Page 416 - Engineering Electromagnetics, 8th Edition

398 ENGINEERING ELECTROMAGNETICS

Figure 11.6 Electric field in the xy plane
of a right circularly polarized plane wave,
as described by Eq. (98). As the wave
propagates in the forward z direction, the
field vector rotates counterclockwise in the
xy plane.

Choosing +π/2 leads to (97), whose field vector rotates in the clockwise direction.
The handedness of the circular polarization is associated with the rotation and propa-
gation directions in the following manner: The wave exhibits left circular polarization
(l.c.p.) if, when orienting the left hand with the thumb in the direction of propagation,
the fingers curl in the rotation direction of the field with time. The wave exhibits right
circular polarization (r.c.p.) if, with the right-hand thumb in the propagation direc-
7
tion, the fingers curl in the field rotation direction. Thus, with forward z propagation,
(97) describes a left circularly polarized wave, and (98) describes a right circularly
polarized wave. The same convention is applied to elliptical polarization, in which
the descriptions left elliptical polarization and right elliptical polarization are used.
Using (96), the instantaneous angle of the field from the x direction can be found
for any position along z through
E y
∓sin(ωt − βz)
θ(z, t) = tan −1 = tan −1 =∓(ωt − βz) (99)
E x cos(ωt − βz)
where again the minus sign (yielding l.c.p. for positive z travel) applies for the choice
of φ =+π/2in (96); the plus sign (yielding r.c.p. for positive z travel) is used if

7 This convention is reversed by some workers (most notably in optics) who emphasize the importance
of the spatial field configuration. Note that r.c.p. by our definition is formed by propagating a spatial
field that is in the shape of a left-handed screw, and for that reason it is sometimes called left circular
polarization (see Figure 11.7). Left circular polarization as we define it results from propagating a
spatial field in the shape of a right-handed screw, and it is called right circular polarization by the
spatial enthusiasts. Caution is obviously necessary in interpreting what is meant when polarization
handedness is stated in an unfamiliar text.