A combined three-dimensional finite element and scattering matrix method for the analysis of plane wave diffraction by bi-periodic, multilayered structures

Dossou, Kokou B.; Botten, L. C.

doi:10.1016/j.jcp.2012.06.034

Cited by 15 publications

(13 citation statements)

References 41 publications

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“…For the computation of the Bloch modes, we have used numerical methods [9,16] which take either the electric field E or the magnetic field H as the main unknown while the other electromagnetic field is obtained analytically from the Maxwell's equations. For instance, when the electric field E is the primary unknown, the magnetic field H associated with the electric field E can be obtained from the Maxwell's equations as…”

Section: A the Adjoint Modes And Biorthogonality Relationsmentioning

confidence: 99%

Effective impedance modeling of metamaterial structures

2016

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We present methods for retrieving the effective impedance of metamaterials from the Fresnel reflection coefficients at the interface between two semi-infinite media. The derivation involves the projection of rigorous modal expansions onto the dominant modes of the two semi-infinite media. It is shown that the effective impedance can also be written as a ratio of averaged field quantities. Thus a number of effective impedance formulas, previously obtained by field averaging techniques, can also be derived from the scattering-based formalism, by an appropriate choice of projection. Within the effective medium limit, it is observed that a simple semi-analytic modelling technique based on the effective impedance can be used to reliably compute the reflection coefficients of metamaterials over a wide range of incidence angles. We use this technique to model planar metamaterial waveguides or surface modes.

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Section: A the Adjoint Modes And Biorthogonality Relationsmentioning

confidence: 99%

Effective impedance modeling of metamaterial structures

2016

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“…The impedance matrix also satisfies a matrix form of some basic algebraic properties of wave impedance between homogeneous media. For example, with three media denoted (1), (2), and (3), we show, in Section 4.B, a transitivity property that relates the impedance matrices between medium (1) relative to medium (2) and medium (2) relative to medium (3) to the impedance matrix of medium (1) relative to medium (3).…”

Section: Introductionmentioning

confidence: 95%

“…The most commonly used methods for modeling three-dimensional (3D) photonic and metamaterial structures are the finite-difference time-domain method (FDTM) [1], the finite element method (FEM) [2,3], and rigorous-coupledwave analysis (RCWA) [4]. Purely numerical techniques such as FEM and FDTM, while important as general-purpose simulation workhorses, provide little physical or theoretical insight into the underlying scattering processes.…”

Section: Introductionmentioning

confidence: 99%

Semi-analytic impedance modeling of three-dimensional photonic and metamaterial structures

2013

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We define the concept of an impedance matrix for three-dimensional (3D) photonic and metamaterial structures relative to a reference medium and show that it satisfies a matrix generalization of the basic algebraic properties of the wave impedance between homogeneous media. This definition of the impedance matrix is motivated by the structure of the Fresnel reflection and transmission matrices at the interface between the media. In the derivation of the Fresnel scattering matrices, the field in each medium is expressed by a Bloch mode expansion, with field matching at the interface being undertaken in a least-squares manner by exploiting a biorthogonality relation between primal and adjoint Bloch modes. A semi-analytic technique, based on the impedance matrix, is developed for modeling the scattering of light by 3D periodic photonic and metamaterial structures. The advantages (in design and intuition) of the formalism are demonstrated through two applications.

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“…While the bulk modes themselves can be extracted to high accuracy from, e.g., finite element method (FEM) calculations (cf. [7,8]), the scattering problem itself is conveniently solved in Fourier space using Floquet's theorem and the orthogonality of plane waves [9][10][11][12]. Hence, the accuracy is lost laterally as a result of the numerical Fourier cutoff.…”

Section: Introductionmentioning

confidence: 99%

Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

Saba

Schröder‐Turk

2015

Crystals

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We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell's equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities ε and µ and coupling matrices ζ. We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction.

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A combined three-dimensional finite element and scattering matrix method for the analysis of plane wave diffraction by bi-periodic, multilayered structures

Cited by 15 publications

References 41 publications

Effective impedance modeling of metamaterial structures

Effective impedance modeling of metamaterial structures

Semi-analytic impedance modeling of three-dimensional photonic and metamaterial structures

Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

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