Resonant scattering of two-dimensional honeycomb PT dipole structure

We studied numerically electromagnetic response of the finite periodic structure consisting of the ${\cal{PT}}$ dipoles represented by two infinitely long, parallel cylinders with the opposite sign of the imaginary part of a refractive index which are centered at the positions of two-dimensional honeycomb lattice. We observed that the total scattered energy reveals series of sharp resonances at which the energy increases by two orders of magnitude and an incident wave is scattered only in a few directions given by spatial symmetry of periodic structure. We explain this behavior by analysis of the complex frequency spectra associated with an infinite honeycomb array of the ${\cal{PT}}$ dipoles and identify the lowest resonance with the broken ${\cal{PT}}$-symmetry mode formed by a doubly degenerate pair with complex conjugate eigenfrequencies corresponding to the $K$-point of the reciprocal lattice.