# Phase difference between incident plane wave incident on a dipole and radiation fields from dipole

i have an incident plane wave and a dipole, consider that plane wave incident on dipole. at this moment what happens to dipole? We know that after incident of plane wave on dipole, the radiation has occurred, and I want to derive the phase difference between radiation field and incident plane wave field ? Please give me some reference.

I'm not completely clear what you are asking, but isn't this just an instance of elastic scattering from unbound charges?

i.e. the dipole oscillates in phase with the electric field of the incoming wave and emits dipole radiation with the same phase.

The example I'm familiar with would be Thomson scattering from free electrons, which oscillate like classical electric dipoles - the electron of course accelerates in antiphase with the electric field of the incoming wave, the displacement is in phase, the oscillation of the dipole moment is thus in antiphase (because of the negative electron charge), and the radiation it then emits is in phase

http://en.wikipedia.org/wiki/Thomson_scattering

Other elastic scattering processes - e.g. Rayleigh scattering from electrons bound in atoms, have in general some phase difference. The phase difference is obtained by analogy with the forcing of a damped harmonic oscillator. If you are familiar with the properties of this then you will know that at about resonance there is a $\pi/2$ phase difference but if the driving frequency is very different then the the phase difference will approach zero at low frequencies and $\pi$ at high frequencies..

• Dipole moment oscillates in phase with the wave only if the wave has much lower frequency than the natural frequency of the dipole. In case of Thomson scattering, the electrons are supposed to be free (no natural frequency) so the dipole moment oscillates 180° behind the external electric field. – Ján Lalinský Nov 3 '14 at 10:29
• Actually, in Thomson scattering electron will move in phase with the electric field so that electric moment can move in antiphase. – Ján Lalinský Nov 3 '14 at 18:08
• @Jan Lalinsky Yes, $(-1)\times(-1)\times (-1)\times (-1)$ ! – ProfRob Nov 3 '14 at 21:59
• You've got me:-) – Ján Lalinský Nov 3 '14 at 22:55