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 possesses this symmetry.
© 2014 Optical Society of America
Original Manuscript: January 29, 2014
Revised Manuscript: February 28, 2014
Manuscript Accepted: March 3, 2014
Published: March 27, 2014
B. M. Rodríguez-Lara, P. Aleahmad, H. M. Moya-Cessa, and D. N. Christodoulides, "Ermakov–Lewis symmetry in photonic lattices," Opt. Lett. 39, 2083-2085 (2014)