The above equations are obtained by assuming the existence of a pair of counter-propagating plane-waves in the absorbing layer, then determining the various unknown amplitudes by matching the boundary conditions for the E-and H-fields while ignoring second-and higher order terms in d/no. (The algebra is straightforward but tedious. The absorbed optical power y within the layer is thus given by 2(1-|p2-|r)nE21Z=(2nKd)E21z X E TE E0/Z0 Fig. 2. A thin absorptive layer of thickness d and complex refractive index n+ in a transparent, homogeneous dielectric medium of refractive index n(same n of the complex index of the absorptive layer ). A monochromatic plane-wave, wavelength Mo=c/f E-field amplitude Eo, and H-field amplitude Ho=nEo coefficients are p and I, respectively. Each absorbed of energy hf equivalent of its Minkowski momentum nhf le to the absorbing layer 6. The force experienced by the absorbing layer may be derived from the Lorentz law, lowing the procedure outlined in [1], then integrated over the film thickness d to yield <F>=(2Tn'xd/oJEEO Thus <F:>=(n/c)% namely, the force experienced by the absorbing layer is (n/c) times the captured optical power. Consequently, the momentum transferred to the layer in a given time interval At must also be(n/c)times the energy absorbed by the layer during the same time interval. For a captured photon of energy hf the momentum transfer is thus equal to nhflc,i.e the Minkowski momentum of the photon in its dielectric environment. Since this is greater than the total photon momentum prior to being absorbed, the host medium(i.e, the dielectric) must experience a recoil equal to the difference between the incident photon,s initial momentum and the Minkowski value picked up by the excited charge carrier Acknowledgments The author is grateful to Ewan Wright, Armis Zakharian, Pavel Polynkin, and Walter Hoyer for many helpful discussions. This work has been supported by the AFOSR contract F49620 02-1-0380 with the Joint Technology Office, by the Office of Naval Research mURi grant No.NO0014-03-1-0793, , and he National Science Foundation STC Pro agreement DMR-0120967 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 2250The above equations are obtained by assuming the existence of a pair of counter-propagating plane-waves in the absorbing layer, then determining the various unknown amplitudes by matching the boundary conditions for the E- and H-fields while ignoring second- and higher￾order terms in d/λo. (The algebra is straightforward but tedious.) The absorbed optical power γ within the layer is thus given by γ = ½(1 – |ρ |2 − |τ |2 ) nEo 2 /Zo = (2π nκ d /λo)Eo 2 /Zo. (14) Fig. 2. A thin absorptive layer of thickness d and complex refractive index n + iκ is embedded in a transparent, homogeneous dielectric medium of refractive index n (same n as the real part of the complex index of the absorptive layer). A monochromatic plane-wave, having vacuum wavelength λo = c/f, E-field amplitude Eo, and H-field amplitude Ho = nEo/Zo, is normally incident on the absorbing layer. The layer’s (amplitude) reflection and transmission coefficients are ρ and τ, respectively. Each absorbed photon of energy hf transfers the equivalent of its Minkowski momentum nhf /c to the absorbing layer. The force experienced by the absorbing layer may be derived from the Lorentz law, following the procedure outlined in [1], then integrated over the film thickness d to yield <Fz > = (2πn2 κ d/λo)εoEo 2 . (15) Thus <Fz > = (n/c)γ, namely, the force experienced by the absorbing layer is (n/c) times the captured optical power. Consequently, the momentum transferred to the layer in a given time interval ∆t must also be (n/c) times the energy absorbed by the layer during the same time interval. For a captured photon of energy hf the momentum transfer is thus equal to nhf /c, i.e., the Minkowski momentum of the photon in its dielectric environment. Since this is greater than the total photon momentum prior to being absorbed, the host medium (i.e., the dielectric) must experience a recoil equal to the difference between the incident photon’s initial momentum and the Minkowski value picked up by the excited charge carrier. Acknowledgments The author is grateful to Ewan Wright, Armis Zakharian, Pavel Polynkin, and Walter Hoyer for many helpful discussions. This work has been supported by the AFOSR contract F49620- 02-1-0380 with the Joint Technology Office, by the Office of Naval Research MURI grant No.N00014-03-1-0793, and by the National Science Foundation STC Program under agreement DMR-0120967. d n ρEo n +iκ Eo τEo Z X Ho = nEo /Zo · · × (C) 2005 OSA 21 March 2005 / Vol. 13, No. 6 / OPTICS EXPRESS 2250 #6629 - $15.00 US Received 18 February 2005; revised 14 March 2005; accepted 15 March 2005