The ponderomotive force: Derivation of the stress-tensor for high-frequency radiation in isotropic dispersive matter by generalization of the Helmholtz method

A formal proof is presented of the generalized Helmholtz stress tensor for high frequency transverse electromagnetic radiation in an isotropic translucent medium with an arbitrary frequency-dispersive refractive index n (ε; rho; T). The refractive index is taken to be dependent on the local density rho and temperature T which themselves may be slowly-varying functions of position and time. Using approximations valid in the geometric-optics limit, the basic Helmholtz method, as hitherto used to determine the stress-tensor in magnetostatics and electrostatics (and also for very low frequency electromagnetic waves), is generalized to high frequencies. This method identifies the stress-tensor from the virtual work term produced by a local gauge transformation representing an arbitrary infinitesimal deformation of fields and material. The result supports earlier conjectures concerning the general validity of the Hemlholtz expression (when expressed in terms of the radiation free energy). The result is used to obtain an expression for the ponderomotive force due to unpolarised radiation with an arbitrary spectral distribution represented by amplitudes (proportional to the rms fields) that are slowly-varying functions of both position and time. Particular care is taken over the momentum-of-light problem and its ramifications regarding the manner of any decomposition into fields/radiation and matter. Consideration is given to the consequences of non-uniform motion of the material medium