$\mathcal{P}\mathcal{T}$-symmetric photonic lattices with type-II Dirac cones

Abstract

The type-II Dirac cone is a special feature of the band structure, whose Fermi level is represented by a pair of crossing lines. It has been demonstrated that such a structure is useful for investigating topological edge solitons, and more specifically, for mimicking the Kline tunneling. However, it is still not clear what the interplay between type-II Dirac cones and the non-Hermiticity mechanism will result in. Here, this question is addressed; in particular, we report the $\mathcal{P}\mathcal{T}$-symmetric photonic lattices with type-II Dirac cones for the first time. We identify a slope-exceptional ring and name it the type-II exceptional ring. We display the restoration of the $\mathcal{P}\mathcal{T}$ symmetry of the lattice by reducing the separation between the sites in the unit cell. Curiously, the amplitude of the beam during propagation in the non-Hermitian lattice with $\mathcal{P}\mathcal{T}$ symmetry only decays because of diffraction, whereas in the $\mathcal{P}\mathcal{T}$ symmetry-broken lattice it will be amplified, even though the beam still diffracts. This work establishes the link between the non-Hermiticity mechanism and the violation of Lorentz invariance in these physical systems.

5 pages, 4 figures, to appear in Optics Letters. Comments are welcome

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