It depends how the radiation pattern was measured. Often patterns are measured by using two of the SAME antennas in a test range. S21 is measured, path loss is estimated and subtracted and the response is divided by two to come up with the gain of one antenna. In this case you would not know the pol since the two antennas are identical.
Another way to measure antenna pattern would be take a known antenna of a particular pol and measure the unknown antenna against it. Often the known antenna will be linearly polarized, so it is possible to rotate it to get measurement at Vertical, Horizontal or any other slant angle. A circularly polarized antenna will have equal response to vertically or horizontally polarized antennas.
thnaks for your answer , I was asking if I am desgning an antenna and I have in the simutaltion my radiation pattern , how do I know I have achevied a cirulcar polarized antenna
You're right that most modeling SW doesn't deal with CP very well (meaning, making it explicit).
You may need to build a simple pair of crossed dipoles in your model and connect them as a CP antenna (with an appropriate phasing harness) - all in the model.
Then measure the coupling when it is the same CP and the opposite CP. You should get good coupling when the same CP and good isolation when the opposite CP. This will prove CP.
Be aware that when you go around the back of some CP antennas, the polarity reverses.
A couple options to just get a feeling whether it's circular or not.
After your first antenna pattern, rotate your antenna 45 degrees and plot the antenna pattern again. Rotate your 90 degrees (from the original position) and plot the antenna pattern a second time. If all the plots look similar, then it's probably circular polarization, where the plots diverge it's not circular. An antenna with one or two dB difference for these antenna patterns is pretty good. For wide angle antennas, even 5 dB difference in the patterns is often acceptable.
Or, a quick measurement on a Vector Network Analyzer, measure S21 from your antenna to a dipole, calibrate on this initial measurement to get a flat line on your analyzer. Then rotate the dipole and see how much the S21 changes relative to your flat reference line. You can repeat that at various angles relative to your antenna boresight by positioning the dipole off axis. Use some absorber around the test area, or keep the two antenna fairly close to one another (a few inches) for strong coupling so that bounces off the operator and other hardware don't hurt the measurement too much.
The most accurate mathematical result is to take two antenna patterns, one with the test chamber transmit antenna vertical, one with the transmit antenna horizontal. You need phase data in the measurement to calculate circular polarization antenna pattern for both right hand and left hand circular.
What frequency are you working at, just curious.
kch
Earlier post clip:
"A circularly polarized antenna will have equal response to vertically or horizontally polarized antennas."
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A linear receive antenna looking only at the H and V fields (in sequence) also will have equal response to a linear source antenna that is inclined 45 degrees from H&V.
The best measure/indicator of c-pol is c-pol axial ratio, which considers radiation in all polarization planes. H&V fields might be equal, but fields at other rotation angles could be quite different - so that doesn't prove c-pol.
Reflections are usually different for h-pol and v-pol, so due care is needed when making c-pol measurements.
If you have relative phase data with H and V pol measurements, that gives you all you need. If the phase is 90 degrees, it's perfect circular polarization.
