Fig. 1. Sketch for necklaces formed by the repetition of identical PT-symmetric dimers. (a) Necklace where intradimer couplings are larger than interdimer couplings, gd>gN, and repetition factor N. (b) Standard PT-symmetric dimer, N=1; (c) PT-symmetric plaquette, N=2; and (d) necklace with repetition factor N=3.

Fig. 2. Real (solid lines) and imaginary (dashed lines) parts of eigenvalues as a function of the gain to interdimer coupling ratio, γ/gN, for arrays of coupled PT-symmetric dimers with homogeneous intra- and inter-dimer couplings, gd=gN with repetition factor (a) N=2 and (b) N=3, and for inhomogeneous couplings, gd=gN/2, with repetition factor (c) N=2 and (d) N=3.

Fig. 3. (a) Waveguide geometry used in the finite element simulation and electric field input for replication of the (b) first and (c) second effective dimers. In (b) and (c), red corresponds to an in-phase beam and blue corresponds to a π-dephased beam.

Fig. 4. Renormalized power propagation, Pj,k(z), showing output replication for (a), (b) homogeneous and (c), (d) inhomogeneous couplings. The dots represent finite element propagation and the lines the analytic coupled mode approximation. See text for details.

Fig. 5. (a) Waveguide geometry used in the finite element simulation and electric field input for replication of the (b) first and (c) second effective dimers. In (b) and (c), red corresponds to an in-phase beam, orange corresponds to a (2π/3)-dephased beam, and yellow corresponds to a (4π/3)-dephased one.

Fig. 6. Renormalized power propagation, Pj,k(z), showing output replication for (a), (b) homogeneous and (c), (d) inhomogeneous couplings. The dots represent finite element propagation and the lines the analytic coupled mode approximation. See text for details.