that agai ins an unknown constant. For a generic property, the continuity law has the form of dp where p is the property density and pv is the property flux vector. It is then a simple matter to derive the conservation laws that correspond to the continuous fluxes. We define flux vectors S=mEle T=aee such that S=S andT=T. Denoting the respective property densities as u and g, we have S/V=-ymEL (11) Integrating the property densities over the appropriate volume, we obtain the conservation laws 1听E如= nE dv+/n2 Eidv n Erd+/neRdy We identify Eq(12)as the conservation law for electromagnetic energy for a monochromatic lane wave. Equation(13)is the conservation law for the property n (14) We only need to show that the conserved quantity G, taken as a vector G= Gez, has prop- erties of linear momentum. The second Fresnel continuity equation, Eq (4), is algebraically equivalent t Likewise, the conservation law (13)can be written as ne二几ne一n小e+2nE Then the conserved quantity has the characteristics of linear momentum in which the momen tum of the reflection is in the negative direction and twice the momentum of the reflection is imputed to the material in the forward direction The constants of proportionality for the conserved quantities cannot be determined by the current procedure due to the nature of the Fresnel relations as linear boundary conditions. How ever,we can identify y=c/(4) based on the known form for the electromagnetic energy for a monochromatic plane wave. By comparison with the prior work [17], the value of a is given in terms of a unit mass density po as a=vc2po/(47). Then the momentum density #77863·S1500USD Received 18 December 2006, accepted 7 January 2007 (C)2007OSA 22 January 2007/ Vol 15, No. 2/OPTICS EXPRESS 717that again contains an unknown constant. For a generic property, the continuity law has the form of ∇· ρv = − ∂ ρ ∂t (7) where ρ is the property density and ρv is the property flux vector. It is then a simple matter to derive the conservation laws that correspond to the continuous fluxes. We define flux vectors S = γn|E| 2 ez (8) T = α|E|ez (9) such that S = |S| and T = |T|. Denoting the respective property densities as u and g, we have u = S/v = n c γn|E| 2 (10) g = T/v = n c α|E|. (11) Integrating the property densities over the appropriate volume, we obtain the conservation laws Z V1 n 2 1E 2 i dv = Z V1 n 2 1E 2 r dv+ Z V2 n 2 2E 2 t dv (12) Z V1 n1Eidv = Z V1 n1Erdv+ Z V2 n2Etdv. (13) We identify Eq. (12) as the conservation law for electromagnetic energy for a monochromatic plane wave. Equation (13) is the conservation law for the property G = α c Z V n|E|. (14) We only need to show that the conserved quantity G, taken as a vector G = Gez , has prop￾erties of linear momentum. The second Fresnel continuity equation, Eq. (4), is algebraically equivalent to Ei = Et −Er +2Er . (15) Likewise, the conservation law (13) can be written as Z V1 n1Eidvez = Z V2 n2Etdvez − Z V1 n1Erdvez +2 Z V1 n1Erdvez . (16) Then the conserved quantity has the characteristics of linear momentum in which the momen￾tum of the reflection is in the negative direction and twice the momentum of the reflection is imputed to the material in the forward direction. The constants of proportionality for the conserved quantities cannot be determined by the current procedure due to the nature of the Fresnel relations as linear boundary conditions. How￾ever, we can identify γ = c/(4π) based on the known form for the electromagnetic energy for a monochromatic plane wave. By comparison with the prior work [17], the value of α is given in terms of a unit mass density ρ0 as α = p c 2ρ0/(4π). Then the momentum density g = r ρ0 4π n|E|ez (17) #77863 - $15.00 USD Received 18 December 2006; accepted 7 January 2007 (C) 2007 OSA 22 January 2007 / Vol. 15, No. 2 / OPTICS EXPRESS 717