Additional waves and additional boundary conditions in local quartic metamaterials

LaBalle, Morgan; Durach, Maxim

doi:10.1364/osac.2.000017

Cited by 6 publications

(7 citation statements)

References 23 publications

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“…This is an explicit expression for the refraction indices of waves in arbitrary reciprocal materials, and this confirms our previous conclusion of Ref [11], that iso-frequency k-surface has reflection symmetry in reciprocal materials.…”

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confidence: 91%

Tri- and Tetrahyperbolic Isofrequency Topologies Complete Classification of Bianisotropic Materials

et al. 2020

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We describe novel topological phases of iso-frequency k-space surfaces in bianisotropic optical materialstri-and tetra-hyperbolic materials, which are induced by introduction of chirality. This completes the classification of iso-frequency topologies for bianisotropic materials, since as we show all optical materials belong to one of the following topological classes: tetra-, tri-, bi-, mono-or non-hyperbolic. We show that phase transitions between these classes occur in the k-space directions with zero group velocity at high k-vectors [Eq. (19)]. This classification is based on the sets of high-k polaritons (HKPs), supported by materials. We obtain the equation describing these sets [Eqs. (14), (17)] and characterize the longitudinal polarization impedance of HKPs [Eqs. (16), (18)]Hyperbolic topologies spark imagination of the science fiction prosaists for almost a century [1]. In turn, the topology of iso-frequency k-surfaces in photonic materials fascinates the optics community workers. The known topologies include bounded k-surfaces such as spheres or ellipsoids, and unbounded k-surfacessingle-and double-leaf hyperboloids [2][3][4], and recently discovered bi-hyperboloids [5]. As can be seen from this list of k-surface topologies the main difference between them and the key to their classification are the high-k modes that propagate or not in these materials (see Fig. 1). The high-k modes are of primary interest in photonics and have already found applications for optical imaging with nanoscopic resolut ion using hyperlenses, emission control due to diverging optic al density of high-k states and emission directivity control [6].In this Letter we theoretically predict novel iso-frequency topology phasestri-and tetrahyperbolic materials and obtain an equation that describes the k-space directions in which the high-k modes exist in terms of the 36 material parameters of an arbitrary bi-anisotropic material [Eqs. (14), (17)]. We also employ a theorem due to Zeuthen (1873) [7], to show that our prediction of the tri-and tetra-hyperbolic topological phases completes the classification of bianisotropic materials, which means that an optical material belongs to one of the classes: tetra -, tri-, bi-, mono-or non-hyperbolic. The novel tetra-and tri-hyperbolic phases which we predict here are induced by introduction of chirality. Chirality induced modification of topology in the energy-momentum space was previously studied for mono-hyperbolic materials [8]; here we discuss the topology of iso-frequency surfaces in k-space.

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confidence: 91%

Tri- and Tetrahyperbolic Isofrequency Topologies Complete Classification of Bianisotropic Materials

et al. 2020

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“…Sec. 5 and [29]). When spatial dispersion occurs, the classical interface conditions are not sufficient to compute the amplitudes of all eigenmodes.…”

Section: Interface Conditions Analysismentioning

confidence: 98%

“…While in a local material and for a given polarization of the electromagnetic field, the dispersion relation says that for a given frequency and transverse wave vector component there is only a single forward and a single backward propagating mode, nonlocal constitutive relations lead to multiple solutions. Therefore, not just ordinary interface conditions are needed but some additional (see, e.g., [29,38]).…”

Section: Introductionmentioning

confidence: 99%

Towards more general constitutive relations for metamaterials: A checklist for consistent formulations

et al. 2020

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When the period of unit-cells constituting metamaterials is no longer much smaller than the wavelength but only smaller, local material laws fail to describe the propagation of light in such composite media when considered at the effective level. Instead, nonlocal material laws are required. They have to be derived by approximating a general response function of the electric field in the metamaterial at the effective level that is accurate but cannot be handled practically. But how to perform this approximation is not obvious at all. Indeed many approximations can be perceived and one should be able to decide as quick as possible which of these possible material laws are mathematically and physically meaningful at all. Here, at the example of a second order Padé approximation of the general response function of the electric field, we present a checklist each possible constitutive relation has to pass in order to be physically and mathematically liable. As will be shown, only one out of these nine Padé approximations passes the checklist. The work is meant to be a guideline applicable to decide which constitutive relation makes actually sense at all. It is an essential ingredient for future research on composite media as any possible constitutive relation to be discussed should pass it.

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“…For example, obtaining Fresnel equations can be challenging at generic bianisotropic interfaces [103]. Another reason for the complications is the need to establish the additional boundary conditions (ABCs) in extreme non-reciprocal cases [104]. Even though a classification of individual SEWs at bianisotropic boundaries can be introduced based on propagation and penetration characteristics of the waves [105] and the invariance classes for individual SEWs with respect to variations of material parameters can be established [105], the classification of the isofrequency curves for SEWs is difficult to obtain [106][107][108][109][110][111].…”

Section: E Hmentioning

confidence: 99%

On Fresnel-Airy Equations, Fabry-Perot Resonances and Surface Electromagnetic Waves in Arbitrary Bianisotropic Metamaterials

Durach¹,

Williamson²,

Adams³

et al. 2022

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We introduce a theory of optical responses of bianisotropic layers with arbitrary effective medium parameters, which results in generalized Fresnel-Airy equations for reflection and transmission coefficients at all incidence directions and polarizations. The poles of these equations provide explicit expressions for the dispersion of Fabry-Perot resonances and surface electromatic waves in bianisotropic layers and interfaces. The existence conditions of these resonances are topologically related to the zeros of the high-k characteristic function h(k) = 0 of bulk bianisotropic materials and taxonomy of bianisotropic media according to the hyperbolic topological classes [32,33].

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Additional waves and additional boundary conditions in local quartic metamaterials

Cited by 6 publications

References 23 publications

Tri- and Tetrahyperbolic Isofrequency Topologies Complete Classification of Bianisotropic Materials

Tri- and Tetrahyperbolic Isofrequency Topologies Complete Classification of Bianisotropic Materials

Towards more general constitutive relations for metamaterials: A checklist for consistent formulations

On Fresnel-Airy Equations, Fabry-Perot Resonances and Surface Electromagnetic Waves in Arbitrary Bianisotropic Metamaterials

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