# Comment on "Inclusion of the backaction term in the total optical force exerted upon Rayleigh particles in nonresonant structures"

## TL;DR

This paper critically examines a modified dipole approximation (MDA) for optical forces on Rayleigh particles, clarifies misconceptions in its interpretation, and discusses its limitations compared to the conventional dipole approximation (CDA).

## Contribution

It corrects misinterpretations of the MDA's force components and analyzes its accuracy and computational complexity relative to the CDA.

## Key findings

- The generalized gradient force is not a true gradient force.
- The generalized radiation pressure is not a true radiation pressure.
- The MDA is inaccurate when the CDA is inaccurate.

## Abstract

The conventional dipole approximation (CDA) assumes that the EM fields a small particle generates in the presence of its surrounding material bodies are equal to the EM fields a point-like dipole generates in the absence of the material bodies. The authors of [Phys. Rev. A 98, 013806 (2018)] investigate a modified dipole approximation (MDA), which assumes that the EM fields the particle generates are equal to the EM fields a point-like dipole generates in the presence of the material bodies. The authors interpret the approximate EM force under the MDA as the sum of four terms named 'generalized gradient force', 'generalized radiation pressure', 'generalized spin curl force', and 'new force term'. I show that such an interpretation is wrong and misleading: the generalized gradient force is not a gradient force; the generalized radiation pressure is not a radiation pressure; and the generalized spin curl force is not a spin curl force. In the case where the particle interacts with only one resonant EM mode of small enough linewidth, which is usually called 'self-induced back-action trapping' in the literature, I rectify some of the statements in their paper, and clear up some common misconceptions in the literature. In the case where the particle does not interact with any EM modes of small enough linewidth, I show that the numerical examples in their paper are inconclusive, and more importantly, the MDA is in principle inaccurate when the CDA is inaccurate. It should be noted that finding the approximate EM force under the MDA is computationally as hard as finding the exact EM force.

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Source: https://tomesphere.com/paper/1905.11168