Optical properties of a nonlinear magnetic charged rotating black hole surrounded by quintessence with a cosmological constant

In this paper,we discuss optical properties of the nonlinear magnetic charged black hole surrounded by quintessence with a non-zero cosmological constant $\Lambda$. Setting the state parameter $\omega=-3/2$ , we studied the horizon, the photon region and the shadow of this black hole. It turned out that for a fixed quintessential parameter $\gamma$, in a certain range, with the increase of the rotation parameter $a$ and magnetic charge $Q$, the inner horizon radius increases while the outer horizon radius decreases. And the cosmological horizon $r_{\Lambda}$ decrease when $\gamma$ or $\Lambda$ incease and increase slightly with increasing $a$ and $Q$. The shapes of photon region were then studied and depicted through graphical illustrations. Finally, we discussed the effects of the quintessential parameter $\gamma$ and the cosmological constant $\Lambda$ on the shadow cast by this balck hole with a fixed observer position.