A wavelet formulation of the finite-difference method: full-vector analysis of optical waveguide junctions

We have developed an efficient, large-stencil finite-difference scheme of the time-dependent Maxwell's curl equations based on the wavelet-collocation formulation in the time-domain. The proposed scheme enables, for the first time within a limited computational resource, full-vector analysis of...

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Bibliographic Details
Published in:IEEE journal of quantum electronics 2001-08, Vol.37 (8), p.1015-1029
Main Authors: Fujii, M., Hoefer, W.J.R.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Beams (radiation)
Circuit properties
Computing time
Devices
Electric, optical and optoelectronic circuits
Electrical junctions
Electronics
Exact sciences and technology
Finite difference method
Finite difference methods
Fundamental areas of phenomenology (including applications)
Integrated optics. Optical fibers and wave guides
Magnetic analysis
Magnetic fields
Mathematical analysis
Mathematical models
Maxwell equations
Optical and optoelectronic circuits
Optical computing
Optical devices
Optical planar waveguides
Optical waveguides
Optical waveguides and couplers
Optics
Physics
Planar waveguides
Time domain analysis
Wave optics
Wave propagation, transmission and absorption
Waveguides, couplers, and arrays
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Summary:We have developed an efficient, large-stencil finite-difference scheme of the time-dependent Maxwell's curl equations based on the wavelet-collocation formulation in the time-domain. The proposed scheme enables, for the first time within a limited computational resource, full-vector analysis of three-dimensional rib waveguides that are typically used in integrated planar optical devices. The formulation takes advantage of compactly-supported interpolating bases to expand and represent the electric and magnetic fields. Moreover, unlike the well-known beam propagation methods, the numerical scheme is based on the first-principle algorithm with no explicit approximation, and thus rigorous and versatile for various types of boundary conditions. We demonstrate the efficiency of the method by first analyzing a straight rib-waveguide and examining the convergence of the results. Then we investigate a Y-shaped junction structure that is electrically too large to analyze with the conventional finite-difference time-domain scheme.
ISSN:0018-9197
1558-1713
DOI:10.1109/3.937391