Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arrays

We address dissipative soliton formation in modulated parity-time (PT)-symmetric continuous waveguide arrays composed from waveguides with amplifying and absorbing sections, whose density gradually increases (due to decreasing waveguide separation) either towards the center of the array or towards its edges. In such a structure, the level of gain/loss at which PT-symmetry gets broken depends on the direction of increase of waveguide density. Breakup of PT-symmetry occurs when eigenvalues of modes localized in the region where waveguide density is largest collide and move into a complex plane. In this regime of broken symmetry, the inclusion of focusing Kerr-type nonlinearity of the material and weak two-photon absorption allows to arrest the growth of amplitude of amplified modes and may lead to the appearance of stable attractors either in the center or at the edge of the waveguide array, depending on the type of array modulation. Such solitons can be stable; they acquire specific triangular shapes and notably broaden with increase of gain/loss level. Our results illustrate how spatial array modulation that breaks PT-symmetry "locally" can be used to control the specific location of dissipative solitons forming in the array.