Re: Light, resonance, index of refraction

[John Denker <jsd@MONMOUTH.COM>]

At 05:20 PM 10/22/99 -0500, Cliff Parker wrote:
> Very nice explanation.  It gives me a new angle to consider. A questions
> follow.

Thanks for the feedback.

> > In good glass, virtually all of the re-radiators have resonances *above*
> > optical frequencies.  Optical light hits them below their resonant
> > frequencies.  Ultraviolet light does hit them on resonance, and is so
> > strongly absorbed that glass is opaque at such frequencies.
>
> So why is it that Ultraviolet light is not re-radiated in large amounts?

The simplest way to think of it is to treat the atomic oscillator as a
plain old damped harmonic oscillator.  The electrical analog is the
following network:

       ___________
                  |
                  |
                inductance L
                  |
                  |
                resistance R
                  |
                  |
                capacitance C
                  |
       ___________|


Far below resonance, the impedance across the terminals of this network is
dominated by the capacitance.  Far above resonance, the impedance is
dominated by the inductance.  Right at resonance, the impedance of the
network is purely resistive and equal to R -- the impedance of the inductor
"cancels" the impedance of the capacitor.

If you drive this circuit from, say, a 50-ohm transmission line, the
maximum dissipation will occur at resonance.  Far above resonance you'll
get a reflection with a +90 degree phase shift, far below resonance you'll
get a reflection with a -90 degree phase shift, and right on resonance
you'll get absorption.

The analogy to light is as follows:  The electromagnetic field in free
space is analogous to the electromagnetic field in the 50-ohm cable.  The
inductance and capacitance are analogous to the mass of the electron and
the springiness of the chemical bond.  The resistance corresponds to two
things:
  1) messy processes that cause excitations of the electron to turn into
heat in the lattice, and
  2) processes that cause excitations to be re-radiated as light.

For glass, type-1 processes (thermalization) are strong enough to make it
opaque (black) at resonance.

Another part of the story is localization, as discussed a few months back
under the heading "how do you make WHITE?"  This would probably make it
opaque (white) if thermalization didn't make it opaque (black) first.

You can see something roughly analogous in clouds as the droplet size changes:
 * nanometer-sized items (individual molecules) = clear air
 * subsubmicron-sized items (small droplets) = white clouds
 * roughly-micron-sized items (larger droplets) = dark clouds

OK?

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com