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28 February 2012 A meshless based solution to vectorial mode fields in optical microstructured waveguides
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A meshless solution to vectorial mode fields has been applied to various micro-structured optical waveguides. The Finite Cloud Method (FCM), has been used to solve coupled field equations for both transverse components of the magnetic field as well as the effective index of refraction for the waveguides. Two methods using either a step-index or a graded-index have been implemented and compared. An approximation to the solution is found using a distribution of points and a cloud about each point, with no mesh and minimal geometric linking knowledge between the points. This gives the ability to use a highly irregular point distribution which can be easily modified or tailored to micro-structured fibers in order to accurately represent the vectorial modal solution. In addition, the use of Bayliss-Gunzburger-Turkel-like transparent boundary conditions (TBC) and an iterative process is compared with a perfectly matched layer (PML), both of which allow for the solution of leaky modes for the structures. Results for ridge waveguides and solid core fibers having low index contrast are in high agreement with the solutions from commercial solvers. Further results with high contrast air hole structures are compared with other solution methods giving promising results and highlight this methods versatility, accuracy and efficiency for a wide range of problems.
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D. R. Burke and T. J. Smy "A meshless based solution to vectorial mode fields in optical microstructured waveguides", Proc. SPIE 8255, Physics and Simulation of Optoelectronic Devices XX, 82550L (28 February 2012);

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