The act of changing the momentum of the material requires a force, specifically, a radiation pressure acting over the illuminated area A of the material. In an increment of time, the change in the pseudomomentum of the reflected field is 8G when the field is normally incident on a homogeneous medium from the vacuum. The change the momentum of the material is twice the pseudomomentum of the reflected field. Then the adiation pressure is (35) during the period of illumination. Integrating the radiation pressure (35)over the illuminated surface area yields the surface force Sec. 4. we demonstrated that momentum is transferred from the field to the material at the point of reflection. In the absence of absorption or free charges, the force that imparts momentum to the material is a surface force The radiation pressure has been attributed previously to a volume Lorentz force [22, 24, 2 26 In the continuum limit, the Lorentz force law becomes mech pE+-J×B)dv Because the volume Lorentz force is nil in the absence of charges and currents, one retains the charge density p and the charge current J in the derivation and, at the end, takes the limit in which these quantities vanish. Then, using the Maxwell equations to eliminate p and J, one d+dt E(VD)-Dx(V×E)-B×(V×B) (39) D×Bdv 4 is the usual Minkowski momentum. Using the usual constitutive relation D=E+4TP, we may write Gm as the sum of the abraham momentum 11 E×Bdh of the electromagnetic field and a mechanical momentum #77863·S1500USD Received 18 December 2006, accepted 7 January 2007 (C)2007OSA 22 January 2007/ Vol 15, No. 2/OPTICS EXPRESS 724The act of changing the momentum of the material requires a force, specifically, a radiation pressure acting over the illuminated area A of the material. In an increment of time, the change in the pseudomomentum of the reflected field is δ|G| = Z A r ρ0 4π n−1 n+1 Eicδtda (34) when the field is normally incident on a homogeneous medium from the vacuum. The change in the momentum of the material is twice the pseudomomentum of the reflected field. Then the radiation pressure is P = 2c r ρ0 4π n−1 n+1 Ei (35) during the period of illumination. Integrating the radiation pressure (35) over the illuminated surface area yields the surface force F = Z A 2c r ρ0 2π n−1 n+1 Eidaez . (36) In Sec. 4, we demonstrated that momentum is transferred from the field to the material at the point of reflection. In the absence of absorption or free charges, the force that imparts momentum to the material is a surface force. The radiation pressure has been attributed previously to a volume Lorentz force [22, 24, 25, 26]. In the continuum limit, the Lorentz force law F = ∑ i qi  E+ vi c ×B  (37) becomes dPmech dt = Z V  ρE+ 1 c J×B  dv. (38) Because the volume Lorentz force is nil in the absence of charges and currents, one retains the charge density ρ and the charge current J in the derivation and, at the end, takes the limit in which these quantities vanish. Then, using the Maxwell equations to eliminate ρ and J, one finds [18] dPmech dt + dGM dt = 1 4π Z V [E(∇·D)−D×(∇×E)−B×(∇×B)]dv (39) where GM = Z V 1 4πc D×Bdv (40) is the usual Minkowski momentum. Using the usual constitutive relation D = E+4πP, we may write GM as the sum of the Abraham momentum GA = Z V 1 4πc E×Bdv (41) of the electromagnetic field and a mechanical momentum Gmech = Z V 1 c P×Bdv (42) #77863 - $15.00 USD Received 18 December 2006; accepted 7 January 2007 (C) 2007 OSA 22 January 2007 / Vol. 15, No. 2 / OPTICS EXPRESS 724