Physics of Dipole and Quadrupole Brewster Angles in Thin Films
The Brewster angle is a well-known-phenomenon that describes the angle at which the intensity of reflection of p-polarized light is zero for a single dielectric interface. We investigate the angle dependent reflection in a simple SiN thin film, with thickness in the hundreds of nanometres, a common thickness used in optical waveguides, Fabry-Perot resonators, sensors and lasers. We describe the reflection of our SiN thin film in terms of electric and magnetic multipoles through a multipole expansion of the fields inside our film. Previous theoretical studies on Fabry Perot modes in GaP films have only considered the reflection of unpolarized light at normal incidence. Our investigation expands on this work to s- and p-polarization and angle dependent effects permitting the study of both Fabry Perot and Brewster angle effects together. Our approach allows us to re-derive the well-known Brewster angle equation from the electric dipole term. We then derive several new Brewster angle equations associated with the magnetic dipole and electric/magnetic quadrupoles in our model. Our model is then validated by obtaining good agreement between the predicted reflection from our multipoles to the measured reflection of the same thin film. The distinction between the standard electric dipole Brewster angle and our newly discovered Brewster angles is the destructive interference between remaining multipoles. It is this destructive interference which produces the zero in measured and modelled reflection, associated with the Brewster angle. In addition, the Brewster condition of the magnetic dipole and quadrupoles are only satisfied at specific wavelengths. This multipole model brings additional understanding of how light interacts with thin film dielectric materials.