Propagation of the fundamental whispering gallery modes in a linear chain of microspheres

Multi-sphere Mie theory is used to analyze the resonance response and the spatial distribution of the electromagnetic field in a system of a linear chain of microspheres. We assume that the system is coupled to a monochromatic source that would have excited a fundamental whispering gallery mode in a single sphere, and study the modification of the resonance frequencies and the spatial distribution of the field induced by optical coupling between spheres. We find that the coupled-mode approach does not give an adequate description of this situation, and that the excitations of the chain cannot be presented as linear combinations of the single-sphere fundamental modes. In the case of chains with an odd number of microspheres, there exists a single collective mode with frequency equal to that of the single-sphere resonance, which reproduces the field pattern of a single-sphere fundamental mode without distortion in every odd-numbered sphere of the chain.