Spin angular momentum of surface modes from the perspective of optical power flow.

We show that the spin angular momentum (SAM) carried by a surface mode can be linked to the expectation value, with respect to the distribution of optical power flow, of its decay constant by itself or divided by the product of permittivity and permeability of the medium. Rewriting the formulas for the SAM of a surface mode using the relation between the SAM density and the Poynting vector and then normalizing the light field so that the surface mode carries unit power, we derive novel formulas that show the linear relation between the SAM and those expectation values. The effect of propagation loss is also discussed briefly.