We investigated the Talbot effect in an anti-parity-time (PT) symmetric synthetic photonic lattice composed of two coupled fiber loops. We calculated the band structures and found that with an increase in the gain-loss parameter, the band transitions from a real spectrum to a complex spectrum. We study the influence of phase in the Hermitian operator on the Talbot effect, and the Talbot effect disappears when the period of the input field is N > 8. Further study shows that the variation of Talbot distance can also be modulated by non-Hermitian coefficients of gain and loss. This work may find significant applications in pulse repetition-rate multiplication, temporal invisibility, and tunable intensity amplifiers.

Synthetic dimensions (SDs) opened the door for exploring previously inaccessible phenomena in high-dimensional space. However, construction of synthetic lattices with desired coupling properties is a challenging and unintuitive task. Here, we use deep learning artificial neural networks (ANNs) to construct lattices in real space with a predesigned spectrum of mode eigenvalues, and thus to validly design the dynamics in synthetic mode dimensions. By employing judiciously chosen perturbations (wiggling of waveguides at desired frequencies), we show resonant mode coupling and tailored dynamics in SDs. Two distinct examples are illustrated: one features uniform synthetic mode coupling, and the other showcases the edge defects that allow for tailored light transport and confinement. Furthermore, we demonstrate morphing of light into a topologically protected edge mode with modified Su–Schrieffer–Heeger photonic lattices. Such an ANN-assisted construction of SDs may advance toward “utopian networks,” opening new avenues for fundamental research beyond geometric limitations as well as for applications in mode lasing, optical switching, and communication technologies.