circularly polarized antennas

Hi all,
I have a confusion regarding the circularly polarized antennas, as I reviewed the literature for the microstrip patch antenna for dual circular polarization. I am confused that if an antenna is circularly polarized, will it generate both LHCP and RHCP or it will generate RHCP and LHCP when it is dual circularly polarized

thanks

Some antennas radiate linear polarized waves, others radiate circularly polarized waves.
A "linear" antenna radiates a wave with a linear polarization, referred to Earth surface as vertical or horizontal.
Such linearly polarized wave can be broken in two circularly polarized waves approximately equal in amplitude, so if such LP wave is received by a circularly polarized antenna, it will respond but with only a half amplitude. Such response will be equal for RHCP as well as LHCP.
If you make a RHCP antenna, it will not radiate a LHCP wave (or strongly suppressed) but such wave can be received by a linearly polarized antenna to give a half-amplitude response while it can be designed to receive either H or V linear polarization.
I think no antenna can be designed to optimally radiate both LHCP AND RHCP , only one way is possible. BUt if you use a linearly polarized antenna, see above.

It depends. It depends from connection point on the patch and they typically aren't rectangle. .

To assist the pretty clear explanation, no antenna can radiate it simultaneously. But a suitable antenna e.g. a cross dipole can generate any polarization with respective phase shift and magnitude of the two input feed lines.