Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points

Abstract

We study theoretical models of three coupled wave guides with a $\mathcal{P}\mathcal{T}$-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

arXiv comment7 pages, 4 figures

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Cited by in corpus (5)

• High-order exceptional points in supersymmetric arrays
• Non-abelian nature of systems with multiple exceptional points
• Symmetry-induced higher-order exceptional points in two dimensions
• Complex symmetric Hamiltonians and exceptional points of order four and five
• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials