  A transparent material exhibits ultra-fast optical nonlinearity and is
subject to optical pressure if irradiated by a laser beam. However, the effect
of nonlinearity on optical pressure is often overlooked, even if a nonlinear
optical pressure may be potentially employed in many applications, as optical
manipulation, biophysics, cavity optomechanics, quantum optics, optical
tractors, and is relevant in fundamental problems as the Abraham-Minkoswky
dilemma, or the Casimir effect. Here we show that an ultra-fast nonlinear
polarization gives indeed a contribution to the optical pressure that also is
negative in certain spectral ranges; the theoretical analysis is confirmed by
first-principles simulations. An order of magnitude estimate shows that the
effect can be observable by measuring the deflection of a membrane made by
graphene.
