Polarization Loss & Axial Ratio
How much signal do you lose when the transmit and receive antennas are not polarized the same way? Set the wave and the antenna, from linear through elliptical to circular, and get the polarization loss factor. Or start from the field components and get the axial ratio, tilt and sense.
What is polarization loss?
An antenna only receives the part of an incoming wave whose polarization matches its own. The polarization loss factor (PLF) is the fraction of the available power that is actually received: 1 for a perfect match and 0 for orthogonal polarizations. Two linear antennas rotated by an angle ψ have PLF = cos²ψ, so a 45° misalignment costs 3 dB and a 90° misalignment blocks the signal. A circular wave received by a linear antenna loses 3 dB whatever the orientation, and that is the price paid for not caring about rotation, for instance on satellite and drone links.
Axial ratio and cross-polar discrimination
The polarization ellipse has a major and a minor axis; their ratio is the axial ratio (AR). Linear polarization has an infinite AR and perfect circular polarization has 0 dB. A real circularly polarized antenna is slightly elliptical, so it leaks into the opposite sense. The cross-polar discrimination is XPD = 20·log[(AR + 1)/(AR − 1)]: an AR of 3 dB gives about 15 dB of discrimination, and an AR of 1 dB gives about 25 dB. Opposite-sense circular antennas are the textbook worst case; their isolation is limited by exactly this figure.
How it is calculated
Each polarization is mapped to a point on the Poincaré sphere through its Stokes parameters. The PLF between two antennas is ½·(1 + cos γ), where γ is the angle between their points on the sphere. This one expression covers linear, circular and elliptical combinations, any tilt, and either sense.