Optical forces through the effective refractive index

TL;DR

This paper compares energy-based optical force calculation methods, demonstrating their agreement with Maxwell Stress Tensor in lossless systems and extending the Response Theory of Optical Forces to complex devices, while cautioning against misinterpretation of the Dispersion Relation method.

Contribution

It explicitly shows the agreement of RTOF and DR methods with MST in linear lossless systems and extends RTOF to multi-source, broadband, and multimode devices.

Findings

RTOF and MST methods agree in lossless systems

RTOF can analyze complex multi-source devices

DR method may overestimate forces when misinterpreted

Abstract

The energy-based methods as the Dispersion Relation (DR) and Response Theory of Optical Forces (RTOF) have been largely applied to obtain the optical forces in the nano-optomechanical devices, in contrast to the Maxwell Stress Tensor (MST). In this work, we apply first principles to show explicitly why these methods must agree with the MST formalism in linear lossless systems. We apply the RTOF multi-port, to show that the optical force expression on these devices can be extended to analyze multiple light sources, broadband sources, and multimode devices, with multiple degrees of freedom. We also show that the DR method, when expressed as a function of the derivative of the effective index performed at a fixed wave vector, may be misinterpreted and lead to overestimated results.