Advanced Light Source - Users Handbook

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1 Inverse problems: retrieval and constitutive parameters Standard media The previous section was concerned with the determination of the electromagnetic fields scattered by a slab of metamaterial structure in order to obtain the reflection and transmission coefficients. This section is devoted to the other aspect of the problem: how to determine the constitutive parameters of an effective medium once the reflection and transmission coefficients are known. In a numerical or experimental setup, the configuration often looks like the one depicted in Fig.

14b) For numerical purposes, the sum in Eq. 14a) is truncated at an upper limit Ns which needs to be determined from convergence considerations. These considerations reveal that Eq. 14a) is slowly convergent, making it somewhat inefficient to calculate the Green’s function (Tsang et al. 2000b). An alternative approach is to convert Eq. 14a) into the spectral domain. 15b) with Im{kz l1 l2 } > 0 and Ω = ax ay is the surface of a periodic unit. The numerical evaluation of this expression shows already a much faster convergence rate than Eq.

5) −∞ where φ(r; t, t ) is called the local response function. We assume here that the polarization that sets in a medium depends on the local fields – an assumption that can be violated at small lengthscales due to correlations in the polarization over a given volume of the material. , all physical quantities depend only on the elapsed time intervals and the above integral becomes a convolution. 6a) dωD(r, ω) e−iωt . 6b) −∞ Introducing these definitions into Eq. 7) where ε(r, ω) is the frequency-dependent dielectric function given by ε(r, ω) = 1 ε0 ∞ dτ φ(r; τ )eiωτ .

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