Does light exert Abraham's force in a transparent medium?

Abraham's force seems to have been observed in very low frequency experiments, but the existence of an Abraham's force exerted by light is still to be proved. Twenty years ago Brevik proposed an experiment for checking what forces light exert in the interior of a transparent medium. It is argued that his proposal is feasible today with a detection method now at hand, thanks to the great improvements achieved in manufacturing optical fibres with the required physical properties.