Electromagnetic Wave Incident on a Dielectric Boundary
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 and , 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.[more]
You can set the frequency (in the range 0.1–0.5 GHz), permittivities and (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 and . Snell's law holds: , where and are incident and transmitted angles. The reflection angle is equal to . The critical angle can be defined in the case . Snapshots 1 and 2 correspond to the cases and , 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.[less]
Snapshot 1: horizontally polarized incident wave with
Snapshot 2: horizontally polarized incident wave with ; the case of total reflection
Snapshot 3: vertically polarized incident wave with ; the case of no reflection
According to Fresnel's equations for the horizontally polarized incident wave's electric field , transmitted and reflected fields are expressed by and . Similar calculations can be made for the vertically polarized incident wave.
Generally, the upper half-space accommodates two waves: incident and reflected; therefore, the Poynting vector pattern is made up of undulating patterns. On the other hand, the lower half accommodates the transmitted wave only, showing a straight plane wave, provided . In the special case of Snapshot 3, the upper space shows the pattern of one plane wave, since there is no reflected wave.
 J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill, 1941 pp. 483–600.