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In optics, it is well-known that when a visible light beam, e.g., traveling from air (or more strictly, vacuum) into a piece of smooth flat glass at an angle relative to the normal of the air-glass interface, some proportion of the light will be bounced off at the reflection angle equal to the incident angle. However, when the light beam is with its oscillating electric field parallel to the plane-of-incidence (POI, i.e., the plane constituted by both propagation vectors of the incident and reflected light waves, as well as the interface normal vector) (called the p-wave), there is a particular incident angle at which no bounce-off would occur. This particular angle is known as the Brewster angle ( B  ) (Hecht, 2002). In contrast, when the light beam is with its electric field vector perpendicular to the plane-of-incidence (called the s-wave), no such angle exists (Hecht, 2002). In fact, this is only true for uniform, isotropic, and nonmagnetic (or equivalently, with its relative magnetic permeability ( r  ) equal to unity at the optic frequency of interest) materials such as the above glass piece. Indeed, it is known that for magnetic materials, there may instead exist Brewster angles for the s-waves, while none for the p-waves (as will be demonstrated in Section 2).

Lightwave Refraction and Its Consequences: A Viewpoint of Microscopic Quantum Scatterings by Electric and Magnetic Dipoles