Shadow and Weak Gravitational lensing of rotating traversable Wormhole in Non-homogeneous Plasma Space-time

In this work, we have studied the behavior of null geodesics within a rotating wormhole space-time in non-magnetized pressure-less plasma. By focusing on the dispersion relation of the plasma and disregarding its direct gravitational effects, we examine how light rays traverse in the mentioned space-time. A key highlight of the work is the necessity of a specific plasma distribution profile to establish a generalized Carter's constant, shedding light on the importance of this parameter. Furthermore, we have derived analytical formulas to distinguish the shadow boundary across various plasma profiles, uncovering a fascinating trend of diminishing shadow size as plasma density increases. Intriguingly, certain limits of the plasma parameters result in the complete disappearance of the shadow. When calculating the deflection angle by a wormhole in plasma space-time, we observe a distinct pattern: the angle decreases as the plasma parameter rises in non-homogeneous plasma space-time, diverging from the behavior observed in homogeneous plasma space-time. Also, leveraging observational data from M$87^{\ast}$, we establish constraints on the throat radius. Furthermore, minimum shadow diameters provide valuable constraints for the radial and latitudinal plasma parameters.