the
behavior of
the resulting wave? Does it arrive somewhere AFTER it was emitted (or=20
reflected) or BEFORE? Does it DIVERGE or CONVERGE?
A standard silvered mirror is indeed an E-field short, and the E-field =
is=20
conjugated, but this does not result in time reversal as can be seen by =
the
fact
that the reflected wave arrives somewhere after it is reflected and
continues to
diverge. The reason why can be understood by analogy to a transmission =
line
example.
The voltage on a transmission line is expressed by:
V(x) =3D Vplus*( e^(-jBx) + e^(+jBx) )
And B =3D 2*PI*f/v, where f =3D frequency, v =3D velocity, x =3D =
distance.
Or: V(x) =3D Vplus*( e^(-j2*PI*f/v*x) + e^(+j2*PI*f/v*x) )
At first glance you might say: "Wow, one term is positive and one is
negative,=20
is this time reversal? The answer is no, this is space reversal =
instead.
The=20
negative sign is associated with the "negative x" direction.
As far as your AM side band theory goes, we can tell from the effects =
that
this=20
is still a time-forward wave, since it arrives somewhere after it is
generated=20
and diverges along the way. Otherwise the lower side band would arrive
before=20
the upper side band, which doesn't happen. I think that the =
explanation for
this is that the "negative f" in the above equation has the same effect =
as
the=20
"negative x". Regarding beating the carrier down to zero, whenever you =
mix
two=20
frequencies, you always get the sum and difference frequencies. If you =
mix
a=20
frequency with itself, you get a doubled frequency and a DC component. =
This
is=20
how commercially available frequency doublers work. No time reversal =
here.
To really understand Optical Phase Conjunction, we need to first =
understand
what
is the difference between a time-forward and a time-reversed EM wave. =
To
this=20
end, I have prepared the attached graphic, which illustrates my =
hypothesis
of=20
the relationship of the E & M fields in these two different kinds of =
waves.
Please refer to this graphic to help make sense of the following =
discussion:
Assuming a linear polarized plane wave, a normal time-forward (or
"retarded")=20
wave obeys the "Right Hand Rule" as follows: Extend the index finger of =
your
right hand so that it is pointing straight out. Then, bend your middle
finger so
that it is at a right angle to your index finger. Now, extend your =
thumb so
that it is at a right angle to both of the above. Align your index =
finger
with=20
the E-field and your middle finger with the H-field and your thumb will =
now
be=20
pointing in the direction of propagation. A time-reversed (or =
"advanced")
wave=20
will obey the corresponding "Left Hand Rule" instead, as illustrated in =
the=20
attached graphic.
How does this work in the case of a reflection from a short circuit? =
Upon=20
encountering a short circuit, the E-field is conjugated, as it must be =
to
assure
zero volts across the short circuit, and the wave is reflected in the =
-x=20
direction. However, the combination of the reversed E-field and the
reversed=20
direction effectively cancel each other out and the reflected wave =
continues
to=20
follow the "Right Hand Rule", as can be visualized by imagining the
time-forward
graphic flipped 180=B0 end-for-end in the E plane.
Similarly, in the case of a reflection from an open circuit, the =
H-field is=20
conjugated, and the wave is reflected in the -x direction, which also =
cancel
each other out, as can be visualized by imagining the time-forward =
graphic=20
flipped 180=B0 end-for-end in the H plane.
So, what does it take to generate a time-reversed reflection? We need
something
that will either conjugate BOTH the E & H fields simultaneously, OR =
NEITHER.
It is also instructive to consider this problem from the particle point =
of
view.
In this view, the time-forward wave consists of a stream of photons. =
When
they
are reflected from a normal mirror, they are still photons that happen =
to
now be
travelling in the opposite direction. However, a time-reversed wave =
may be=20
considered to consist of a steam of anti-photons. Quantum mechanics =
tells
us=20
that any anti-particle may be viewed simply as the original particle
travelling=20
backwards in time. In the case of particles with mass, like an =
electron, it
is=20
apparently impossible to turn a particle into its' anti-particle and if =
the
two=20
should ever meet they result in total annihilation. However, quantum
mechanics=20
also tells us that the massless photon is its' own anti-particle and =
this=20
provides some hope that it may be possible to turn a photon into an
anti-photon.
This is not necessarily what is happening in the case of the Optical =
Phase=20
Conjunction Mirror though. Most of these devices seem to rely upon the
quantum=20
mechanical effect of an atom absorbing a photon and emitting one or =
more=20
correlated anti-photons instead, as I will explain below.
In scanning the Internet for information on Phase Conjugated Mirrors, I
found=20
that there are a number papers describing this phenomena in all sorts =
of=20
different media. What most of these papers seem to have in common =
though,
is=20
that they use a media that is suitable for producing a laser beam. =
That is,
they use a media that can be excited, or "pumped", by a pair of =
cross-fired=20
laser beams, to excite the electrons in the media to higher orbital =
states,
so=20
that when stimulated by the "tickler beam" these excited electrons will =
drop
back down and emit a photon that is correlated to the "tickler beam". =
These
cross-fired laser beams also set up a standing wave in the non-linear =
media
that
tends to act as sort of an electromagnetic diffraction grating.
Now, returning to the wave description, one can imagine the "tickler =
beam"
to be
the time-forward wave as illustrated in the graphic. From the graphic, =
one
can=20
also see that if the direction of propagation of the time-reversed beam =
is=20
flipped around, then the E & M fields can be brought into alignment =
with the
time-forward beam. It is my hypotheses that the "tickler beam" =
imprints
its' EM
field pattern on the excited atoms and causes them to emit their =
photons in=20
synchronization with this, while the "electromagnetic diffraction =
grating"=20
somehow causes the photons to be spit out in the opposite direction, =
thereby
effectively creating a stream of anti-photons that travel backwards in =
time.
Is it possible to turn a photon into an anti-photon without going =
through
this=20
absorption and emission process? Maybe. I have found an abstract for =
a
paper=20
(Theory of Optical Phase Conjunction in Kerr Media, H.F. Arnoldus and =
T.F.=20
George, Physical Review A 51 ,1995, p4250) that claims to have solved
Maxwell's=20
equations for four wave mixing in a crystal media that not only =
predicts the
time-reversed reflected wave, but also a time-reversed transmitted wave =
in=20
addition to the time-forward reflected and transmitted waves. When I
finally=20
located the body of the paper at the Physical Review web site=20
(http://prola.aps.org/abstract/PRA/v51/i5/p4250_1), the server informed =
me
that=20
I need to first send them $100 for an annual subscription before I can
download=20
the paper. This seems to be a bit of a high price to pay for a single =
paper
that may or may not be helpful in understanding this phenomena. If =
anybody
out=20
there has a subscription to this site, I would appreciate if you could
forward a
copy of this paper to me (john.kooiman@andrew.com).
Since there is a microwave equivalent to a laser, called a MASER. It =
would
seem
that it should at least be possible to reproduce the optical phase
conjugation=20
technique using microwaves. The most common Maser uses a chromium =
doped
ruby=20
crystal as its media, biased in a magnetic field to split the energy =
states
of=20
the + and - spin electrons. This is necessary to split their =
corresponding=20
spectral frequencies, so that it can be pumped at one frequency and =
emit at
a=20
slightly different frequency. It also has to be super cooled to 2=B0K =
to
prevent=20
the thermal noise from overwhelming the electron energy states. =
Therefore,
a=20
likely starting point would be to try four wave mixing in this =
magnetically=20
biased, chromium doped, ruby crystal media. The frequencies and the
strength of
the magnetic field all have to be chosen very carefully, in order to =
get=20
everything to match up correctly with the appropriate electron energy
states, to
make this work. This would seem to offer the possibility of a =
backwards in
time
communication device, but I'm not sure how this would relate to =
anti-gravity
or=20
time distortion. Anybody know where one can obtain this material? It =
sure=20
would be nice to be able to send myself the results of next week's =
stock
market=20
activity, so that I can make better investments today:)
That's all for now.
John