Four-wave mixing in a parity-time (PT)-symmetric coupler.

Parity-time (PT) symmetry allows for implementing controllable matching conditions for the four-wave mixing in 1D coupled waveguides. Different types of the process involving energy transition between slow and fast modes are established. In the case of defocusing Kerr media, the degenerated four-wave mixing is studied in detail. It is shown that unbroken PT symmetry supports the process existing in the conservative limit and, at the same time, originates new types of matching conditions, which cannot exist in the conservative system. In the former case, a slow beam splits into two fast beams, with nearly conserved total power, while in the latter case, one slow beam and one fast beam are generated. In the last process, the energy of the input primary slow beam is not changed and growth of the energy of the generated slow beam varies due to gain and loss of the medium. The appreciable generation of the fifth mode, i.e., the effect of the secondary resonant interactions, is observed.