Simulation of Waveguide Crossings and Corners With Complex Mode-Matching Method

Wang, Rui; Han, Lin; Mu, Jianwei; Huang, Wei‐Ping

doi:10.1109/jlt.2012.2187325

Cited by 12 publications

(14 citation statements)

References 15 publications

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“…It is also highly desirable to develop a strategy for choosing computational parameters (including those for PMLs) to reach a given level of accuracy. The computational complexity of the VMEM is dominated by the step for solving the final linear system (11). We hope that a more efficient solver for Eq.…”

Section: Resultsmentioning

confidence: 99%

“…Overall, the time spent on computing the 4N DtN operators is negligible, compared with the time for solving the final linear system (11).…”

Section: Dtn Maps For 2d Helmholtz Equationsmentioning

confidence: 99%

“…In that case, it is desirable and often possible to develop special numerical or semi-analytic methods that are more efficient than the general methods. The standard mode-matching method (MMM, also called modal method), including its numerical variants [6][7][8][9][10][11][12], is useful when the structure is piecewise uniform in one spatial direction. It is based on expanding the electromagnetic field in each uniform layer in transverse eigenmodes.…”

Section: Introductionmentioning

confidence: 99%

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Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background

Shi

2015

J. Opt. Soc. Am. A

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The vertical mode expansion method (VMEM) [J. Opt. Soc. Am. A31, 293 (2014)] is a frequency-domain numerical method for solving Maxwell's equations in structures that are layered separately in a cylindrical region and its exterior. Based on expanding the electromagnetic field in one-dimensional vertical modes, the VMEM reduces the original three-dimensional problem to a two-dimensional (2D) problem on the vertical boundary of the cylindrical region. However, the VMEM has so far only been implemented for structures with circular cylindrical regions. In this paper, we develop a VMEM for structures with an elliptic cylindrical region, based on the separation of variables in the elliptic coordinates. A key step in the VMEM is to calculate the so-called Dirichlet-to-Neumann (DtN) maps for 2D Helmholtz equations inside or outside the ellipse. For numerical stability reasons, we avoid the analytic solutions of the Helmholtz equations in terms of the angular and radial Mathieu functions, and construct the DtN maps by a fully numerical method. To illustrate the new VMEM, we analyze the transmission of light through an elliptic aperture in a metallic film, and the scattering of light by elliptic gold cylinders on a substrate.

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Section: Resultsmentioning

confidence: 99%

“…Overall, the time spent on computing the 4N DtN operators is negligible, compared with the time for solving the final linear system (11).…”

Section: Dtn Maps For 2d Helmholtz Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background

Shi

2015

J. Opt. Soc. Am. A

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“…Similarly, multiplying the equations for the -field continuity at by ( ) and integrating from to yields (13) where (14)…”

Section: Mode Matching In Mixed Coordinate Systemsmentioning

confidence: 99%

“…Using staircase approximation and the generalized scattering matrix, open periodic waveguides with an arbitrary unit cell can be approximately analyzed in the Cartesian coordinate system [12]. A complex mode-matching method combined with the perfectly matched layer (PML) [13] opened a new way to obtain the reflection and transmission spectra of optical-waveguide interconnects. In addition, the fast scattering analyses of electrically large substrate integrated waveguide (SIW) devices were performed with a mode-matching technique using cylindrical mode expansion [14].…”

Section: Introductionmentioning

confidence: 99%

Efficient Mode-Matching Analysis of 2-D Scattering by Periodic Array of Circular Cylinders

Cho

Kwon

2013

IEEE Trans. Antennas Propagat.

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Based on a common-area concept and insertion of an infinitesimal perfect magnetic conductor (PMC) wire, a new mode-matching method for mixed coordinate systems is proposed for the analysis of periodic magnetodielectric, perfect electric conductor, and PMC circular cylinder arrays. Our scattering solutions were computed and they showed favorable agreements with other known results in terms of power scattering coefficients, resonant frequency of nanostructures, and the sum rule of extinction width. The low-frequency solutions of periodic arrays were also formulated and compared with the full-wave counterparts.

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Algebra of 2D periodic operators with local and perpendicular defects

Kutsenko

2016

Journal of Mathematical Analysis and Applications

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Simulation of Waveguide Crossings and Corners With Complex Mode-Matching Method

Cited by 12 publications

References 15 publications

Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background

Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background

Efficient Mode-Matching Analysis of 2-D Scattering by Periodic Array of Circular Cylinders

Algebra of 2D periodic operators with local and perpendicular defects

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