Optical force laws for guided light in linear media

TL;DR

This paper develops a comprehensive stress tensor formalism to accurately calculate optical forces in dielectric waveguides, clarifying controversies and enabling experimental validation of different force laws.

Contribution

It introduces a general stress tensor approach for guided light, compares existing force laws, and highlights the importance of divergence theorem application in force calculations.

Findings

Proper divergence theorem application is crucial for accurate force calculation.

Different stress tensors predict significantly different forces in complex geometries.

The novel force law derived offers a more complete description of optical forces in waveguides.

Abstract

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.