2007
DOI: 10.1109/jlt.2007.901438
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Hybrid Analytical/Numerical Coupled-Mode Modeling of Guided-Wave Devices

Abstract: A general version of coupled-mode-theory for frequency domain scattering problems in integrated optics is proposed. As a prerequisite a physically reasonable field template is required, that typically combines modes of the optical channels in the structure with coefficient functions of in principle arbitrary coordinates. Upon 1-D discretizations of these amplitude functions into finite elements, a Galerkin procedure reduces the problem to a system of linear equations in the element coefficients, where given in… Show more

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Cited by 31 publications
(49 citation statements)
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“…There is therefore an increasing demand for a modeling tool accurate even in these extreme conditions. A wide variety of methods is available for modeling the interaction of electromagnetic radiation with matter: couple-mode theory [8], finite-difference time-domain [9], plane-wave expansion [10], finite elements method [11] (FEM). The FEM is proven very accurate, flexible to handle realistic structures [12], and produces sparse matrices efficiently solved with specific algorithms.…”
Section: Introductionmentioning
confidence: 99%
“…There is therefore an increasing demand for a modeling tool accurate even in these extreme conditions. A wide variety of methods is available for modeling the interaction of electromagnetic radiation with matter: couple-mode theory [8], finite-difference time-domain [9], plane-wave expansion [10], finite elements method [11] (FEM). The FEM is proven very accurate, flexible to handle realistic structures [12], and produces sparse matrices efficiently solved with specific algorithms.…”
Section: Introductionmentioning
confidence: 99%
“…Then one proceeds along the hybrid CMT approach (HCMT) of Ref. Hammer (2007): By variational means (Vassallo 1991;Sopaheluwakan 2006;van Groesen and Molenaar 2007) one extracts a linear system of equations for the coefficients of the resonator fields, and for the amplitude functions of the bus modes, discretized in terms of finite elements, as unknowns. Section 5 compares the model with rigorous numerical calculations.…”
Section: Figmentioning
confidence: 99%
“…Hammer (2007), the unknown functions u and d are discretized by 1-D linear finite elements. Discrete coefficients u l , d l replace the functions, such that the template (2) assumes the abstract form…”
Section: Solution Proceduresmentioning
confidence: 99%
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“…Provided that suitable QNM basis fields can be made available by analytical or numerical means, generalizations could be based on the functional representations of the frequency domain Maxwell equations for higher dimensions [84], [85]. …”
Section: Discussionmentioning
confidence: 99%