Solitons in a ${\mathscr{PT}}$-symmetric grating-assisted co-directional coupler

We explore a co-directional coupling arrangement between two waveguides mediated by a PT-symmetric sinusoidal grating characterized by an index-modulation parameter κ and a gain/loss parameter g. We show that the device supports soliton-like solutions for both the ${\mathscr{PT}}$-conserving regime g < κ and the ${\mathscr{PT}}$-broken regime g > κ. In the first case the coupler exhibits a gap in wave-number k and the solitons can be regarded as an extension of a previous solution found for pure index modulation. In the second case the coupler exhibits a gap in frequency ω and the solutions are entirely new.