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Interest of improved three-point formulas for finite-difference modeling of optical devices

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Abstract

The accuracy of finite-difference computations is limited by the errors inherent in the classical three-point formula for x2 (of order h2) and in the discretization of discontinuities in the refractive index (of order from h0 to h2). Various improvements are reviewed and analyzed, both for normal-mode derivations and for the beam propagation method (BPM). For the BPM it seems that sophisticated discretizations for discontinuities have a limited interest, whereas using a h4-accurate three-point formula for x2 often allows the use of fewer grid points and hence faster computations; also it makes the operation of transparent boundaries with Bérenger layers considerably more efficient. Finally, the permittivity should always be averaged mesh by mesh.

© 1997 Optical Society of America

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