Formalism for a Single Dipole

Consider a classical electric dipole of moment p oscillating with angular frequency at position r in a bulk medium of refractive index n. The spatial part of the vector potential Ap. p produced at position r is given by 

The electric field of the electric dipole is then given by Dip ) = w Dip( )  

The time-averaged power radiated per unit solid angle is 

The field with angular frequency w inside the particle includes contributions from the dipole and the particle 

The contributions from the particle (4.25,26) are necessary to satisfy the boundary conditions given by (4.9,10) which state that the tangential components of E and H must be continuous across the boundary. The presence of fields at other frequencies inside or outside the particle can be ignored as long as suitable filters or monochromators are employed in measuring the scattered radiation. 

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