Modified finite-difference formula for the analysis of semivectorial modes in step-index optical waveguides

The modified finite-difference formula is presented for the second derivative of a semivectorial field in a step-index optical waveguide. The present formula achieves a truncation error of O(/spl Delta/x/sup 2/) provided the discontinuity coincides with a mesh point or lies midway between two mesh p...

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Bibliographic Details
Published in:IEEE photonics technology letters 1997-07, Vol.9 (7), p.961-963
Main Authors: Yamauchi, J., Sekiguchi, M., Uchiyama, O., Shibayama, J., Nakano, H.
Format: Article
Language:English
Subjects:
Equations
Finite difference methods
Finite wordlength effects
Image analysis
Optical propagation
Optical refraction
Optical waveguides
Propagation constant
Slabs
Waveguide discontinuities
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Summary:The modified finite-difference formula is presented for the second derivative of a semivectorial field in a step-index optical waveguide. The present formula achieves a truncation error of O(/spl Delta/x/sup 2/) provided the discontinuity coincides with a mesh point or lies midway between two mesh points. Furthermore, the formula allows a general position of the interface, when used with the beam-propagation method (BPM). To demonstrate the effectiveness of the formula, asymmetric step-index waveguides are analyzed using the imaginary-distance BPM.
ISSN:1041-1135
1941-0174
DOI:10.1109/68.593366