  Polarizable dipoles, such as atoms, molecules or nanoparticles, subject to
laser radiation, may attract or repel each other. We derive a general formalism
in which such laser-induced dipole-dipole interactions (LIDDI) in any geometry
and for any laser strength are described in terms of the resonant dipole-dipole
interaction (RDDI) between dipoles dressed by the laser. Our expressions
provide a physically clear and technically simple route towards the analysis of
LIDDI in a general geometry. This approach can treat both mechanical and
internal-state interactions between the dipoles. Our general results reveal
LIDDI effects due to nonlinear dipole-laser interactions, unaccounted for by
previous treatments of LIDDI. We discuss, via several simple approaches, the
origin of these nonlinear effects and their absence in previous works.
