Thales Fernando Damasceno Fernandes and Pierre-Louis de Assis
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. However, the fundamental aspects of such forces have always been surrounded by controversies, and several different formulations have been proposed. In this paper, we propose a general stress tensor formalism to put all optical forces in a consistent presentation that allows us to study how different predictions emerge, and use the specific case of light propagating as a superposition of guided modes in lossless dielectric waveguides as a physical example. 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 in a framework that permits distinguishing where there will be differences between the force laws proposed. The general formalism also allows us to 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 in vacuum. Finally, it is known that discrepancies in the predicted forces arise from the incompleteness of each stress tensor with respect to the total-energy-momentum tensor of the system. A better understanding of how different stress tensors predict very different forces for certain waveguide geometries should open a pathway to identifying how to properly assemble the full tensor, as well as for experimental tests to confirm the predictions.
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