Mielnik's evolution loop hexagon in new light

The problem of controlling quantum wavefunctions by means of potential jolts and periods of free evolution was broached by Bogdan Mielnik in 1977. This quantum control became a subject of great interest for the preparation of atomic and particle systems. We point out here that these manipulations are also realized in paraxial geometric and wave optics, with lenses and free spaces, and even more transparently than with matter.