A Geometrical Approach to Duality Transformations for Tellegen Media

Prudêncio, Filipa R.; Matos, Sérgio A.; Paiva, Carlos R.

doi:10.1109/tmtt.2014.2326108

Cited by 13 publications

(23 citation statements)

References 32 publications

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“… k are precisely the same for the original crystal and for a duality-transformed crystal [39]. This shows that the Bloch modes of a Tellegen photonic crystal with media in the same equivalence class must be degenerate    for propagation along the stratification direction.…”

Section: B Band Diagrams For Tellegen Periodic Structuresmentioning

confidence: 75%

“…This can be rather useful because if a solution for the duality transformed problem can be found, then the solution of the original problem can be readily obtained by applying an inverse duality mapping [42]- [44]. For example, if a Tellegen photonic crystal is reducible to a crystal formed by only simple isotropic media using a duality transformation, then the dispersion diagrams of the original structure are exactly the same as the diagrams of the transformed photonic crystal [39]. It was shown in [39] that typically three different Tellegen media cannot be transformed into simple isotropic media using the same duality transformation, or in other words, they do not belong to the same Tellegen equivalence class [39].…”

Section: Appendix A: Axion Electrodynamics and The Tellegen Mediummentioning

confidence: 99%

“…These results were developed using a geometric approach wherein the Tellegen equivalence classes reducible to the simple isotropic media class are represented by circles in the Riemann sphere [39]. For more details, a reader is referred to our previous work [39].…”

Section: Appendix A: Axion Electrodynamics and The Tellegen Mediummentioning

confidence: 99%

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Asymmetric band diagrams in photonic crystals with a spontaneous nonreciprocal response

2015

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Section: B Band Diagrams For Tellegen Periodic Structuresmentioning

confidence: 75%

Section: Appendix A: Axion Electrodynamics and The Tellegen Mediummentioning

confidence: 99%

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Asymmetric band diagrams in photonic crystals with a spontaneous nonreciprocal response

2015

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“…The key observation is that a duality transformation acts exclusively on the fields, leaving the space and time unaffected [23,52,53]. Thereby, the wave phenomena and topological properties of two systems linked by a duality transformation are fundamentally the same.…”

Section: A Kane-mele Model In a Nonreciprocal Systemmentioning

confidence: 99%

“…Thereby, the wave phenomena and topological properties of two systems linked by a duality transformation are fundamentally the same. In particular a duality transformation preserves the band diagram dispersion and the immunity to back-scattering [23,52,54].…”

Section: A Kane-mele Model In a Nonreciprocal Systemmentioning

confidence: 99%

Photonic analogues of the Haldane and Kane-Mele models

Lannebère

Silveirinha

2019

Nanophotonics

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The condensed matter Haldane and Kane-Mele models revolutionized the understanding of what is an "insulator", as they unveiled novel classes of media that behave as metals near the surface, but are insulating in the bulk. Here, we propose exact electromagnetic analogues of these two influential models relying on a photonic crystal implementation of "artificial graphene" subject to an effective magnetic field. For the Haldane model, the required effective magnetic field for photons can be emulated with a spatially variable pseudo-Tellegen response. For the Kane-Mele model, the spin-orbit coupling can be mimicked using matched anisotropic dielectrics with identical permittivity and permeability, without requiring any form of bianisotropic couplings. Using full wave numerical simulations and duality theory we verify that the nontrivial topology of the two proposed platforms results in the emergence of topologically protected gapless edge states at the interface with a trivial photonic insulator. Our theory paves the way for the emulation of the two condensed matter models in a photonic platform, and determines another paradigm to observe topologically protected edges-states in a fully reciprocal all-dielectric and non-uniform anisotropic metamaterial.

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First principles calculation of topological invariants of non-Hermitian photonic crystals

Prudêncio

Silveirinha

2020

Commun Phys

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Topological photonic systems have recently emerged as an exciting new paradigm to guide light without back-reflections. The Chern topological numbers of a photonic platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green’s function method to determine from first principles the topological invariants of photonic crystals. The proposed formalism does not require the calculation of the photonic band-structure, and can be easily implemented using the operators obtained with a standard plane-wave expansion. Furthermore, it is shown that the theory can be readily applied to the classification of topological phases of non-Hermitian photonic crystals with lossy or gainy materials, e.g., parity-time symmetric photonic crystals.

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A Geometrical Approach to Duality Transformations for Tellegen Media

Cited by 13 publications

References 32 publications

Asymmetric band diagrams in photonic crystals with a spontaneous nonreciprocal response

Asymmetric band diagrams in photonic crystals with a spontaneous nonreciprocal response

Photonic analogues of the Haldane and Kane-Mele models

First principles calculation of topological invariants of non-Hermitian photonic crystals

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