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Nhng tin b trong Quang hc, Quang ph và ng dng VI ISSN 1859 - 4271

Nhng tin b trong Quang hc, Quang ph và ng dng VI ISSN 1859 - 4271

Nhng tin b trong Quang hc, Quang ph và ng dng VI ISSN 1859 - 4271

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Advances in Optics, Photonics, Spectroscopy & Applications <strong>VI</strong> <strong>ISSN</strong> <strong>1859</strong> - <strong>4271</strong>N λ= 2.053ExactLFE-92b x( =κ∆sinθ )10-1-2-3-3 -2 -1 0 1 2 3b ( =κ∆cosθ )zFig. 2: Spatial dispersion diagram for the LFE-9 formulation with a N λ= 2.05IV. CONCLUSIONThe traditional FD-FD method requires a more than 10 points per wavele<strong>ng</strong>th sampli<strong>ng</strong> of thetime-harmonic EM wave field. As a result, the FD-FD matrix equation becomes too large formost 3D problems and in many cases for some complex 2D optical waveguide devices. Wepropose a new nine-point stencil based on local Fourier-Bessel expansion for the 2-D Helmholtzequation in a homogeneous medium. This would reduce the sampli<strong>ng</strong> density to a value close toNyquist-Shannon spatial sampli<strong>ng</strong> of two points per wavele<strong>ng</strong>th.V. ACKNOWLEDGMENTSWe are grateful to the support by the Ministry of Education, Taiwan, under the Aim-for-the-Top University Plan.REFERENCES[1] Hu<strong>ng</strong>-Wen Cha<strong>ng</strong> and Sin-Yuan Mu, “Novel nine-point FD coefficients for two-dimensionalHelmholtz equation”, Cross Strait Four-Regional Radio Science and Wireless TechnologyConference, 2010, Hanan, China, Aug 2010.90

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