Analysis of Finite Periodic Dielectric Gratings by the Finite-Difference Frequency-Domain Method With the Sub-Entire-Domain Basis Functions and Wavelets

Zheng, Gang; Wang, Bing‐Zhong; Li, Hua; Liu, Xiaofei; Ding, and Shuai

doi:10.2528/pier09111502

Cited by 9 publications

(10 citation statements)

References 13 publications

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“…The local errors of the LFE-9 equations are proportional to the 8th power of the normalized frequency V and the unknown 8th local Fourier-Bessel coefficient a 8 .…”

Section: Local Lfe-9 Errorsmentioning

confidence: 99%

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Theoretical Foundation for the Method of Connected Local Fields

Mu¹,

Chang²

2011

PIER

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Abstract-The method of connected local fields (CLF), developed for computing numerical solutions of the two-dimensional (2-D) Helmholtz equation, is capable of advancing existing frequency-domain finitedifference (FD-FD) methods by reducing the spatial sampling density nearly to the theoretical limit of two points per wavelength. In this paper, we show that the core theory of CLF is the result of applying the uniqueness theorem to local EM waves. Furthermore, the mathematical process for computing the local field expansion (LFE) coefficients from eight adjacent points on a square is similar to that in the theory of discrete Fourier transform. We also present a theoretical analysis of both the local and global errors in the theory of connected local fields and provide closed-form expressions for these errors.

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“…The local errors of the LFE-9 equations are proportional to the 8th power of the normalized frequency V and the unknown 8th local Fourier-Bessel coefficient a 8 .…”

Section: Local Lfe-9 Errorsmentioning

confidence: 99%

“…From these FourierBessel coefficients we derived FD-like, compact nine-point stencils for the 2D Helmholtz equation. We show that CLF is capable of advancing existing FD-FD methods [5][6][7][8][9] by reducing the sampling density to just a little more than two points per wavelength, which is theoretical limit for spatial sampling.…”

Section: Introductionmentioning

confidence: 98%

Theoretical Foundation for the Method of Connected Local Fields

Mu¹,

Chang²

2011

PIER

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“…In this paper, using some previously published papers on the application of wavelets in electromagnetics [8][9][10][11][12], a new RPIM supplemented by the wavelet frames, is proposed by which RPIM is able to simulate electromagnetic problems in multi scales with less computational time consumption. This supplement affords by an ability of proposing shape functions, directly, without any need to MMIS.…”

Section: Introductionmentioning

confidence: 99%

Proposing a Wavelet Based Meshless Method for Simulation of Conducting Materials

Afsari¹,

Movahhedi²

2013

PIER M

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Abstract-This work focuses on the development of multiscale meshless technique in area of scattered fields from paramagnetic scatterers. The radial point interpolation method (RPIM), as the most common meshless technique, is employed for above purpose. Due to high frequency analysis, some special considerations must be applied, particularly in subdomains near the incident face. So, to ensure the accuracy, a multiscale meshless technique in wavelet frames sounds necessary. Simulating the scatterers using above method, specifically an elliptic paramagnetic scatterer, shows some efficient aspects such as less computational time and more precision compared with some other numerical methods.

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“…Analytical formulas such as Maxwell-Garnett mixing formula [3] is derived based on spherical inclusions and applied to the case when the size of inclusions is small comparing with the period. In recent years, numerical techniques such as method of moments (MoM), finite difference method (FDM), and finite element method (FEM) have been adopted to solve the problem [4][5][6][7]. The MoM methods usually have better accuracy.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of Periodic Objects Embedded in Layered Media

Zhao¹,

Song²,

Kamgaing³

et al. 2015

PIER Letters

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Abstract-An effective medium modeling technique is proposed to homogenize the periodic objects embedded in layered media. The homogenization is based on the same scattering coefficients. An integral equation based approach is adopted to solve the scattering problem of original structures. Our modeling results are compared with Maxwell-Garnett mixing formula and published results. Good agreements have been observed. Periodic metal patches embedding in layered dielectric structure is fabricated and measured to validate the modeling technique. The difference between experiment results and proposed modeling results is less than 3%.

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Analysis of Finite Periodic Dielectric Gratings by the Finite-Difference Frequency-Domain Method With the Sub-Entire-Domain Basis Functions and Wavelets

Cited by 9 publications

References 13 publications

Theoretical Foundation for the Method of Connected Local Fields

Theoretical Foundation for the Method of Connected Local Fields

Proposing a Wavelet Based Meshless Method for Simulation of Conducting Materials

Homogenization of Periodic Objects Embedded in Layered Media

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