wave optics and boundary conditions

[Doug]

Dear Group,

I have a question (confusion) about wave optics and boundary
conditions. It is my understanding that at the boundary of two media
with different dielectric constants, only Maxwell equations can account
for the reflected and refracted waves, because they have something to
do with polarizations. My question is, if we do not take into account
of polarization, can wave optics successfully explain phenomena such as
total reflection, refractions and alike?

If so, I'd be grateful if you could introduce me a reference.

Thanks,
Doug

[Timo A. Nieminen]

On Wed, 9 May 2006, Doug wrote:

> I have a question (confusion) about wave optics and boundary
> conditions. It is my understanding that at the boundary of two media
> with different dielectric constants, only Maxwell equations can account
> for the reflected and refracted waves, because they have something to
> do with polarizations. My question is, if we do not take into account
> of polarization, can wave optics successfully explain phenomena such as
> total reflection, refractions and alike?

Wave optics _is_ the Maxwell equations. Since the amplitudes of the
reflected and refracted waves depend on the polarisation, you need to use
a vector theory. These days, classical electrodynamics (ie Maxwell etc),
but you can do it without the full Maxwell theory, if you can guess
suitable boundary conditions. Note that the Fresnel reflection
coefficients are named after Fresnel, who did his work pre-Maxwell.

A scalar wave theory can explain things like Snell's law, total internal
reflection, and can give the correct reflected and transmitted amplitudes
for normal incidence (when both polarisation must give the same result).
The angles involved in reflection, refraction, and phenomena like total
internal reflection (was there a pre-Maxwellian theoretical treatment of
FTIR, or did they miss this one?) depend on (a) the speed (and therefore
the wavelength and wavenumber) of the wave is different in the two media,
and (b) the component of the wavevector parallel to the interace must be
the same in both media. These apply to scalar waves as well as to vector
waves.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
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