Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion

We show that eigenmodes of dielectric optical waveguides exert surface dilation forces on waveguide boundaries owing to radiation pressure, and we develop an exact scaling law relating modal dispersion of an arbitrary dielectric waveguide to the magnitude of optical forces generated by radiation pressure. This result points to highly dispersive waveguides as an optimal choice for the generation of large optical forces in nano-optomechanical systems. Exact agreement with ab initio calculations is demonstrated.