We propose that the full Poincar{e} beam with any polarization geometries can be pictorially described by the hybrid-order Poincar{e} sphere whose eigenstates are defined as a fundamental-mode Gaussian beam and a Laguerre-Gauss beam. A robust and eff
icient Sagnac interferometer is established to generate any desired full Poincar{e} beam on the hybrid-order Poincar{e} sphere, via modulating the incident state of polarization. Our research may provide an alternative way for describing the full Poincar{e} beam and an effective method to manipulate the polarization of light.
