Reflectance Enhancement Factor Associated with Coherent Interference of Light in an Unbacked or Embedded Quarter-Wave Layer

If a semi-infinite transparent substrate is replaced by a quarter-wave layer (QWL) of the same material, which is embedded in the same ambient, the intensity reflectance is increased by a significant factor. A simple expression is derived for this reflectance enhancement factor (REF) n that results from coherent multiple-beam interference of monochromatic light within the QWL. The REF n is a monotonically decreasing function of the Fresnel intensity reflectance at the ambient-layer interface with maximum and minimum values of 4 and 1, respectively. The expression for n is applicable for the p and s linear polarizations, at any angle of incidence and for any wavelength within the common transparency bandwidth of both layer and ambient. The results are particularly relevant to light reflection by index-near-one materials and Brewster-angle reflection polarizers that use high-index, IR-transparent semiconductors such as Ge and Si, in bulk and pellicle form.