  Despite the benefits that directional coupler based 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 investigate directional couplers built of asymmetric
waveguides that do not fulfill 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-symmetric
systems. We find an analytical condition relating gain and loss that enables
such a behavior. Moreover, if the individual waveguides composing the
asymmetric 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.
