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Suppose I have a system where the functions ##\mathbb{E}(\mathbf{r},t)## and ##\mathbb{B}(\mathbf{r},t)## (time and position dependent electric and magnetic fields) are known. I would like to have an explicit formula for calculating the position, wavelength and direction dependent spectral intensity (as defined here: https://en.wikipedia.org/wiki/Radiant_intensity#Spectral_intensity ) from these functions... I suppose I should write the fields as some kind of a Fourier integral, convert the plane wave components of different wavelengths and directions to Poynting vectors, and then take the time averages of the Poynting vector magnitudes over one period of oscillation. Am I going to the right direction here?

I'm currently doing work on the modelling of radiative heat transfer, and there one obviously doesn't use the Maxwell equations to calculate radiative quantities, as the wavelengths of IR radiation are much smaller than the dimensions of the physical systems considered (you would need a huge discrete lattice to simulate that kind of a system using discretized Maxwell equations). However, in my earlier studies I have mainly approached these kinds of problems using the actual microscopic fields, and I'd like to see the explicit connection of these macroscopic intensity functions to them.