Theory of reflection from antireflection coatings

The reflection that occurs when a beam, rather than a plane wave, is incident normally on a quarter-wavelength matching layer can be of vital importance in semiconductor laser design. An analysis in three dimensions is given for the general case of a field of arbitrary form and polarization incident on the matching layer. The field is represented as an angular spectrum of plane waves, each component plane wave being modified by the appropriate Fresnel reflection coefficient to give the field reflected back onto the diode structure. Brown's antenna reciprocity theorem is used to determine the amplitude of the corresponding mode traveling back down the diode.