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