We investigate the topological bound modes in a binary optical waveguide array with anti-parity-time (PT) symmetry. The anti-PT-symmetric arrays are realized by incorporating additional waveguides to the bare arrays, such that the effective coupling coefficients are imaginary. The systems experience two kinds of phase transition, including global topological order transition and quantum phase transition. As a result, the system supports two kinds of robust bound modes, which are protected by the global topological order and the quantum phase, respectively. The study provides a promising approach to realizing robust light transport by utilizing mediating components.

We theoretically investigate the Goos-Hänchen (GH) shifts of optical beam in a defective photonic crystal composed of dielectric multilayers and graphene. The system is non-Hermitian and possesses exceptional points (EPs) as the scattering matrix becomes defective at the zero points of reflection. The reflective wave at EPs experiences an abrupt phase change and there the eigenvalues of scattering matrix coalesce. The GH shifts are extremely large near EPs in parametric space composed of dielectric refractive index and incident angle. The positive and negative maxima of GH shifts could be as high as 10³ times of the incident wavelength. The direction of GH shifts switches at EPs and the EPs position can be readily controlled by the chemical potential of graphene. Moreover, the GH shifts should remarkably change as the incident waves impinge on the structure from opposite directions. The study of GH shifts in the graphene incorporated multilayers may find great applications in highly sensitive sensors.

The non-Hermitian skin effect (NHSE), which involves an extensive number of bulk modes collapsing to open boundaries as skin modes, unveils a variety of unprecedented topological physics. However, achieving this effect in photonic waveguides has been challenging due to the difficulty of establishing the required non-Hermitian asymmetric couplings. Here, we investigate NHSE in photonic waveguide arrays via Floquet engineering. By periodically driving the waveguides along the propagation direction, we create an artificial gauge field (AGF) that interacts with on-site dissipation, yielding non-Hermitian asymmetric coupling and eventually giving rise to NHSE. The localization direction of NHSE is tunable by AGFs and can be detected from light propagation. In particular, we explore the interplay between NHSE and dynamical localization, whereby NHSE is suppressed by dynamical localization due to the collapse of quasienergies. Our proposed method can be extended to explore the non-Bloch Su-Schrieffer–Heeger model, with potential implications for steering light transport with the aid of NHSE.

We investigate the topological edge modes in a rhombic waveguide array with imaginary coupling, which is realized by incorporating auxiliary waveguide between the coupled waveguides. By suitably tuning both real and imaginary couplings to generate an effective flux, a non-Hermitian analog of Aharonov-Bohm (AB) cage is formed as the band structures become flat and coalesce into third-order exceptional points (EPs). We show the array can support gapped topological edge modes, which can be explained by mapping the system Hamiltonian into the square root of an anti-parity-time (PT) -symmetric waveguide array. In contrast to the linear power increase of bulk modes, the propagation of edge modes can be conserved or exponentially amplified depending on which termination is initially excited. Our study provides a promising way to realizing robust light propagation.