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Radiation losses and dark mode at light guiding by a linear chain of nanoparticles.

A new general formula is presented for a collective extinction cross section of a dielectric or a metallic nanoparticle ensemble in terms of incident electric field work on currents excited inside particles. The formula is obtained by identical transformation of the well-known expression for the summing power of electromagnetic field energy losses caused by particle ensemble scattering and absorption. The derived formula is applied to the problem of radiation losses at electromagnetic excitation transfer along a straight chain of particles. Our general formula predicts a zero collective extinction cross section for an infinite straight chain of nonabsorbing dielectric particles providing that the projection of the wave vector of an incident electromagnetic wave on the chain axis does not coincide with its counterpart of the Bloch wave vector of propagating excitation. In another case of a finite chain of particles, with only the first particle of the chain irradiated by an incident narrow electromagnetic wave beam, the derived formula shows that only the irradiated particle directly contributes to the collective extinction cross section despite how large the total number of particles can be, which makes a direct summing contribution of all other particles to wave scattering as if they were unviewed (dark mode). Using a recently developed quasi-separable T-scattering operator approach that leads to the equation system for self-consistent currents excited inside particles by an incident electromagnetic wave field and restricting ourselves to the electric dipole single scattering and neighbor coupling approximation, we revealed a few gigahertz transparency band in the terahertz frequency range (orange color) in the spectra of a straight chain of closely spaced gold nanospheres of a certain radius and a length of a few millimeters. A resonant mechanism of filtering the dark mode from radiation losses established in this work allowed us to reveal a few-fold-more narrow passband in the spectra of a longer gold particle chain with the full length of a few centimeters.