Coherent anti-Stokes Raman scattering (CARS) microscopy can break through the optical diffraction limit by applying the additional probe beam induced phonon depletion (APIPD). Using this method, we can obtain a spatial resolution beyond the optical diffraction limit by introducing a doughnut additional probe beam to deplete phonons at the periphery of the focal spot. To achieve higher spatial resolution and better phase matching conditions, it is necessary to use high numerical aperture objectives, whereas scalar diffraction theory is no longer valid. According to the full vector diffraction theory, we calculate the intensity distributions at the focal plane when the linearly and circularly polarized lights pass through a spiral phase plate and an objective with high numerical aperture successively. The result shows that the circular polarization can generate the perfectly doughnut-shaped focal spot, which is more suitable for the additional beam than the linear polarization induced beam. Furthermore, we analyze the APIPD induced CARS process with the full quantum theory. Simulations indicate that a spatial resolution as high as 45 nm could be realized when the ratio between the intensities of additional probe and probe is 80. And the spatial resolution turns higher with increasing the power of additional probe.