Plasmons are collective excitations of the conduction electrons in metal structures in which the electrons oscillate coherently.Often metal structures have several plasmon modes, such as is illustrated to the right. In this case an array of gold cubes on a gold film have two modes: a localized gap mode and a delocalized lattice mode. For certain choices of array periodicity and cube size, these two modes can occur at the same energy. However when this happens the modes couple and split. In this work, it was demonstrated that mode coupling can lead to splittings as high as 0.3 eV, which is one of the highest electromagnetic coupling effects known for visible frequency light.This is relevant to applications in plasmonic devices.