Self-ordering and collective dynamics of transversely illuminated point-scatterers in a 1D trap

Abstract

We study point-like polarizable particles confined in a 1D very elon-gated trap within the evanescent field of an optical nano-fiber or nano-structure. When illuminated transversely by coherent light, collective light scattering into propagating fiber modes induces long range inter-actions and eventually crystallisation of the particles into regular order. We develop a simple and intuitive scattering-matrix based approach to study these long-range interactions by collective scattering and the re-sulting light-induced self-ordering. For few particles we derive explicit conditions for self-consistent stable ordering. In the purely dispersive limit with negligible back-scattering, we recover the prediction of an equidistant lattice as previously found for effective dipole-dipole in-teraction models. We generalize our model to experimentally more realistic configurations including backscattering, absorption and a di-rectional scattering asymmetry. For larger particle ensembles the re-sulting self-consistent particle-field equations can be numerically solved to study the formation of long-range order and stability limits.