Comment on fiTrapping force, force constant, and potential depths for dielectric spheres in the presence

Comment on “Trapping force, force constant, andpotential depths for dielectric spheres in thepresence of spherical aberrations”Patrick C. ChaumetI point out a confusion that is rather common in optical forces, i.e., that the time average of the Lorentzforce on a dipole for a harmonic time-varying field is sometimes assumed to be a gradient force that isdue to omission of the radiative reaction term in the polarizability of the dipole. © 2004 Optical Societyof AmericaOCIS codes: 290.0290, 180.0180, 260.0260.1. Introduction made by those authors was to interpret mr, tt as1 the difference between the time-averaged modulus ofIn a recent paper Rohrbach and Stelzer derived thethe Poynting vector scattered by the particle and theoptical force acting on a lossless dielectric particleincident Poynting vector; they wroteilluminated by a harmonic time-varying field. Theauthors started by calculating the electromagneticfr fr, tdensity force i.e., the force per unit volume fr, tacting on a small polarizable particle with dipole mo- mr, t mr, t after beforement pr, t. The density force was written as for Ir , (3)2c tmore details of their method, see Ref. 2where the subscripts “before” and “after” refer topr, tfr, t pr, t Er, t Br, t. (1) times before and after scattering, respectively. Notetthat the first term in Eq. 3 is the gradient force;after some tedious calculations Rohrbach and StelzerThis is the ...