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Photonic analogues of the Haldane and Kane-Mele Models

Lannebère, S. ; Silveirinha, M. G.

Photonic analogues of the Haldane and Kane-Mele Models, Proc Days on Diffraction, Saint Petersburg, Russia, Vol. , pp. - , June, 2018.

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Abstract
The Haldane model played a fundamental role in the development of topological concepts in electronics. This model describes the electronic properties of a graphene-type material under the influence of a periodic magnetic field with zero-spatial average. Furthermore, the Haldane model is effectively the backbone of the theory of topological insulators: the Kane-Mele model consists of two copies of the Haldane model with opposite magnetic field. However, despite the numerous connections between topological electronics and photonics developed in recent years, so far there is no precise electromagnetic counterpart of these models, mainly due to the difficulties to
mimic an effective magnetic field for photons.
Here building on our previous works and using an analogy between the two dimensional Schrödinger and Maxwell equations, we propose an implementation of the Haldane model in a photonic crystal with honeycomb symmetry made of dielectric cylinders embedded in a metallic back-ground and a spatially variable pseudo-Tellegen response that emulates a periodic effective magnetic field for photons. The non-trivial electromagnetic topological properties of such a platform and in particular the presence of topologically protected unidirectional edge states at the interface with a trivial photonic insulator are demonstrated with numerical simulations. In addition, it is shown that by applying a duality transformation to the photonic Haldane model one obtains a precise analogue of the Kane-Mele model in photonics. Remarkably, the Kane-Mele model can be implemented using matched anisotropic dielectrics with identical permittivity and permeability, without requiring any form of bianisotropic couplings. The Kane-Mele model consists of two copies of the Haldane model, with each copy associated with a specific wave polarization. These findings evidence the possibility to observe bi-directional topologically protected edges-states in a fully reciprocal all-dielectric and non-uniform anisotropic metamaterial.