Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres

The origin and properties of non-Lorentzian spectral lines in linear chains of nanospheres are discussed. The lines are shown to be super-exponentially narrow with the characteristic width proportional to exp[-C(h/a)(3)] where C is a numerical constant, h the spacing between the nanospheres in the chain and a the sphere radius. The fine structure of these spectral lines is also investigated.