Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field

The force and torque exerted on a body of arbitrary shape and constitution by a stationary radiation field are in principle given by integrals of Minkowskiʹs stress tensor over a surface surrounding the body. Similarly the absorbed energy is given by an integral of the Poynting vector. These integrals are notoriously difficult to evaluate, and so far only spherical bodies have been considered. It is shown here that the integrals may be cast into a simpler form by use of Debye potentials. General expressions for the integrals are derived as sums of bilinear expressions in the coefficients of the expansion of the incident and scattered waves in terms of vector spherical waves. The expressions are simplified for small particles, such as atoms, for which the electric dipole approximation may be used. It is shown that the calculation is also relevant for bodies with nonlinear electromagnetic response.