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Re: teeny atoms absorb huge EM waves



At 02:15 PM 7/29/99 -0700, William Beaty wrote:
I've always been befuddled by the ability of atoms and molecules to
intercept waves which are >> than the diameter of the atom. Those waves
refuse to pass through an atom-sized pinhole. Why then are they blocked
by an atom-sized obstruction?

Here's a possible answer. In a paper on VLF radio receivers, the authors
pointed out that small antennas will absorb large amounts of propagating
EM energy if the antenna is connected to a resonant circuit. As energy
builds up in the resonator, an AC field appears around the antenna, and
this field interacts coherently with the received waves as if the antenna
was much larger than it actually is.

That's true, and it's part of the answer to your question.

At first glance this seems silly. How can an *oscillator* enhance the
process of EM absorbtion?

It doesn't seem silly to me. Consider the AR (anti-reflective) coating on
lenses. How can adding another layer "suck" more light into the lens?
But it does. It's classic (and classical) wave mechanics.

A resonant circuit would transmit at the same
time it receives!

Absolutely it does. Any absorber does. There's a paper by Feynman and
Wheeler on this. (One of the first scientific papers Feynman ever wrote,
IIRC.)

At the very least, the waves from such a transmitter
would simply superpose with the received waves and have no effect. EM
fields obey superposition. By transmitting, I cannot affect the waves
which are already propagating past my transmitter, since one wave won't
interact with another. But wait... if the transmitter is phase-locked in
lagging phase with the incoming radiation, then it would partially cancel
the EM fields of the incoming wave, and the volume of this "cancelling"
effect would be larger than that of a passive antenna.

Right. And if you carry out the calculation you just described, you will
derive the optical theorem. As the name suggests, it is completely
classical wave mechanics. OTOH since hardly anybody studies classical wave
mechanics any more, you may find it easier to find a discussion in your
quantum mechanics books.

Aha, EM is *not* linear where power is concerned. There's an e^2.

That's for sure.

If the above is true, then at its resonant absorbtion frequency, an atom
would act much larger than it actually is. In a wave-based model, the
atom would be surrounded with oscillating fields, and these fields would
extend the reach of the tiny atom. It would behave more like a half-wave
dipole antenna than like a pinhole where the diameter << wavelength.

That's all true, except for the emphasis on resonance. In the Born
approximation, the scattering power depends on the size *and* on the depth
of the scattering potential. You can have a delta-function shaped
scatterer with zero size and quite hefty scattering. The pinhole
scatterer is small *and* not very deep.

Modern radio
receivers would not employ this effect, since their antennas are decoupled
from any resonant circuits by the input amplifier stage. (We want our
antennas to be relatively broad-band, not sharply tuned.)

Radio receivers wouldn't benefit. They care about signal-to-noise ratio,
not absolute signal energy. (To say it another way: nowadays the noise
temperature of the RF preamp is really, really low.) A tuned antenna would
resonate with noise just as well as signal. Receivers can cut down the
noise bandwidth electronically just as well as they could with a resonator.

How would I perform calculations on this system to show that extra energy
would flow into an oscillating antenna? Use a numerical simulation of the
near-field space around a short dipole antenna? (Gah!)

Read up on
* Optical theorem
* Born approximation
* Hugyhens' construction. I saw a manuscript that David A. B. Miller
wrote a few years ago on this, showing that the usual hand-wavy version of
H.C. could be made quite rigorous. I don't know if/where that got
published. If you can't find it let me know and I'll bug DABM for it.