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We study theoretical models of three coupled wave guides with a$\mathcal{PT}$-symmetric distribution of gain and loss. A realistic matrixmodel is developed in terms of a three-mode expansion. By comparing with apreviously postulated matrix model it is shown how parameter ranges with goodprospects of finding a third-order exceptional point (EP3) in an experimentallyfeasible arrangement of semiconductors can be determined. In addition it isdemonstrated that continuous distributions of exceptional points, which renderthe discovery of the EP3 difficult, are not only a feature of extended waveguides but appear also in an idealised model of infinitely thin guides shapedby delta functions.

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