Ermakov-Lewis symmetry in photonic lattices
  We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator where the mass and frequency depend on the propagation distance. In these photonic lattices refractive indices and second neighbor couplings define the mass and frequency of the analog quantum oscillator, while first neighbor couplings are a free parameter to adjust the model. The quantum model conserves the Ermakov-Lewis invariant, thus the photonic crystal also posses this symmetry. 
B. M. Rodr\'iguez Lara, P. Aleahmad, H. M. Moya-Cessa, and D. N.   Christodoulides
physics.optics quant-ph