By Leibniz Gottfried Wilhelm
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Extra resources for A Unitary Principle of Optics, Catoptrics, and Dioptrics
G. Ref. 10. e. P(T, t) = ap~:, t) + V x M(f, t) , (59) where aP / at and V x M are the so-called polarization and magnetization current densities. At once , one should notice that the division in Eq. (59) does not define P and M uniquely. Thus, if N(f, t) is an arbit rary vector, differentiable in time and space, it is readily realized that a replacement of P and M in Eq. (59) by the new vectors P' and M' given by P'(f, t) = P(f, t) - V x N(f, t) , (60) = M(f, t) + aN~:, t) (61) and M'(T, t) does not alter the induced current density.
95) Next, by combination of Eqs . (17)) one finds V X HT(r, t) - Jf(r, t) - £0 8EHr,t) 8 t 1 = -V X Po BT(r, t) - h(T, t) - £0 = iT + if (see 8ET(r,t) 8 . (96) t On t he basis of the divergence-free part ofthe Maxwell-Lorentz equation in (2) it is realized that the right hand side of Eq. (96) vanishes . This implies that V X - (_) HT r, t 8EHr,t) = J-e(-) 8t . T r, t + £0 (97) If this equation is compared with the divergence-free part of the Maxwell-Lorentz equation in (9) for the external fields, it is realized that (98) Since , as we already know, the irrotational part of the H-field does not enter the theory one ca n of course chose HL freely.
E(Z/)dz', (192) in the random-phase-approximation (RPA) approach, under the assumption that the entire system exhibits translational invariance parallel to the plane of the quantum well and is excited by a plane, monochromatic wave having a wave vector ~I along the surface. The kernel in Eq. (192) is given by J = -ip,ow G~«z, Zl) . (j(Z",zl)dz ll. K(2:, Z/) (193) In Eq. (192), EB(z) is the background field consisting of the incident field plus the field reflected from the 'substrate in the absence of the quantum well.