  Optical forces in dielectric structures are typically analyzed by utilizing
either the Maxwell stress tensor or energy-based methods from which they can be
derived by means of the eigenfrequencies and the effective refractive indices
involved. While the equivalence of these two methods has been discussed in
several studies, it would seem that a general electrodynamic proof of this
aspect is still lacking. In this work, we provide a rigorous electrodynamic
derivation based on the Minkowski-Helmholtz formula and the electromagnetic
variation theorem, from which one can directly conclude that under Hermitian
conditions these two approaches are formally equivalent to each other. The
results of our study universally apply to any dielectric waveguide or cavity
configuration. In addition, this methodology can be employed in graded index
systems that do not exhibit sharp interfaces. Importantly, our analysis offers
a straightforward route for predicting optical forces in a variety of photonic
arrangements, including dielectric scatterers and multielement array
configurations.
