magnetic momentum inside the dielectric, while an additional momentum is transferred to the medium in the form of mechanical force. Equation(la)may be rewritten as follows p=Rea(E×H)a2+%Real(P×B*) (1b) In the above equation, the first term is the Abraham momentum density of the field, while the second term is the mechanical momentum density imparted to the medium. (If the coefficient of the second term were 2 instead of / 4, the total momentum density p would have been equal to the Minkowski momentum. )The electromagnetic and mechanical momenta of the light inside the dielectric are not decoupled from each other. This fact is better appreciated if one observes, for instance, that the same beam of light, upon emerging into the free-space at the exit facet of a dielectric slab, recovers its total initial momentum (i.e, the momentum it possessed before entering the slab) by re-converting the mechanical momentum(manifested in the motion of the medium)to electromagnetic momentum [1]. If, for simplicity' s sake, we assume that the entrance and exit facets of the dielectric slab are anti-reflection coated then upon transmission, the emerging beams momentum will be identical to the momentum it possessed before entering the slab; in other words, the(partial)conversion of the beam's momentum into mechanical form that takes place while the beam passes through the slab, is fully reversed when the beam leaves the slab and returns to the free space. Another example of the"connectedness"of the electromagnetic and mechanical momenta was provided in [6] where the radiation pressure on a dielectric wedge and its surrounding liquid was found to arise from the total momentum of the beam as opposed to, say, from one or the other of its constituents The present paper extends the results of our previous work to the case of light beams that propagate in dispersive dielectrics. We show that the earlier results obtained for non- dispersive media remain valid if the abraham momentum is assumed to travel with the group velocity Vg=c/n+nf) inside the dielectric. (f is the optical frequency, n=dn/df is the derivative of the refractive index n )Our new expression for the mechanical momentum density reverts to the old expression, 74 Real(Px B ) in the limit of n0, i.e., when the medium becomes dispersionless. Finally, to resolve the discrepancy between the theory and certain experiments in which the light appears to possess the Minkowski momentum, we propose a model system for analyzing the photon drag effect observed in certain bulk semiconductors 2. Superposition of two plane waves in free space Figure I shows a beam of light consisting of two equal-amplitude plane-waves of differing frequencies f i and i, incident on a semi-infinite dielectric medium of refractive index n(f) The beam is linearly polarized, having its E-field along the x-axis and H-field along the y axis. The field amplitudes in free space are given by Ex=,t=Eo sin(2T fi[(=c)-t1-Eo sin(2Tf2((/)-JF H(=,D)=(EZ)sin{2f[(/c)-l}-(E/Z)sin{2f[(=lc)-l]}(2b) Here Zo=NudE is the free-space impedance, and c= 1/lE is the speed of light in vacuum The traveling wave is readily seen to be a sinusoid of frequency f=7(fi+/2), modulated with another(envelope)sinusoid of frequency Af=fi-fi, exhibiting a beat period T=1 and traveling(in free-space)with the speed c The Poynting vector S=ExH has a component only along the z-axis, S(=,n) Ere, OH, n). For a fixed value of = if S(=, t) is averaged over the time interval T, and if terms of order Af and higher are neglected, the time-averaged Poynting vector will bece independent of the coordinate : and will be given by 6629-$1500US Received 18 February 2005; revised 14 March 2005; accepted 15 March 2005 (C)2005OSA 21 March 2005/Vol 13. No 6/ OPTICS EXPRESS 2246magnetic momentum inside the dielectric, while an additional momentum is transferred to the medium in the form of mechanical force. Equation (1a) may be rewritten as follows: p = ½Real (E × H*)/c2 + ¼ Real (P × B*). (1b) In the above equation, the first term is the Abraham momentum density of the field, while the second term is the mechanical momentum density imparted to the medium. (If the coefficient of the second term were ½ instead of ¼, the total momentum density p would have been equal to the Minkowski momentum.) The electromagnetic and mechanical momenta of the light inside the dielectric are not decoupled from each other. This fact is better appreciated if one observes, for instance, that the same beam of light, upon emerging into the free-space at the exit facet of a dielectric slab, recovers its total initial momentum (i.e., the momentum it possessed before entering the slab) by re-converting the mechanical momentum (manifested in the motion of the medium) to electromagnetic momentum [1]. If, for simplicity’s sake, we assume that the entrance and exit facets of the dielectric slab are anti-reflection coated, then, upon transmission, the emerging beam’s momentum will be identical to the momentum it possessed before entering the slab; in other words, the (partial) conversion of the beam’s momentum into mechanical form that takes place while the beam passes through the slab, is fully reversed when the beam leaves the slab and returns to the free space. Another example of the “connectedness” of the electromagnetic and mechanical momenta was provided in [6], where the radiation pressure on a dielectric wedge and its surrounding liquid was found to arise from the total momentum of the beam as opposed to, say, from one or the other of its constituents. The present paper extends the results of our previous work to the case of light beams that propagate in dispersive dielectrics. We show that the earlier results obtained for non￾dispersive media remain valid if the Abraham momentum is assumed to travel with the group velocity Vg = c/(n+ n′ f ) inside the dielectric. ( f is the optical frequency; n′ = dn/df is the derivative of the refractive index n.) Our new expression for the mechanical momentum density reverts to the old expression, ¼Real(P×B*), in the limit of n′→0, i.e., when the medium becomes dispersionless. Finally, to resolve the discrepancy between the theory and certain experiments in which the light appears to possess the Minkowski momentum, we propose a model system for analyzing the photon drag effect observed in certain bulk semiconductors. 2. Superposition of two plane waves in free space Figure 1 shows a beam of light consisting of two equal-amplitude plane-waves of differing frequencies f1 and f2, incident on a semi-infinite dielectric medium of refractive index n( f ). The beam is linearly polarized, having its E-field along the x-axis and H-field along the y￾axis. The field amplitudes in free space are given by Ex(z, t) = Eo sin{2π f1 [(z /c) – t]} – Eo sin{2π f2 [(z /c) – t]} (2a) Hy(z, t) = (Eo/Zo)sin{2π f1 [(z /c) – t]} – (Eo/Zo)sin{2π f2 [(z /c) – t]} (2b) Here Zo = √µo/εo is the free-space impedance, and c = 1/√µoεo is the speed of light in vacuum. The traveling wave is readily seen to be a sinusoid of frequency f = ½( f1 + f2), modulated with another (envelope) sinusoid of frequency ∆f = f2 – f1, exhibiting a beat period T= 1/∆f, and traveling (in free-space) with the speed c. The Poynting vector S = E×H has a component only along the z-axis, Sz(z, t) = Ex(z, t)Hy(z, t). For a fixed value of z, if Sz(z, t) is averaged over the time interval T, and if terms of order ∆f and higher are neglected, the time-averaged Poynting vector will become independent of the coordinate z, and will be given by (C) 2005 OSA 21 March 2005 / Vol. 13, No. 6 / OPTICS EXPRESS 2246 #6629 - $15.00 US Received 18 February 2005; revised 14 March 2005; accepted 15 March 2005