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

摘要

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