My students and I have just finished several pieces of work on perfect imaging when I am preparing the course of university physics:

1. Luneburg-Lissajous lens:
https://arxiv.org/abs/2002.03114

2. Duplex Mikaelian/Maxwell lens:
https://arxiv.org/abs/2002.03122

3. Morse lens (inspired by Morse potential 90 years ago)
https://arxiv.org/abs/2002.03884

The simple harmonic oscillation is of Hooke potential, its 2D version is Lissajous, while the cylindrical/spherical version is Luneburg; By a power mapping, it changes into Eaton/Coulomb/Newton, and all are related to Morse potential by an exponential mapping; Eaton and Maxwell are of k-r reciprocity, while Luneburg is of self k-r reciprocity; Maxwell is related to Mikaelian by an exponential mapping.

Further reading in:U. Leonhardt and T. Philbin, Geometry and Light: The Science of Invisibility (Courier Corporation, Chelmsford, MA, 2012).