  The mechanical response of transparent materials to optical forces is a topic
that concerns a wide range of fields, from the manipulation of biological
material by optical tweezers to the design of nano-optomechanical systems
(NOMS). However, the fundamental aspects of such forces have always been
surrounded by controversies, and several different formulations have been
proposed. In this work, we focus on the specific case of light propagating as a
superposition of guided modes in lossless dielectric waveguides as a physical
example upon which to build a general stress tensor. We use this formalism to
calculate optical forces for straight and curved waveguide sections and all
possible excitation configurations for a given set of coupled eigenmodes, and
then compare the results for each of the known proposed optical force laws as
well as a novel one derived from this general stress tensor. We show that
proper use of the divergence theorem is crucial to account for all force terms,
many of which vanish if the procedure most commonly used is applied for
situations other than eigenmodes in straight waveguides. A better understanding
of how different stress tensors predict very different forces for certain
waveguide geometries opens a pathway for new experimental tests of each
formulation.
