Abstract
A completely general treatment of refraction at a planar interface is given using the Hilbert-space formulation of the angular spectrum representation of electromagnetic wave fields. Although the incident wave fields are completely general, they are naturally expressed as a unique sum of a TE and TM component. These transverse electric and transverse magnetic components are understood in the wave guide sense. Each of these two components is truly scalar and is acted upon independently in the refractive process. Thus our treatment of the problem is somewhat analogous to the classical treatment, where two cases of polarization are handled separately. The above treatment forms a natural background for discussing the power transmission properties of two superposed general wave fields propagating in the same or opposite directions. The power interaction term between the two superposed wave fields involves only their homogeneous parts or only their evanescent parts when propagating in the same or opposite directions respectively. The implications of these results for measurements taken in close proximity to material objects is discussed.
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