Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients

Lackner, Christoph; Meng, Shixu; Monk, Peter

doi:10.1016/j.cam.2019.03.027

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…d/20. The eigenvalues are obtained by first converting (2.4) to a larger-size, linear eigenvalue problem [32] and then solving the latter via Arnoldi iterations [33]. The first 200 ‘unfiltered’ eigenvalues κn∈C are plotted in figure 5 b , while their restriction to the essential strip (2.13) is shown in figure 5 c .…”

Section: Numerical Resultsmentioning

confidence: 99%

Plug-and-play analytical paradigm for the scattering of plane waves by ‘layer-cake’ periodic systems

Salasiya,

Meng,

Guzina

2024

Proc. R. Soc. A.

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We investigate the scattering of scalar plane waves in two dimensions by a heterogeneous layer that is periodic in the direction parallel to its boundary. On describing the layer as a union of periodic laminae, we develop a solution of the scattering problem by merging the concept of propagator matrices and that of Bloch eigenstates featured by the unit cell of each lamina. The featured Bloch eigenstates are obtained by solving the quadratic eigenvalue problem (QEVP) that seeks a complex-valued wavenumber normal to the layer boundary given (i) the excitation frequency, and (ii) real-valued wavenumber parallel to the boundary—that is preserved throughout the system. Spectral analysis of the QEVP reveals sufficient conditions for discreteness of the eigenvalue spectrum and the fact that all eigenvalues come in complex-conjugate pairs. By deploying the factorization afforded by the propagator matrix approach, we demonstrate that the contribution of individual eigenvalues (and so eigenmodes) to the solution diminishes exponentially with absolute value of their imaginary part, which then forms a rational basis for truncation of the factorized Bloch (FB)-wave solution. The proposed methodology caters for the optimal design of rainbow traps, energy harvesters and metasurfaces, whose potency to manipulate waves is decided not only by the individual dispersion characteristics of the component laminae, but also by ordering and generally fitting of the latter into a composite layer. Using the FB approach, evaluation of trial configurations—as generated by the permutation and window translation/stretching of the component laminae—can be accelerated by decades.

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Section: Numerical Resultsmentioning

confidence: 99%

Plug-and-play analytical paradigm for the scattering of plane waves by ‘layer-cake’ periodic systems

Salasiya,

Meng,

Guzina

2024

Proc. R. Soc. A.

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“…Finally, the proper way to ensure the divergence condition [23] in a weak sense is to use ϕ as a Lagrange multiplier. We are now in position to reformulate the eigenvalue problem at stake in this section.…”

Section: Variational Formulation Of the Spectral Problemmentioning

confidence: 99%

Discontinuities in photonic waveguides: rigorous Maxwell-based 3D modeling with the finite element method

Demésy¹,

Renversez²

2020

J. Opt. Soc. Am. A

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In this paper, we present a general framework to study rigorously discontinuities in open waveguides using a full vector description given by Maxwell's equations and using the finite element method. The discontinuities are not necessarily a small perturbation of the initial waveguide and can be very general, such as plasmonic inclusions of arbitrary shape. The leaky modes of the invariant structure are computed first ; then serve as incident fields on the full structure with obstacles using a scattered field approach ; the resulting scattered field is finally projected on the modes of the invariant structure making use of their bi-orthogonality. A complete energy balance is performed. Finally, the modes open waveguides periodically structured along the propagation direction are computed we compare the relevant complex propagation constants to the transmission obtained for a finite number of identical cells. The relevance and complementarity of the two approaches are highlighted on a numerical example encountered in infrared sensing. Finally, open source models allowing to retrieve most of the results of this paper are provided.

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A fast method to compute dispersion diagrams of three-dimensional photonic crystals with rectangular geometry

Markel

Schobinger²,

Hollaus³

2022

Computer Physics Communications

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Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients

Cited by 5 publications

References 34 publications

Plug-and-play analytical paradigm for the scattering of plane waves by ‘layer-cake’ periodic systems

Plug-and-play analytical paradigm for the scattering of plane waves by ‘layer-cake’ periodic systems

Discontinuities in photonic waveguides: rigorous Maxwell-based 3D modeling with the finite element method

A fast method to compute dispersion diagrams of three-dimensional photonic crystals with rectangular geometry

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