Principles of Modern Radar - Volume 2 1891121537

13.2 Polarization 595Therefore, we examine the locus described by the tip of the electric field vector E in theplane z = 0, as time changes, for different values of E 0x , E 0y and δ.13.2.1.1 Linear PolarizationWhen the phase difference δ = 2nπ, n an integer, the two components are in phase, andwe have E x /E 0x = E y /E 0y . Thus, the wave is linearly polarized with its locus traversinga positive slope in the first and third quadrants (Figure 13-2a). When the phase differenceis an odd multiple of 2π, that is, δ = (2n + 1) π, we have E x /E 0x =−E y /E 0y , and thestraight line locus traverses negative slope in second and fourth quadrants (Figure 13-2b).13.2.1.2 Circular PolarizationWhen the amplitudes of the two components in (13.1) are equal (E 0x = E 0y = E 0 ) andthe phase difference δ =±π/2, the electric field is given byE(t) = ˆxE 0 cos(ωt) ∓ ŷE 0 sin(ωt) (13.2)It can be seen that as ωt increases from 0 to 2π, the tip of the electric field vectortraverses a circle, and thus the wave is circularly polarized. When δ =+π/2, the tip rotatescounterclockwise with the observer looking into the direction of propagation (out of thepage in Figure 13-2), and the wave is said to be left-hand polarized. Equivalently, if the lefthandthumb points to the direction of propagation while the fingers of the left hand curl inthe direction of rotation of the electric vector, the wave is left-hand polarized. Conversely,the wave is right-hand polarized when the sense is described by right-hand thumb andfingers, as can be verified for the case δ =−π/2. For example, the loci for these twosenses of circular polarization are depicted in Figure 13-2c (RCP) and Figure 13-2d (LCP).It may be seen that the tip rotates along the circle of radius E 0 with a constant angular rate ω.yyFIGURE 13-2E 0yE 0yEx0x xE 0x(a)(b)yyE 0 Ex 0x(c)(d)yyE 0y E 0yE 0x E 0xxxPolarization statesin a planeperpendicular todirection ofpropagation.(a) linear polarization(LP) with positiveslope. (b) LP withnegative slope.(c) Right circularpolarization (RCP).(d) Left circularpolarization (LCP).(e) Right-handedelliptical polarization(EP). (f) Left-handedEP. The propagationdirection is out ofthe page.(e)(f)