What is the intensity of this light?

[Gavroy]

I am struggling with a derivation that calculates the cross sections for Mie scattering and since the incident light is considered to be a x-polarized plane wave I thought that we would have[ tex ] I_i = \frac{1}{2} \sqrt{\frac{\epsilon}{\mu}} \vert E_0 \vert^2 [ /tex ] , but I do not understand this derivation then, since a factor [ tex ] 2 \pi [ /tex ] seems to be missing.

It starts with an expression for the scattered field, explains how they got this expression by using some orthogonality properties and then - in my opinion argue - that this [ tex ] Re(g_n)[ /tex ]. But then I do not understand what they take as the incident intensity in order to get the expression [ tex ]C_{sca} [ /tex ] Does anybody have an idea?!

 

[Valerie Park]

The expression for the scattered field is given by:[tex] E_s = \frac{2 \pi k^2}{\epsilon_0 c} \sum_{n=1}^\infty Re(g_n) E_0 \hat{e_s} [ /tex ]where [ tex ] g_n = \frac{a_n + b_n}{a_n - b_n} [ /tex ] is the Mie coefficient. The expression for [ tex ] g_n [ /tex ] can be obtained from the orthogonality properties of the spherical harmonics and the incident and scattered fields. Using this expression for [ tex ]E_s[ /tex ], the total scattering cross section [ tex ] C_{sca} [ /tex ] is given by:[ tex ] C_{sca} = \frac{\pi}{k^2} \vert \sum_{n=1}^\infty Re(g_n) \vert^2 I_i [ /tex ]where [ tex ] I_i [ /tex ] is the incident intensity.