Analysis of diffraction gratings by using an edge element method

Optical Society of America
Publication Type:
Journal Article
Journal of the Optical Society of America A: Optics Image Science and Vision, 2005, 22 (2), pp. 278 - 288
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Typically the grating problem is formulated for TE and TM polirizations by using, respectively, the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence, and this leads to a one-field-component problem. For some grating profiles such as metallic gratings with a traingular profile, the prediction of TM polarisation by using a standard finite-element method experiences a slower convergence rate, and this reduces the accuracy of the computed results and also introduces a numerical polarisation effect. This discrepency cannot be seen as a simple numerical issue, since it has been observed for different types of numerical methods based o the classical formulation. Hence an alternative formulation is proposed, where the grating problem is modeled by taking the electric field as unknown for TM polarisation. The application of this idea to both TE and TM polarisation leads to a two-field component problem. The purpose of the paper is to propose an edge finite-element method to solve this wave problem. A comparison of the results of the proposed formulation and the classical formulation shows improvement and robustness in the new approach.
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