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We study one-dimensional lattices with imaginary-valued Aubry-Andre-Harper(AAH) potentials. Such lattices can host edge states with purely imaginaryeigenenergies, which differ from the edge states of the Hermitian AAH model andare stabilized by a non-Hermitian particle-hole symmetry. The edge states arisewhen the period of the imaginary potential is a multiple of four latticeconstants. They are topological in origin, and can manifest on domain wallsbetween lattices with different modulation periods and phases, as predicted bya bulk polarization invariant. Interestingly, the edge states persist andremain localized even if the real line gap closes. These features can be usedin laser arrays to select topological lasing modes under spatially extendedpumping.

Topological Transitions with an Imaginary Aubry-Andre-Harper Potential