In most textbooks, after discussing the partial transmission and reflection of a plane wave at a
planar interface, the power (energy) reflection and transmission coefficients are introduced by
calculating the normal-to-interface components of the Poynting vectors for the incident, reflected
and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to
be interpreted as the energy flux density, on the incident (reflected) side, the electric and
magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields,
instead of the partial fields which are just the incident (reflected) fields. The interpretation of
the cross product of partial fields as energy flux has not been obviously justified in most
textbooks. Besides, the plane wave is actually an idealisation that is only ever found in textbooks,
then what do the reflection and transmission coefficients evaluated for a plane wave really mean for
a real beam…