Superradiance and Synchronization of 2D Spaser Array

Recently [E. S. Andrianov et al. Phys. Rev. B, 85, 165419 (2012)] it has been shown that a 1D chain of spasers may be synchronized via dipole-dipole interaction of quantum dots with plasmonic nanoparticles of neighboring spasers. We demonstrate that the same mechanism can synchronize a 2D array of spasers too, so that dipole moments of all nanoparticles oscillate in phase and in parallel to the array plane. This results in supperradiance in the direction perpendicular to the plane. Futhermore, the increase of the number of spasers N results in narrowing of the radiation pattern. Certainly, the intensity is restricted by power of pumping.