The C-method as an Initial Value Problem: Application to Multilayer Gratings

Cihui Pan 1, 2, 3 Richard Dusséaux 3 Nahid Emad 2, 1
Abstract : We study our approach of the C-method as an initial value problem for the efficient calculation of the N-dimensional scattering matrix of a grating. We apply this method to multilayer gratings with an arbitrary number of interfaces. The interfaces can have different functional form and amplitude and can be parallel or not. For each interface separating two homogeneous media, we consider two horizontal planes above and below the interface, and define a coordinate system such that the interface and both horizontal planes correspond to coordinate surfaces. Inside the area delimited by the two horizontal planes, the Maxwell's equations lead to an initial value problem which can be solved with initial conditions satisfying the boundary conditions. Outside this area, the fields are represented by Rayleigh expansion. The scattering matrix between two consecutive media is obtained by using continuity relations between different components of fields on the horizontal planes. We consider a n + 1 layer diffraction grating, thus there are n interfaces separating the layers. From the uppermost to downmost, these layers are composed of medium 1 to medium n + 1. Each medium has a constant optical index. Thus we can calculate the scattering matrix Si,i+1 which associate the incoming and outcoming waves from medium i and i + 1. Then we collect all the scattering matrix of adjacent medium, Si,i+1, i = 1; : : : ; n and obtain the global matrix S1,n+1 by combination of elementary matrices Si,i+1, i = 1; : : : ; n. The proposed method gives the e±ciencies with a good accuracy. Experiments are performed on a three layer grating with interfaces described by Trigonometric functions. We also study the anomalies of coated dielectric gratings.
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Conference papers
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Submitted on : Sunday, August 23, 2015 - 2:24:14 PM
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  • HAL Id : insu-01186016, version 1

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Cihui Pan, Richard Dusséaux, Nahid Emad. The C-method as an Initial Value Problem: Application to Multilayer Gratings. Proceedings of PIERS 2015, Progress In Electromagnetics Research Symposium, Jul 2015, Prague, Czech Republic. pp.1297-1301. ⟨insu-01186016⟩

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