Multi-domain spectral method for modal analysis of optical waveguide

Alharbi, Fahhad H.; Scott, J. C.

doi:10.1007/s11082-010-9365-3

Cited by 11 publications

(7 citation statements)

References 27 publications

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“…Mesh-free SM is a special family of the weighted residual methods [15][16][17][18]. In these methods, the unknown functions are approximated by either an expansion or interpolation (known as a collocation method) using preselected basis sets.…”

Section: Spectral Methods and The Exponential Basis Setsmentioning

confidence: 99%

“…To avoid this problem, the computational window is divided into homogeneous domains where the discontinuities lie at the boundaries. This approach is known as the multidomain spectral method (MDSM) [15][16][17][18][19]. In general MDSM methods allow handling very complicated and discontinuous functions.…”

Section: Spectral Methods and The Exponential Basis Setsmentioning

confidence: 99%

“…Recently, the mesh-free SMs have started to gain growing attention because of their high levels of analyticity and accuracy [15][16][17][18][19]. In these methods, the unknown functions are approximated by expansion using preselected basis sets.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we combine FSS method with the meshfree spectral method (SM) to calculate quantum critical parameters. Lately, the meshfree SMs start gaining growing attention because of their high levels of analyticity and accuracy [15][16][17][18][19]. In these methods, the unknown functions are approximated by expansion using preselected basis sets.…”

Section: Introductionmentioning

confidence: 99%

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Quantum criticality analysis by finite-size scaling and exponential basis sets

Alharbi

Kais

2013

Phys. Rev. E

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We combine the finite-size scaling method with the mesh-free spectral method to calculate quantum critical parameters for a given Hamiltonian. The basic idea is to expand the exact wave function in a finite exponential basis set and extrapolate the information about system criticality from a finite basis to the infinite basis set limit. The used exponential basis set, though chosen intuitively, allows handling a very wide range of exponential decay rates and calculating multiple eigenvalues simultaneously. As a benchmark system to illustrate the combined approach, we choose the Hulthen potential. The results show that the method is very accurate and converges faster when compared with other basis functions. The approach is general and can be extended to examine near-threshold phenomena for atomic and molecular systems based on even-tempered exponential and Gaussian basis functions.

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Section: Spectral Methods and The Exponential Basis Setsmentioning

confidence: 99%

Section: Spectral Methods and The Exponential Basis Setsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum criticality analysis by finite-size scaling and exponential basis sets

Alharbi

Kais

2013

Phys. Rev. E

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“…In addition to this, there are many physical problems that have a wide range of decay rates and multi-harmonics that the mapping should be able to account for concurrently. Sinc and Hermite polynomials fail for such problems [6,14,16,19,[26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Efficient Mapping of High Order Basis Sets for Unbounded Domains

Mumtaz¹,

Alharbi²

2018

CICP

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Many physical problems involve unbounded domains where the physical quantities vanish at infinities. Numerically, this has been handled using different techniques such as domain truncation, approximations using infinitely extended and vanishing basis sets, and mapping bounded basis sets using some coordinate transformations. Each technique has its own advantages and disadvantages. Yet, approximating simultaneously and efficiently a wide range of decaying rates has persisted as major challenge. Also, coordinate transformation, if not carefully implemented, can result in non-orthogonal mapped basis sets. In this work, we revisited this issue with an emphasize on designing appropriate transformations using sine series as basis set. The transformations maintain both the orthogonality and the efficiency. Furthermore, using simple basis set (sine function) help avoid the expensive numerical integrations. In the calculations, four types of physically recurring decaying behaviors are considered, which are: non-oscillating and oscillating exponential decays, and non-oscillating and oscillating algebraic decays. The results and the analyses show that properly designed high-order mapped basis sets can be efficient tools to handle challenging physical problems on unbounded domains. Decay rate ranges as large of 6 orders of magnitudes can be approximated efficiently and concurrently.

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Comparative analysis of spectral methods in half-bounded domains; implementation of predefined exponential and Laguerre basis sets to study planar dielectric and plasmonic waveguides

Alharbi

2009

Opt Quant Electron

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Two types of basis sets are used to analyze half bounded domains within the frame of multi-domain spectral method, namely the predefined exponential and physical Laguerre basis sets. Different planar waveguides are used for comparisons and the comparisons demonstrate the superiority of the predefined exponential basis set. The physical Laguerre basis set suffers from the slow convergence and its high sensitivity to scaling. Also, a narrow range of exponentially decaying rates can be calculated simultaneously. On the other hand, the predefined exponential basis set can handle wide spectrum of decaying range simultaneously with a small number of bases. It results in accuracies comparable to the machine accuracy with about 20 bases in most of the presented analyses.

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Multi-domain spectral method for modal analysis of optical waveguide

Cited by 11 publications

References 27 publications

Quantum criticality analysis by finite-size scaling and exponential basis sets

Quantum criticality analysis by finite-size scaling and exponential basis sets

Efficient Mapping of High Order Basis Sets for Unbounded Domains

Comparative analysis of spectral methods in half-bounded domains; implementation of predefined exponential and Laguerre basis sets to study planar dielectric and plasmonic waveguides

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