Coupled-mode theory analysis of optical forces between longitudinally shifted periodic waveguides

We develop a coupled-mode theory that describes the dependence of optical gradient forces between side-coupled periodic waveguides on the longitudinal shift between the waveguides. Our approach is fully applicable to waveguides with a strong refractive-index modulation and in the regime of slow-light enhancement of optical forces, associated with the group-velocity reduction at the photonic band edge. Our method enables fast calculation of both the transverse and longitudinal forces for all longitudinal shifts, based on numerical simulations of mode profiles only at particular shift values. We perform a comparison with direct numerical simulations for photonic-crystal nanowire waveguides and demonstrate that our approach provides very accurate results for the slow-light enhanced transverse and longitudinal forces, accounting for the key features of force suppression and sign reversal at critical shift values.