In most cases of interest, the modulus of the Poynting vector is proportional to the modulus squared of the electric field (which explains why we often that a shortcut and just talk about |E|²).

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March 19, 2026 - 16:33 UTC

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So the quantity we measure is proportional to |Eᵢₙ +Eₛ|², which is the sum of the Poynting vector of the incident field, the Poynting vector of the scattered field, plus the cross terms.

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These cross terms are what we usually call "extinction" and are the result of the interference between the incident and scattering fields (and the reason why you get a "shadow" behind the scatterer).

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