Optical Tautochrone and Squeezing Dynamics in Non-uniform Lattices

TL;DR

This paper explores the analogy between classical optical waveguide lattices and quantum phenomena like tautochrone and squeezing, demonstrating how non-uniform couplings influence light dynamics and enabling advanced beam control.

Contribution

It introduces a novel analogy between classical optical lattices and quantum states, extending to 2D systems and analyzing nonlinear effects on light propagation.

Findings

Exact analogy between tautochrone and squeezed states in optical lattices

Extension to two-dimensional lattices with complex trajectories

Kerr nonlinearity influences diffraction and beam behavior

Abstract

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.