This Demonstration shows an electromagnetic wave incident on a planar dielectric boundary in terms of the Poynting vector on both sides of the boundary. Taking the incident plane and boundary planes to be
, respectively, the resulting Poynting vector pattern is shown on the incident
plane. The incident wave is assumed to be linearly polarized either horizontally or vertically with respect to the electric field. (The horizontal wave and vertical wave are sometimes called the p-wave and s-wave, respectively.) In all the cases, the power density (Poynting vector intensity) of the incident wave is set to
on average, that is, to peak at
The instantaneous Poynting vector is calculated by
are the time-varying electric and magnetic fields of the incident, reflected, and transmitted waves. In addition to the superposed fields, you can select each of those waves to show the Poynting vector pattern.
You can set the frequency
(in the range 0.1–0.5 GHz), permittivities ϵr1
(in the range 1–5), and the incident angle
(in the range 0–90°). You can set the time of display
(phase) and you can vary the time automatically.
Let the relative permittivities of the lower and upper dielectrics be
. Snell's law holds:
are incident and transmitted angles. The reflection angle
is equal to
. The critical angle
can be defined in the case ϵr1<ϵr2
. Snapshots 1 and 2 correspond to the cases
, respectively. The latter is the case of total reflection, in which the transmitted angle
is complex. Calculations using the complex angle give diminishing fields in the region
. In the case of a vertically polarized incident wave, the Brewster angle is
. No reflections occur for
, which is shown in Snapshot 3. Those special angles, if any, are shown in the table on the right.