Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework

Jamid, H.A.; Akram, Muhammad Nadeem

doi:10.1109/jlt.2002.800350

Cited by 14 publications

(7 citation statements)

References 19 publications

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“…For devices that are periodic in the longitudinal direction, the improved scattering matrix formulation enables a very simple, fast and efficient algorithm to model devices composed of many hundreds or thousands of periods [2]. First, the scattering matrix for one unit cell is constructed, which may be the combination of any number of scattering matrices.…”

Section: Doubling Algorithm For Scattering Matricesmentioning

confidence: 99%

“…It then updates the global scattering matrix using the star product as S (global) = S (global) ⊗S (1) . The main loop then iterates a second time by calculating the scattering matrix for the second layer S (2) and updating the global scattering matrix as S (global) = S (global) ⊗ S (2) . After the main loop iterates through all of the layers, the global scattering matrix describes propagation through the entire device.…”

Section: Scattering Matrix Algorithmmentioning

confidence: 99%

“…Two popular semi-analytical techniques are the method of lines (MOL) [1,2] and rigorous coupled-wave analysis (RCWA) [3,4]. The MOL usually applies the finite-difference method to analyze the layer cross sections, but other techniques like finite-elements can also be used.…”

Section: Introductionmentioning

confidence: 99%

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Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Rumpf¹

2011

PIER B

142

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Abstract-The literature describing scattering matrices for semianalytical methods almost exclusively contains inefficient formulations and formulations that deviate from long-standing convention in terms of how the scattering parameters are defined. This paper presents a novel and highly improved formulation of scattering matrices that is consistent with convention, more efficient to implement, and more versatile than what has been otherwise presented in the literature. Semi-analytical methods represent a device as a stack of layers that are uniform in the longitudinal direction. Scattering matrices are calculated for each layer and are combined into a single overall scattering matrix that describes propagation through the entire device. Free space gaps with zero thickness are inserted between the layers and the scattering matrices are made to relate fields which exist outside of the layers, but directly on their boundaries. This framework produces symmetric scattering matrices so only two parameters need to be calculated and stored instead of four. It also enables the scattering matrices to be arbitrarily interchanged and reused to describe longitudinally periodic devices more efficiently. Numerical results are presented that show speed and efficiency can be increased by more than an order of magnitude using the improved formulation.

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Section: Doubling Algorithm For Scattering Matricesmentioning

confidence: 99%

Section: Scattering Matrix Algorithmmentioning

confidence: 99%

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Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Rumpf¹

2011

PIER B

142

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“…It is useful to create a separate function that constructs these matrices because it will make the FDFD code cleaner and the same function can also be used in other numerical methods that use finite-differences like the method of lines [24,25], beam propagation method [26,27], and more [18,21,28]. Given the derivative operators and the diagonal materials matrices, the wave matrix A is calculated using an equation from Table 1. Step 3 -Calculate the source vector b…”

Section: Implementation Of Fdfdmentioning

confidence: 99%

Simple Implementation of Arbitrarily Shaped Total-Field/Scattered-Field Regions in Finite-Difference Frequency-Domain

Rumpf¹

2012

PIER B

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Abstract-The total-field/scattered-field (TF/SF) formulation is a popular technique for incorporating sources into electromagnetic models like the finite-difference frequency-domain (FDFD) method. It is versatile and simplifies calculation of waves scattered from a device. In the context of FDFD, the TF/SF formulation involves modifying all of the finite-difference equations that contain field terms from both the TF and SF regions in order to make the terms compatible. While simple in concept, modifying all of the equations for arbitrarily shaped TF/SF regions is tedious and no solution has been offered in the literature to do it in a straightforward manner. This paper presents a simple and efficient technique for implementing the TF/SF formulation that allows the TF/SF regions to be any shape and of arbitrary complexity. Its simplicity and versatility are demonstrated by giving several practical examples including a diffraction grating, a waveguide problem, and a scattering problem with a cylindrical wave source.

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“…It also found that the newly developed CMMM yields improvement for the numerical accuracy in comparison with TMM method as more modes have been considered. Moreover, a cascading and doubling algorithm which previously used in beam propagation method (BPM) has been adopted within the framework of CMMM to save the computation efforts [20], the benefits become more pronounced with the increase of periods.…”

Section: Introductionmentioning

confidence: 99%

Investigation of long-range surface plasmon polaritons gratings by complex mode matching method

Zhang

Huang

2007

SPIE Proceedings

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Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework

Cited by 14 publications

References 19 publications

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Simple Implementation of Arbitrarily Shaped Total-Field/Scattered-Field Regions in Finite-Difference Frequency-Domain

Investigation of long-range surface plasmon polaritons gratings by complex mode matching method

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