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We investigate binary lenses with $1/r^n$ potentials in the asymmetric casewith two lenses with different indexes $n$ and $m$. These kinds of potentialshave been widely used in several contexts, ranging from galaxies with halosdescribed by different power laws to lensing by wormholes or exotic matter. Inthis paper, we present a complete atlas of critical curves and caustics formixed binaries, starting from the equal-strength case, and then exploringunequal-strength systems. We also calculate the transitions between alldifferent topology regimes. Finally we find some useful analytic approximationsfor the wide binary case and for the extreme unequal-strength case.

Caustics in gravitational lensing by mixed binary systems