Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response

Vortex solitons in parity-time ($\mathcal{PT}$) symmetric and partially $\mathcal{PT}$ (p$\mathcal{PT}$) azimuthal lattices are demonstrated for a media with quadratic nonlinear response. Stability properties of the vortices investigated comprehensively by linear spectra evolution governing equations, it is shown that, although existence domain $\mathcal{PT}$-symmetric p$\mathcal{PT}$-symmetric identical, stability region lattice narrower than that lattice. It also observed deeper real part potentials supports vortex solitons, whereas imaginary strong electro-optic effects impoverish vortices. Moreover, there different vorticity values, while no such difference potentials.