Photon energy dependence of the light pressure exerted onto a thin silicon slab

Abstract

We review the theory of ponderomotive forces of classical nonionizing electromagnetic (EM) radiation exerted on dispersive matter. Minkowski's EM energy and momentum density lack any dispersion term in contrast to Nelson's theory, where they are included naturally. By considering force experiments on a dielectric mirror immersed in weakly dispersive liquids [R. V. Jones and B. Leslie, Proc. R. Soc. London, Ser. A 360, 347 (1978)], we found that the appearance of the dispersive term should depend on the phase of the mirror reflectivity. It thus matters if the electric or the magnetic field is dominant at the interface. Accordingly, the force measurements depend on the boundary condition and do not permit to uniquely determine the EM momentum in the liquids. Force measurements as a function of the reflectivity phase would permit to experimentally verify the expressions for the EM energy density in a dispersive medium. In our experiments, we chop light beams of different photon energies to excite the motion of a very thin and long Si slab near its mechanical resonance under UHV conditions. This permits to study the force response, where the power reflectivity of the sample varies from 0.7 to smaller than 10${}^{\ensuremath{-}3}$. The determination of the velocity of the slab with a Doppler interferometer yields the effective force exerted by the light beam. The measurements also confirm our theoretical considerations that the observed forces due to EM radiation cannot be traced to the EM momentum in matter, as the observed forces primarily depend on the boundary conditions. Minkowski's stress tensor remains applicable in our case thanks to the embedding of the Si slab in vacuum. Our quantitative analysis of the experimental data reveals an extra force of thermal origin most likely associated with the difference of the native oxide thickness on the surfaces of the slab. The estimated difference in oxide layer thickness amounts to \ensuremath{\sim}4 nm.