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

TL;DR

This paper investigates how transversely illuminated point-like particles in a 1D trap self-organize into regular structures due to collective light scattering, providing a simple model and analyzing stability and ordering conditions.

Contribution

It introduces a scattering-matrix based approach to study long-range interactions and self-ordering in 1D particle systems under transverse illumination, including realistic effects.

Findings

Explicit conditions for stable self-ordering of few particles.

Recovery of equidistant lattice prediction in dispersive limit.

Numerical analysis of long-range order formation in larger ensembles.

Abstract

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.