Simple High-order Galerkin Finite Element Scheme for the Investigation of Both Guided and Leaky Modes in Anisotropic Planar Waveguides

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Uranus, H.P. and Hoekstra, H.J.W.M. and Groesen, E. van (2004) Simple High-order Galerkin Finite Element Scheme for the Investigation of Both Guided and Leaky Modes in Anisotropic Planar Waveguides. Optical and quantum electronics, 36 (1-3). pp. 239-257. ISSN 0306-8919

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Abstract: A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with a diagonal permittivity tensor. Transparent boundary conditions derived from the Sommerfield radiation conditions are used to model the fields at the computational boundaries that allow the radiation into the high index cladding/substrate and decay into the low index cladding/substrate, hence work for both guided and leaky modes. Richardson's extrapolation is employed to achieve high-order accuracy by only using simple first-order-polynomial basis functions. Schemes up to sixth-order of accuracy in the effective index are demonstrated. The resulted non-linear sparse matrix eigenvalue equation is solved using an iterative procedure. The ability of the scheme to compute leaky and guided modes of various structures with isotropic and anisotropic materials, step and graded index profiles is demonstrated; including its applications to investigate the properties of ARROW structures.
Item Type:Article
Copyright:© 2004 Springer
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/47177
Official URL:http://dx.doi.org/10.1023/B:OQEL.0000015643.52433.f0
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