Electric dipole approximation

[Mat' G.]

Hello,

Could someone please explain me why in, eg, in the source term of a
nonlinear crystal the electric dipole term P exceeds the magnetic dipole
term M and the electric quadrupole term Q by a factor lambda/(2 pi a),
where lambda is the wavelength of the incident light and a the lattice
constant of the material.

I keep reading it, but I miss the point.

Thanks for helping!

Mat

[Ronald Hyde]

It's obviously being treated as a perturbation expansion in the only two
quantities expressed in the equation. It's pretty much a sure fire way
to get some predictive result out of a set of observations, find a
quantity, energy say, find all the dimensional combinations that result
in energy, then make a perturbation expansion in two or more of the
quantities that yield energy. Might get you a Nobel.

[Jos Bergervoet]

Radiation is caused by current. In a magnetic dipole it flows in a
loop, therefore radiation from opposing sides almost cancels, except
for difference in phase factor because of the distance to the observer.

If this difference in distance is the size, a, of the object, then
the phase difference is a / (lambda/2Pi). This (small) number is then
the reduction factor for the radiation from a loop, compared with the
radiation from a simple straight line element of current. And those
are exactly the two cases you compare: a magnetic dipole and electric
dipole, which explains your formula.

The rule is universal. It holds for radiation from a single atom, but
also for macroscopic structures. Of course in the latter case, a isn't
very small, so the difference will vanish. (Also, the loop can have
multiple turns for a macroscopic antenna.)

--
Jos

[Anon E. Mouse]

Some non-linear optical materials like natural quartz refract light more al=
ong crystal axis A and less along B, taken at 90*.=20

This is called birefringence. Many Chiral proteins and similar organic semi=
-crystaline molecules exhibit a similar birefringence for transmitted light=
and a hetero-dyne convergence anti-reaction used in epi-flourescent micros=
copy and q-switched laser microscopy.

These are the types of asymetric optic effects that occur in nature and bec=
ause they are important in physics and medicine modelling them in QM is als=
o done. Perhaps if you observe some of these effects personally the mathema=
tical models will make more sense.