By John M. Jarem

This article introduces and examines numerous spectral computational concepts - together with k-space thought, Floquet conception and beam propagation - which are used to investigate electromagnetic and optical problems.

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In this case the electric and magnetic ®eld equations at y~ ˆ 0 are the same as in the ®rst example. Thus 2
1 E ˆ a11 C12 ‡ a12 C22 1 0 …2:2:35† where a11 and a12 have been de®ned previously. At y~ ˆ ÀL~ the tangential component of the electric ®eld must vanish due to the presence of the metal. This leads to the equation 0 ˆ C12 exp…À
2 L† ‡ C22 exp…
2 L† …2:2:36† From these equations C12 and C22 can be determined as well as all other coef®cients in the system. Figure 5 shows the Re…Ex †, Im…Ex †, and jEx j plotted versus the distance y~ ˆ Ày~ from the Region 1±2 interface, using the material parameter Copyright © 2000 Marcel Dekker, Inc.

This is interesting as one would usually associate only positive values with typical power dissipation terms. Figure 13 shows plots of normalized energy±power terms as result from Eqs. 21±27 using the example of this section. In this ®gure as in the previous one, the Poynting box has been chosen to extend a half wavelength into Region 1 (see Fig. 13 inset) and to extend a variable distance y~ out Copyright © 2000 Marcel Dekker, Inc. Figure 13 Plots of normalized energy±power terms as results from Eqs.

11, the material slab represents a mismatched medium to the incident wave and thus the incident and re¯ected waves interfere in Region 1 forming a standing wave pattern. In Region 2, because the layer is lossy, one also observes that all three EM ®eld magnitudes Copyright © 2000 Marcel Dekker, Inc. Figure 11 Plots of the magnitudes of the Ex , Ey , and Uz ˆ 0 Hz electromagnetic ®elds in Regions 1±3 as a function of y ˆ Ày, which is the location of the ®eld relative to the incidence side of the Region 1±2 interface (see Fig.

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