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It is apparent from Figure 4-20 that the linear polarization is always found along the equator; the right-hand circular resides along the south pole and the left-hand circular along the north pole.Also the range of values of the axial ratio (AR) should be 1 <= |AR|<= 00, with positive values to represent CCW (left-hand) polarization and negative values to represent CW (right-hand) polarization.In general, points on the principal xz elevation plane, aside from the two intersecting points on the equator and the north and south poles, are used to represent elliptical polarization when the major and minor axes of the polarization ellipse of Figure 4-19 coincide with the principal axes.
It is apparent from Figure 4-20 that the linear polarization is always found along the equator; the right-hand circular resides along the south pole and the left-hand circular along the north pole. The remaining surface of the sphere is used to represent elliptical polarization with left-hand elliptical in the upper hemisphere and right-hand elliptical on the lower hemisphere. Because the Poincaré sphere parameter pairs (7, 8) and (e, 7) are related by transcendental functions, of (4-60a) and (4-60b), there may be some ambiguity at which quadrant should the angles be chosen. The angles should be selected to each satisfy respectively the range of values given by (4-58a) and (4-58b), and (4-57c), and each set should represent the same point on the Poincaré sphere. Also the range of values of the axial ratio (AR) should be 1 ≤ |AR|≤ 00, with positive values to represent CCW (left-hand) polarization and negative values to represent CW (right-hand) polarization. A MATLAB computer program, Polarization_Propag, has been written and it is part of the website that accompanies this book. In general, points on the principal xz elevation plane, aside from the two intersecting points on the equator and the north and south poles, are used to represent elliptical polarization when the major and minor axes of the polarization ellipse of Figure 4-19 coincide with the principal axes. If the polarization state of a wave is defined as Pw and that of an antenna as Pa, then the voltage response of the antenna due to the wave is obtained by [10, 19]
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