Engineering wavefront caustics trajectories in $\mathcal{P}\mathcal{T}$-symmetric lattices

We utilize caustic theory in $\mathcal{P}\mathcal{T}-$symmetric lattices to design focusing and curved beam dynamics. We show that the gain and loss parameter in these systems provides an addition degree of freedom which allows for the design of the same caustics trajectories with different intensity distribution in the individual waveguides. Moreover we can create aberration-free focal points at any paraxial distance $z_f$, with anomalously large focal intensity.