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

[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

[Mat' G.]

2012-07-29 11:30, Jos Bergervoet scripsit:

Thank you Jos!