Wolfram Demonstrations Project

This Demonstration shows an electromagnetic wave incident on a perfect conductor calculates the corresponding Poynting vector. The incident wave is assumed to be linearly polarized in the horizontal or vertical direction (with respect to the electric field). The resulting Poynting vector pattern is shown on the incident

plane. In all cases, the amplitude of the incident electric field is set to

, which corresponds to

in power density.

The Poynting vector is calculated using

, where

and

are the electric and magnetic fields. The fields can be calculated by superposing the fields for the incident and reflected waves. You can show the individual Poynting vectors of the incident wave, the reflected wave, or their superposition.

You can set the frequency in the range 0.1–1.0 GHz and the incident angle at 0–90°. The phase of the sinusoidal cycle can be changed, but this results in time-consuming computations.

Contributed by: Y. Shibuya

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Snapshot 1: Poynting vector plot for vertically polarized incident wave at angle

Snapshot 2: Poynting vector plot for incident wave of

(same for horizontal or vertical waves)

Snapshot 3: Poynting vector plot for reflected wave for incident wave of

(same for horizontal or vertical waves)

For the horizontally-polarized electromagnetic wave propagating along the

axis, the electric field is given by

, while for the vertically-polarized wave,

. Here,

is the propagation factor. In both cases, the corresponding magnetic field is given by

, where

is the propagation direction, and

is the wave impedance.

Similarly, the fields for the incident angle

can be determined for both incident reflected waves as

. Then the resultant fields

and

can be obtained by superposition. The Poynting vector can be calculated accordingly.

The Poynting vector pattern of the incident wave (or reflected wave) is the same whether the polarization is horizontal or vertical. However, the superposed pattern is different because the reflected wave's phase depends on the polarization.

The Poynting vector's intensity and direction are shown by colors and arrows in the output pattern. The intensity increases as