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Despite the benefits that directional coupler based parity-time symmetricsystems may offer to the field of integrated optics, the realization of suchcouplers relies on rather strict design constraints on the waveguideparameters. Here, we investigate directional couplers built of asymmetricwaveguides that do not fulfill parity-time symmetry. Nevertheless, wedemonstrate that for properly designed parameters, at least one mode of suchcouplers shows a behavior similar to the one observed in parity-symmetricsystems. We find an analytical condition relating gain and loss that enablessuch a behavior. Moreover, if the individual waveguides composing theasymmetric coupler are designed such that the propagation constants of theirmodes are identical, the behavior of both super-modes supported by the couplerresembles that of the parity-time symmetric systems.

Meta-$\mathcal{PT}$ Symmetry in Asymmetric Directional Couplers