title: Complex reflection coefficients for the parallel and perpendicular polarizations of a film-substate system.
abstract: The complex reflection coefficients Rv(phi,zeta) of a film-substrate system for the parallel (v = p) and perpendicular (v = s) polarizations are examined in detail as functions of the angle of incidence phi(0 </+S 90 degrees) and the reduced normalized film thickness zeta(0 </= zeta </= 1). For definiteness, the reflection of light of wavelength lambda = 0.6328 microm by the air-SiO2-Si system is assumed. Families of circles that represent the constant-angle-of incidence contours, their envelopes, and the associated constant-thickness contours of Rv, and Rs are all presented in the complex plane. Furthermore, the amplitude-reflectance and phase-shift functions, Rv (phi, zeta) and argRv(phi, zeta), are plotted vs zeta with phi constant and vs phi with zeta constant. It is shown that Rp or Rs can assume the same complex value at two different angles of incidence (i.e., the film-substrate system can have identical reflection characteristics for a given polarization at two angles) for certain ranges of film thickness. The distinct case of internal reflection is represented by a separate example.
authors.affiliation: University of New Orleans, Electrical Engineering Department, Lakefront, New Orleans, Louisiana 70148, USA.
authors.forename: R M
authors.initials: RM
authors.lastname: Azzam
authors.forename: M E
authors.initials: ME
authors.lastname: Khan