Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry

We propose a family of {\it local} $\mathcal{P}\mathcal{T}$-symmetric photonic lattices with transverse index gradient $\omega$, where the emergence of {\it stable} Bloch-Zener oscillations are controlled by the degree of non-Hermiticity $\gamma$ of the lattice. In the exact $\mathcal{P}\mathcal{T}$-symmetric phase we identify a condition between $\omega$ and $\gamma$ for which a wavepacket self -imaging together with a cascade of splittings and giant recombinations occurs at various propagation distances. The giant wavepacket recombination is further enhanced by introducing local impurities.