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The vertical mode expansion method (VMEM) is a special numerical method for scattering problems involving cylindrical structures in a layered background. The method is implemented for structures where the cross sections have sharp corners, and used to analyze bowtie metallic nanoparticle structures with sharp corners.
Sensitivity analysis is important for evaluating the performance of practical devices which are affected by fabrication errors. It is also very useful in optimal designs for various structures and devices. Based on the Dirichlet-to-Neumann map method, which is an efficient numerical method for modelling photonic crystal devices, we perform a sensitivity analysis for photonic crystal waveguide-cavity...
Guided modes may exist on periodic structures above the lightline, and they are called bound states in the continuum (BICs). For BICs on a 1D periodic array of circular cylinders, we show that the BICs disappear and become resonant modes when the cylinders are slightly distored so that the reflection symmetries are broken.
An efficient numerical method is developed to analyze light transmission through subwavelength apertures in metallic films, where the apertutres can have arbitrary cross sections and be surrounded by many grooves. The method is tailor-made for three-dimensional structures that are layered in different regions. It relies on field expansions in one-dimensional vertical modes, and boundary integral equations...
For the scattering of light by cylindrical metallic nanoparticles on a substrate, we present an efficient numerical method that relies on expanding the field in one-dimensional vertical modes. The method is used to analyze a single cylin-drical particle of arbitrary cross section and a pair of circular cylindrical particles.
A new integral equation mode solver is developed for dielectric waveguides with sharp corners and high index-contrast. The method makes use of a Nyström method for discretizing integral operators with logarithmic singularities, a graded mesh technique for handling corners, and computes boundary operators for domains of constant refractive indices. The method is illustrated by a number of numerical...
The boundary integral equation (BIE) method is one of the most effective numerical methods for analyzing diffraction gratings. The recently developed BIE-Neumann-to-Dirichlet (BIE-NtD) method is particularly simple to use, since it avoids the quasi-periodic Green's functions. In this paper, we present an improved BIE-NtD method. Numerical results indicate that our new BIE-NtD method achieves a high...
We present an extremely compact three-frequency wavelength division multiplexer in a square-lattice photonic crystal. The structure is obtained by optimizing the radii of rods in the crossing region of two perpendicular photonic crystal waveguides. The optimization is performed with the recently developed Dirichlet-to-Neumann (DtN) map method.
A simple model for two-dimensional photonic crystal devices is a finite set of circular cylinders centered on a square or triangular lattice and surrounded by a homogeneous medium. The Dirichlet-to-Neumann (DtN)map method (Yuan and Lu, Communications in Computational Physics 9, 113–128, 2011)is an efficient numerical method for scattering problems associated of such structures. In this paper, the...
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