Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence

Belkhir, Abderrahmane; Arar, O.; Benabbés, Saâdi; Lamrous, Omar; Baida, Fadi

doi:10.1103/physreve.81.046705

Cited by 21 publications

(15 citation statements)

References 11 publications

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“…In this paper the extended formulation for implementing Lorentz model in SF-FDTD is reported. This implementation of Drude-Lorentz model has considerably reduced number of variables compared to the previously reported works [9,10].…”

Section: Introductionmentioning

confidence: 98%

“…The other method of SF-FDTD for dispersive media [9,10] uses 112 variables for implementation of Drude-Lorentz dispersion model. The large number of variables not only increases the runtime, but also may prohibit the implementation of the algorithm on a GPU card, due to its limited memory.…”

Section: Formulation Of Lorentz Model In Sf-fdtdmentioning

confidence: 99%

“…SF-FDTD method has the advantage of wideband analysis of periodic structures by considering only one unit cell. This method has been used for analyzing dielectric or lossy [1][2][3][4][5][6][7], anisotropic [8] and dispersive [9,10] periodic structures. We have recently reported an improved formulation of 3D SF-FDTD [11] for analyzing dispersive media.…”

Section: Introductionmentioning

confidence: 99%

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Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Shahmansouri¹,

Rashidian²

2012

PIER

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Abstract-Split-field finite-difference time-domain (SF-FDTD) method can overcome the limitation of ordinary FDTD in analyzing periodic structures under oblique incidence. On the other hand, huge run times of 3D SF-FDTD, is practically a major burden in its usage for analysis and design of nanostructures, particularly when having dispersive media. Here, details of parallel implementation of 3D SF-FDTD method for dispersive media, combined with totalfield/scattered-field (TF/SF) method for injecting oblique plane wave, are discussed. Graphics processing unit (GPU) has been used for this purpose, and very large speed up factors have been achieved. Also a previously reported formulation of SF-FDTD based on the Drude model for dispersive media, is extended to cover Drude-Lorentz model, which is usually needed for materials such as gold. The resulting reduction in the number of variables in this formulation, not only helps in reducing the computational time, but also makes it possible to be implemented in GPU, where its memory limitation is a major concern. As an example for demonstrating the importance of this method in optimization of nanophotonics structures, improvement in the performance of a refractive index sensor, made of an array of nanodisks, using suitable angle of incidence is reported. To the best of our knowledge this is the first report of GPU implementation of SF-FDTD method, capable of analyzing periodic dispersive media under oblique incidence.

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Section: Introductionmentioning

confidence: 98%

Section: Formulation Of Lorentz Model In Sf-fdtdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Shahmansouri¹,

Rashidian²

2012

PIER

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“…Secondly, the implementation of the periodic boundary condition (PBC) in the time domain is straightforward for the normal incident wave and becomes complicated for the oblique incident because of the time delay in the transverse plane [16]. To deal with this problem, several methods have been introduced, such as Sine-Cosine method [23] and split-field method [24][25][26]. Recently, another new formulation, named spectral FDTD (SFDTD) was proposed to deal with the problem [27,28], because the constant wave-number (CTW) wave is used, there is no delay in the transverse plane and the PBC can be implemented directly in the time domain.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

Mao¹,

Chen²,

Liu³

et al. 2012

PIER

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Abstract-This paper combines a hybrid implicit-explicit (HIE) method with spectral finite-difference time-domain (SFDTD) method for solving periodic structures at oblique incidence, resulting in a HIE-SFDTD method. The new method has the advantages of both HIE-FDTD and SFDTD methods, not only making the stability condition weaker, but also solving the oblique incident wave on periodic structures. Because the stability condition is determined only by two space discretizations in this method, it is extremely useful for periodic problems with very fine structures in one direction. The method replaces the conventional single-angle incident wave with a constant transverse wave-number (CTW) wave, so the fields have no delay in the transverse plane, as a result, the periodic boundary condition (PBC) can be implemented easily for both normal and oblique incident waves. Compared with the ADI-SFDTD method it only needs to solve two untridiagonal matrices when the PBC is applied to, other four equations can be updated directly, while four untridiagonal matrices, two tridiagonal matrices, and six explicit equations should be solved in the ADI-SFDTD method. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed algorithm. Results show the new algorithm has better accuracy and higher efficiency than that of the ADI-SFDTD method, especially for large time step sizes. The CPU running time for this method can be reduced to about 45% of the ADI-SFDTD method.

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“…The split-field finite-difference time-domain (SF-FDTD) approach [20][21][22][23][24][25][26] is a powerful method for analyzing periodic structures under oblique incidence, a situation in which the ordinary FDTD approach encounter difficulties. In SF-FDTD only one period is considered rather than the whole structure, which has obvious advantages as far as numerical efficiency is concerned.…”

Section: Introductionmentioning

confidence: 99%

Tensorial split-field finite-difference time-domain approach for second- and third-order nonlinear materials

2013

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The split-field finite-difference time-domain (SF-FDTD) method for one-dimensionally periodic structures is extended to include the coefficient-tensor description of second-and third-order nonlinear-optical media. A set of nonlinear equations related to the split-field values of the electric field is established. An iterative fixed-point approach for solving the coupled nonlinear system of equations needed to update the electric field components in the SF-FDTD is then developed. The third-order nonlinear susceptibility dispersion is also considered by means of the Raman effect and its implementation in the SF-FDTD scheme. Different scenarios are considered in order to verify the reliability of the method for simulating second-and third-order nonlinear-optical media. First, second-harmonic generation and its efficiency are investigated in a homogeneous layer with and without the quasi-phase-matching technique. Second, the nonlinear dispersion is analyzed by means of the generation of solitons in Kerr media due to the Raman effect. Last, a set of binary phase gratings with nonlinear pillars is considered under oblique incidence. Here the nonlinear refractive index is generated by different physical mechanisms modeled with the nonscalar third-order susceptibility.

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Implementation of dispersion models in the split-field–finite-difference-time-domain algorithm for the study of metallic periodic structures at oblique incidence

Cited by 21 publications

References 11 publications

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

Tensorial split-field finite-difference time-domain approach for second- and third-order nonlinear materials

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