Electromagnetic (EM) waves exert forces on objects. The nonconservative part of these forces is determined by the gradient of phase (wavevector) of EM field. Through special structures, manipulation of the direction of these forces becomes possible. Here we investigate numerically the forces created by left-handed negatively refracting photonic crystals - these can create EM waves with the Poynting vector and wave vector pointing in opposite directions. We show that negative gradient of phase still creates a positively directed electromagnetic force.
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