University of Twente Student Theses


Optimization of a 3-beam splitter by means of the Rigorous Coupled Wave Analysis

Averkamp, Astrid (2011) Optimization of a 3-beam splitter by means of the Rigorous Coupled Wave Analysis.

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Abstract:This master thesis introduces and explains an algorithm called the Rigorous Coupled Wave Analysis. It was developed in the early 80ies to simulate electromagnetic waves meeting a periodic grating structure. Foundation are the Maxwell equations: a set of partial differential equations describing the behaviour of electrical and magnetical fields in space and time. These are to be solved in the frequency domain. The periodic grating is approximated by means of a Fourier expansion. We use three different ans¨atze: One for the incoming and reflected part of the field, one for the grating area and the last one for the transmitted waves. These are inserted in the Maxwell equations, resulting in the coupled wave equations for the grating area. This system of second order differential equations can be solved by means of its eigenvalues. At the end the reflected and transmitted fields can be computed by the continuous interface conditions. The details of the mathematical formulation of the algorithm are explained, followed by the stable implementation in Matlab. The program is now able to calculate the fields of binary multi-layer systems with incoming waves of TE- and TM-polarization. This algorithm is then used to design a periodic grating in such a way, that an incoming laser beam is split into three fractions of equal power. The design parameters are optimized until the relative output power approaches 1/3 for each diffraction order. An almost perfect configuration was found, but it appeared to be difficult to produce, due to fine, highly relevant details. Therefore also gratings with slightly worse performances but more realistic parameters are presented.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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