Optical Tautochrone and Squeezing Dynamics in Non-uniform Lattices

We present exact analogies between the tautochrone problem of mechanics and the squeezed states of quantum optics, to optical lattices. Both phenomena emerge in the same physical system, that of waveguide arrays with non-uniform couplings. Extension to two dimensions yields Lissajous-type trajectories and multidirectional tautochrone focusing. Furthermore, we investigate the impact of Kerr nonlinearity and show that it determines the diffraction behavior, namely coherent-state-like or squeezed propagation. These quantum inspired classical lattices highlight the role of the coupling coefficients to beam engineering and light control in complex media.