Scattering approach to two-colour light forces and self-ordering of polarizable particles

Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long range interactions, whose properties can be tailored by choice of injected laser powers, frequencies and polarizations. We use a transfer matrix approach to study the forces induced by non-interfering fields of orthogonal polarization or different frequencies in a 1D geometry and find long range self-ordering of particles without a prescribed order. Adjusting laser frequencies and powers allows to tune inter-particle distances and provides a wide range of possible dynamical couplings not accessible in usual standing light wave geometries with prescribed order. In this work we restrict the examples to two frequencies and polarisations but the framework also allows to treat multicolour light beams with random phases. These dynamical effects should be observable in existing experimental setups with effective 1D geometries such as atoms or nanoparticles coupled to the field of an optical nanofibre or transversely trapped in counterpropagating Gaussian beams.