Part 1 : Nanoparticles Module 6 : Mie theory for Scattering and absorption by                    a sphere and ellipsoids
Lecture 3 : Cross-section and scattering matrix
 
where $g_l=-i\xi_l^*\,\xi_l '$. For $r\ge R$, the medium is non-absorbing and $\rho=qr$ is real so that the function $\xi_l$ is also real, which implies that Re$[g_l] =1$. Therefore
\begin{displaymath}C_{sca}= \frac{W_s}{I_i}=\frac{2\pi}{q^2}\,\sum_{l=1}^\infty\,(2l+1)\,\left[\vert a_l\vert^2+\vert b_l\vert^2\right]\,,\end{displaymath}
Proceeding in a similar manner, one finds
\begin{displaymath}C_{ext}= \frac{W_{ext}}{I_i}=\frac{2\pi}{q^2}\,\sum_{l=1}^\infty\,(2l+1)\,{\rm Re}\left[a_l+b_l\right]\,.\end{displaymath}