Radar Cross Section (RCS) - MATLAB Simulations for Radar Systems Design - page 504

11.4.1. Polarization

The x and y electric field components for a wave traveling along the positive
z direction are given by

E x = E 1 sin ( ω tkz – )

(11.7)

E y = E 2 sin ( ω tkz – + δ )

(11.8)

where , is the wave frequency, the angle is the time phase
angle which leads , and, finally, and are, respectively, the wave
amplitudes along the x and y directions. When two or more electromagnetic
waves combine, their electric fields are integrated vectorially at each point in
space for any specified time. In general, the combined vector traces an ellipse
when observed in the x-y plane. This is illustrated in Fig. 11.9 .

k = 2πλ ⁄ ω δ

E y E x E 1 E 2

The ratio of the major to the minor axes of the polarization ellipse is called
the Axial Ratio (AR). When AR is unity, the polarization ellipse becomes a cir-
cle, and the resultant wave is then called circularly polarized. Alternatively,
when

E 1 = 0 and AR = ∞ the wave becomes linearly polarized.

Eqs. (11.7) and (11.8) can be combined to give the instantaneous total elec-
tric field,

E ó x E 1 ó y E 2

= sin ( ω tkz – ) + sin ( ω tkz – + δ )

(11.9)

Y

E 2

E

X

Z

E 1

Figure 11.9. Electric field components along the x and y directions.
The positive z direction is out of the page.