# Absorbance by using Poynting vector

How should I compute the amount of energy of an EM wave absorbed by a material? Can I just use the divergence of the Poynting vector?

-
Welcome to physics SE. What have you tried to solve this problem? – Stefan Bischof Mar 6 '13 at 7:31
i tried joule heating, electrical conductivity times E square ， but it turns out bad, because it's kinda linearly proportion to electrical conductivity. but when the electrical goes up th like 10^7 , the power absorbed is obviously too high. as is for the poynting vector, the formula is Pabs=-0.5xReal(div(S)) where S is the poynting vector. but i don't have the imaginary part here. so I used div(S) only. I don't have the results yet ,the codes are still running but i got a bad feeling about it .:) thank you – Duran Deng Mar 6 '13 at 9:57
Can you outline the setup a bit better? Is this a plane wave travelling in a medium that has a conductivity, or a wave incident upon the surface of such a substance? – Rob Jeffries Aug 18 '14 at 18:55

There is another possible approach. You can calculate the flux of the Poynting vector over the boundary of the absorbing volume (http://ocw.mit.edu/resources/res-6-001-electromagnetic-fields-and-energy-spring-2008/chapter-11/11.pdf , 11.1, eq. (1)). I used this approach to calculate the power absorbed in a thin cylinder heated by a broad electromagnetic beam (http://arxiv.org/abs/physics/0405091 , http://arxiv.org/abs/physics/0611169 ). The results were later confirmed in experiments (http://arxiv.org/abs/1109.1626 , http://arxiv.org/abs/1208.0066)

-

Yes you can, as the thread in the lumerical knowledge base mentioned. https://kb.lumerical.com/en/layout_analysis_pabs_simple.html There is another method included in that thread. Hope that can help too.

The related material is listed as follows: The absorption per unit volume can be calculated from the divergence of the Poynting vector,

Pabs=-0.5real(div.vec_P).

It is possible to calculate the absorption directly from this formula (see the Divergence of Poynting vector section), but divergence calculations tend to be very sensitive to numerical problems. Fortunately, there is a more numerically stable form. It can be shown that the above formula is equivalent to

Pabs=-0.5real(iwvec_Evec_D) (w is the radian frequency)

With a little more work, we get the desired result

Pabs=-0.5*w*E^2*imag(epsilon)

To calculate the absorption as a function of space and frequency, we only need to know the electric field intensity and the imaginary part of the permittivity. Both quantities are easy to measure in an FDTD simulation.

-
Hello and Welcome to Stack Exchange! While this link may answer the question, it is discouraged to post link-only answers here (as sites may vanish from the internet or be moved, etc.). Could you maybe provide a sketch of the answers in the linked thread? – Martin Oct 26 '15 at 9:59