Angular momentum of dipole radiation

It has been shown experimentally that a beam o circularly-polarized light exerts a torque on any optical component, such as a quarter- or half-wave plate, which changes the state of polarization of the light. This corresponds to a transfer of angular momentum from the radiation fields to the material system. To calculate the rate at which angular momentum is radiated by an electric dipole 

Associated with the time-averaged flux, N, in the direction R is an energy density U given by lj. = N/c. The relativistic energy equation 

Substituting for the time-averaged Poynting vector from equation (2.46) and expanding the triple vector product, we obtain L in terms of the fields  

For electric dipole radiation the first term in equation (2.76) is identically zero since the magnetic field H is everywhere perpendicular to r, equation (2.66). The electric field in the wavezone, equation (2.70), is also perpendicular to r and therefore in the second term of equation (2.76) we retain the intermediate field contribution to E which varies as (1/r ). We obtain 

Finally if we use the term in (1/r) for the magnetic field, equation (2.69), we obtain a result which is independent of the radius r of the absorbing sphere  

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