Optical lattices with higher-order exceptional points by non-Hermitian coupling

Abstract

Exceptional points (EPs) are degeneracies in open wave systems with coalescence of at least two energy levels and their corresponding eigenstates. In higher dimensions, more complex EP physics not found in two-state systems is observed. We consider the emergence and interaction of multiple EPs in a four coupled optical waveguides system by non-Hermitian coupling showing a unique EP formation pattern in a phase diagram. In addition, absolute phase rigidities are computed to show the mixing of the different states in definite parameter regimes. Our results could be potentially important for developing further understanding of EP physics in higher dimensions via generalized paradigm of non-Hermitian coupling for a new generation of parity-time (PT) devices. It is well-known that systems with open boundaries 1 or material loss and gain 2 can be described by Hamiltonians that are non-Hermitian. Non-Hermitian systems have recently attracted great scientific interests, both theoretically and experimentally, in open systems with energy gain or loss. A non-Hermitian Hamiltonian can exhibit many of intriguing phenomena beyond that of a Hermitian system. Consequently, researchers have become increasingly aware of the potential effects and applications reminiscent of the non-Hermitian systems. For instance, a non-Hermitian Hamiltonian have nonorthogonal eigenfunctions with complex eigenvalues where the imaginary part corresponding to decay or growth 2 . At certain points in parameter space fin as exceptional points (EPs) 3 or non-Hermitian

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