Optical cooperative effects of multiemitters in a one-dimensional (1D) dense array

We theoretically explore cooperative effects of equally spaced multiemitters in a 1D dense array driven by a low-intensity probe field propagating through a 1D waveguide by modeling the emitters as point-like coupled electric dipoles. We calculate the collective optical spectra of a number of 1D emitter arrays with any radiation-retention coefficient η using both exact classical-electrodynamics and mean-field-theory formalisms. We illustrate cooperative effects of lossless 1D emitter arrays with η = 1 at the emitter spacings, which are displayed by steep edges accompanied by a deep minimum and Fano resonances in the plots of transmissivities as a function of the detuning of the incident light from the emitter resonance. Numerical simulation of the full width of such optical bandgaps reveals that cooperativity between emitters is greater in a small array of size N ≤ 8 than in a larger one of size N > 8. For a lossy 1D emitter array in which the radiation retention coefficient is equal to or less than 0.1 the transmissivity obtained by exact-electrodynamics scheme exhibits no bandgap structures, being in good agreement with the mean-field-theory result. We propose that a 1D multiemitter array may work as a nanoscale filter blocking transmission of light with a frequency in the range of optical bandgaps.