Quantum chaos analysis for characterizing a photonic resonator lattice

Highlights: • The localization of Hamiltonian eigenstates in the photonic resonator lattice with a harmonically modulated phase is observed as a result of the impact of phase and the location of interface. • Level spacing distribution and so random matrix theory is capable of characterizing the behavior of a photon in regions with different magnetic properties. • In weak modulation phases, the location of interface has no effect on the appearance of localized states; but in strong phases it is found a threshold value for location of interface above which all eigenstates are delocalized. - Abstract: Tailoring the propagation of light in an arbitrarily manner has motivated a great of interest on nanophotonics. As a new mechanism for this purpose, the generation of an effective magnetic field leading to a Lorentz force for photons is recently proposed in a photonic resonator lattice. Here, we consider a photonic resonator lattice with a harmonically modulated phase and with an interface splitting the lattice into two magnetically different regions. Considering this lattice, we try to explore the impact of phase and the location of interface on the localization of Hamiltonian eigenstates by applying level spacing distribution as a cornerstone of random matrix theory. The obtained results show that while the location of interface has no effect on the appearance of localized states in weak phases, in strong phases it is found a threshold value for location of interface above which all eigenstates are delocalized. As a result, level spacing distribution and so random matrix theory is capable of characterizing the behavior of a photon in regions with different magnetic properties.