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Electromagnetic Wave Incident on a Dielectric Boundary

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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.

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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.

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Contributed by: Y. Shibuya (October 2013)
Open content licensed under CC BY-NC-SA

Snapshots

Details

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.

Reference

[1] J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill, 1941 pp. 483–600.

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