Re: teeny atoms absorb huge EM waves

[William Beaty <billb@ESKIMO.COM>]

On Sun, 1 Aug 1999, John Denker wrote:

> 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?

<snip>

> > 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.

Bingo, I went to the UW physics library on friday and found some
references on this. One is:

  Craig F. Bohren, "How can a particle absorb more than the light incident
  on it?"  Am. J. Phys, 51(4)  Apr. 1983  pp 323-327

In his intro, Bohren points out a misconception associated with this
topic:

  To those who first encountered in neutron physics the concept of the
  area that a target presents to a projectile (i.e., its cross section),
  it comes as no suprise that targets can sometimes extend beyond their
  strict geometrical boundaries, even greatly so.  Indeed, the very unit
  for neutron cross sections, the barn, encourages one to think big.  But
  photons are supposed to behave more soberly than neutrons; every
  physics student knows that photons travel through free space mostly in
  straight lines, although they do sometimes exhibit a bit of waywardness
  in the vicinity of edges.  Notions about what photons can and cannot do
  are formed in traditional optics courses, which emphasize visible light
  interacting wtih large bodies, usually transparent.  With time these
  notions become deep-seated prejudices and are often difficult to
  dislodge.  Yet it is incontrovertible that there are many circumstances,
  by no means exotic, under which small particles (smaller than the
  wavelength) can absorb more than the light incident on them.  My first
  task in this paper is to examine some of these circumstances.  Then I
  shall give a pictorial representation of absorbtion of light by a
  particle in a way which, to the best of my knowledge, has not been done
  before.

Bohren goes on to analyze the Poynting field around a small metal sphere
at UV frequencies where surface plasmon resonance cause significant
absorbtion, and around a NaCl sphere at IR frequencies where surface
phonons are the absorbers.  His results are very interesting.  Also
interesting is that there are very few papers on this topic.  Looks like a
possible "hole in physics", where a widespread misconception diverts our
attention from an interesting phenomenon.


> > 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.

Small particles might act as larger scatterers, but doesn't scattering
behave differently near a resonance?

Bohren's paper concentrates on absorbtion rather than scattering.  He
offers a 2D plot of the Poynting field around a tiny aluminum sphere at
the resonant frequency of 8.8eV and at an off-resonance frequency of 5 eV.
Very interesting!  At the non-resonant frequency, the Poynting field
passes the sphere almost as if it was not there.  The lines of energy-flow
are parallel except within one radius of the sphere, where they
temporarily spread apart and then close behind it without touching its
surface; much like a fluid flow around an object at very low Reynolds
number.  He gives the absorbtion efficiency as 0.1, as if the sphere was
*much smaller* than its geometrical area.

At resonance, the depicted Poynting field is very different.  Lines of
energy flow which were far from the axis through the sphere are bent
inwards and hit the surface of the sphere.  The sphere is "funneling"
energy into itself and acting as a much larger object.  Bohren estimates
that the absorbtion cross-sectional area is 18 times larger than expected,
and the "absorbtion radius" is 4.2 times greater than the geometrical
radius.

I had suspected that something strange might occur at resonance, but I
didn't expect that an object would act *smaller* than its geometrical size
at off-resonant frequencies.


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