  We study point-like polarizable particles confined in a 1D very elongated
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 interactions 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 resulting 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 interaction models. We generalize
our model to experimentally more realistic configurations including
backscattering, absorption and a directional scattering asymmetry. For larger
particle ensembles the resulting self-consistent particle-field equations can
be numerically solved to study the formation of long-range order and stability
limits.
