Revisiting optical absorption power density of inhomogeneous plane waves

We review the analytical expressions for the complex Poynting’s vector in the case of arbitrary plane-waves in a lossy isotropic medium. We demonstrate how these expressions can be used to recover the optical absorption power density $Q$, considering the divergence of the time-averaged Poynting vector. This quantity, proportional to the imaginary part of the dielectric function and the field intensity, i.e. $Q\propto {\left|E\right|}^2\varepsilon$”, is usually established for harmonic fields, using the Poynting’s identity. The derivation from the complex Poynting vector expression is more direct for TE-polarized homogeneous waves, but the derivation encompasses the other cases like inhomogeneous TM plane waves. As an application, the optical absorption profile $Q\left(x\right)$ within 1D multilayers is detailed using matrix transfer method for both TE and TM plane waves, including the evanescent case.