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This paper presents a new discretisation of Cartesian meshes based on spatial anti-aliased filtering of geometry boundaries in TLM. The method is compared against some other techniques presently used to alleviate stair casing error when representing circular boundaries. The antialiasing method provides the best convergence to actual resonances for E-waves amongst the techniques studied. For H-waves,...
In this paper, we discuss challenges in modelling circular geometries in Cartesian time domain numerical methods. The main focus of this paper is to reduce the apparent shift in the deduced resonance frequencies. We show that this shift is completely dependent on the discretisation technique and hence propose a resolution to minimise it. In addition, we discuss the limitations of extracting resonances...
The thickness of the layers comprising optical structures is usually very thin. When modelling such thin features using a traditional numerical method, for instance the transmission-line modelling (TLM) method, a very small space step is often used to properly discretize the material geometry. This consequently results in large memory storage and longer run time. In this paper a new technique embedding...
Non-linear materials are central to many useful integrated photonics applications. Increasingly complex geometries have to be dealt with in full-wave numerical electromagnetic simulators. In this paper we discuss and present techniques for embedding non-linear material response into one such numerical technique, the Transmission Line Modelling (TLM) Method. We discuss the progression from 1D through...
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