Effect of loss on the dispersion relation of photonic and phononic crystals

Laude, Vincent; Escalante, José M.; Martı́nez, Alejandro

doi:10.1103/physrevb.88.224302

Cited by 30 publications

(32 citation statements)

References 23 publications

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“…It is found that numerical results follow closely the perturbation theory in Ref. [11], according to which the damping of a given Bloch wave can be estimated at any frequency from a volume average of the viscoelastic constituents weighted by the Bloch wave distribution. In particular, the complex-eigenfrequency band structure ω(k) does not capture any spatial propagation information but provides one with information complementary to the complex band structure k(ω).…”

Section: Introductionsupporting

confidence: 75%

“…In the small damping limit, the first-order perturbation theory of Ref. [11] applies. The main result of this theory in our context is that the relative variation of the frequency of a band at a fixed value of the Bloch wavevector is given by…”

Section: Discussionmentioning

confidence: 99%

“…In the literature on phononic crystals, having a reliable measure of the effect of material loss on wave propagation has been a standing salient problem, with obvious practical implications [5][6][7][8][9][10][11][12][13][14]. Since the band structure gives the dispersion relation of Bloch waves, i.e., of the eigenmodes of phononic crystals, it is natural to try to generalize it to complex quantities describing attenuation in space or damping in time.…”

Section: Introductionmentioning

confidence: 99%

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Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals

et al. 2019

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The consideration of material losses in phononic crystals leads naturally to the introductionof complex valued eigenwavevectors or eigenfrequencies representing the attenuation of elastic wavesin space or in time, respectively. Here, we propose a new technique to obtain phononic band structureswith complex eigenfrequencies but real wavevectors, in the case of viscoelastic materials, wheneverelastic losses are proportional to frequency. Complex-eigenfrequency band structures are obtainedfor a sonic crystal in air, and steel/epoxy and silicon/void phononic crystals, with realistic viscouslosses taken into account. It is further found that the imaginary part of eigenfrequencies are wellpredicted by perturbation theory and are mostly independent of periodicity, i.e., they do not accountfor propagation losses but for temporal damping of Bloch waves.

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Section: Introductionsupporting

confidence: 75%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals

et al. 2019

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“…Importantly, in this process we also calculate the exceptional point (EP)-the point at which the spectrum of the perturbed assembly has a non-Hermitian degeneracy, where two of its eigenmodes coalesce, together with their corresponding complex frequencies [26][27][28]. This occurs in our example for an assembly comprising a lossy slab with specific viscoelastic shear modulus [29].…”

Section: Introductionmentioning

confidence: 99%

Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

Gal¹,

Moiseyev²

2020

Phys. Rev. Applied

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Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics-a theory that phenomenologically describes the time-dependent macroscopic response of materials.Here, we open route to transfer additional tools from non-Hermitian quantum mechanics. We begin by identifying the differences and similarities between the one-dimensional elastodynamics equation and the time-independent Schrödinger equation, and finding the condition under which the two are equivalent. Subsequently, we demonstrate the application of the non-Hermitian perturbation theory to determine the response of elastic systems; calculation of leaky modes and energy decay rate in heterogenous solids with open boundaries using a quantum mechanics approach; and construction of degeneracies in the spectrum of these assemblies. The latter result is of technological importance, as it introduces an approach to harness extraordinary wave phenomena associated with non-Hermitian degeneracies for practical devices, by designing them in simple elastic systems. As an example of such application, we demonstrate how an assembly of elastic slabs that is designed with two degenerate shear states according to our scheme, can be used for mass sensing with enhanced sensitivity by exploiting the unique topology near the exceptional point of degeneracy. arXiv:1910.07306v2 [cond-mat.soft]

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“…For frequency-dependent systems, the estimation of the group velocity is not trivial. 38,39 Equation 4 is differentiated and multiplied by the left eigenvector ψ l i T following the procedure proposed by 38 such that…”

Section: Group Velocitymentioning

confidence: 99%

Design and experimental validation of a temperature-driven adaptive phononic crystal slab

Billon¹,

Ouisse²,

Sadoulet-Reboul³

et al. 2019

Smart Mater. Struct.

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In this paper, an adaptive phononic crystal slab based on the combination of metallic parts and highly dissipative polymeric interfaces is designed. Cylindrical pillars are composed of shape memory polymer and aluminum deposited periodically on the aluminum slab. The mechanical properties of the polymer depend on both temperature and frequency and can radically change from glassy to rubbery state, with various combinations of high/low stiffness and high/low dissipation. A 3D finite element model of the cell is developed for the design of the metamaterial. The shifted-cell operator technique is used to correctly handle damping effects in the dispersion analysis. In order to validate the design and the adaptive character of the metamaterial, results issued from a full 3D model of a finite structure embedding an interface composed by a distributed set of the unit cells are presented. Various driving temperatures are used to change the behaviour of the system, and numerical results obtained on the adaptive structure are compared to experimental ones. Two states are obtained by changing the temperature of the polymeric interface: at 25 • C a bandgap is visible around a selected resonance frequency, and it doesn't exist anymore above the glass transition temperature, where the phononic crystal slab tends to behave as an homogeneous plate. Numerical and experimental results show energy propagation along the borders of the slab in the bandgap.

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Effect of loss on the dispersion relation of photonic and phononic crystals

Cited by 30 publications

References 23 publications

Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals

Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals

Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

Design and experimental validation of a temperature-driven adaptive phononic crystal slab

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