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arXiv · 1601.05489

Exceptional contours and band structure design in parity-time symmetric photonic crystals

Alexander Cerjan·Aaswath Raman·Shanhui Fan
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Abstract

We investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies which can undergo thresholdless $\mathcal{PT}$ transitions. We derive a $\mathbf{k} \cdot \mathbf{p}$ perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless $\mathcal{PT}$ transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a $\mathcal{PT}$-superprism effect, and unidirectional behavior.

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Alexander Cerjan, Aaswath Raman, Shanhui Fan. 2016-01-21. Exceptional contours and band structure design in parity-time symmetric photonic crystals. https://doi.org/10.1103/physrevlett.116.203902

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