Application of plane wave expansion and stiffness matrix methods to study transmission properties and guided mode of phononic plates

Farjallah, Hajer; Ketata, Hajer; Ghozlen, Mohamed Hédi Ben

doi:10.1016/j.wavemoti.2016.03.001

Cited by 8 publications

(2 citation statements)

References 20 publications

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“…The plane wave method (PWM) is a numerical solver often employed in physics and engineering [1] [2] [3]. In the field of photonics, PWM is commonly applied to structures such as the Bragg array, photonic crystals, micro-structured fi-bers… [4] [5] [6] and can provide information on the field profiles of supported states (eigenvectors) and propagation information through the band diagrams (eigenvalues).…”

Section: Introductionmentioning

confidence: 99%

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

Gauthier¹

2021

OPJ

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The plane wave numerical technique is recast from Ampere's and Faraday's laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.

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Section: Introductionmentioning

confidence: 99%

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

Gauthier¹

2021

OPJ

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“…Past works demonstrate that nonlinear partial differential equations (NLPDEs) are used widely in various domains to explain complex phenomena. Many efficient and significant mathematical methods have been developed for solving these NLPDEs to have a conception of these complex phenomena such as Hirota's bilinear method, 1 tanh‐coth method, 2 Jacobi elliptic function method, 3 semi‐inverse variational principle, 4 expansion method, 5 Darboux transformation, 6 extended direct algebraic method, 7 sine–cosine method, 8 variational method, 9 exponential‐fitting method, 10 plane‐wave expansion method, 11 Adomian's decomposition method 12 and many more.…”

Section: Introductionmentioning

confidence: 99%

A computational approach for finding the numerical solution of modified unstable nonlinear Schrödinger equation via Haar wavelets

Abdullah

Rafiq

2021

Math Methods in App Sciences

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In this work, we combined the Haar wavelet collocation method with the backward Euler difference formula to determine the approximate solutions of the modified unstable nonlinear Schrödinger equation. The backward Euler difference formula estimates the time derivative term and the Haar wavelet collocation method estimate the space derivative terms of the modified unstable nonlinear Schrödinger equation. This approach reduces the modified unstable nonlinear Schrödinger equation into a finite system of linear equations. In addition, we substantiate the efficiency and accuracy of the method graphically and numerically with the help of four examples.

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Study of the transmission properties of piezoelectric/piezomagnetic phononic composite laminates

et al. 2023

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Application of plane wave expansion and stiffness matrix methods to study transmission properties and guided mode of phononic plates

Cited by 8 publications

References 20 publications

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

A computational approach for finding the numerical solution of modified unstable nonlinear Schrödinger equation via Haar wavelets

Study of the transmission properties of piezoelectric/piezomagnetic phononic composite laminates

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