Investigating tunneling-like transmission of solitons through a non-Hermitian metamaterial

Non-Hermiticity in quantum and classical lattices is commonly obtained via two main mechanisms: the addition of gain and loss at the

lattice sites, or by inducing non reciprocal couplings between the sites. The resulting spectrum, usually complex-valued, sheds new light on

the originally Hermitian concepts of topological invariants, bulk-boundary correspondence and its breakdown, and the associated topological

protection of boundary modes. The resulting wave dynamics leads to new regimes of wave propagation, such as accelerated waves with

growing amplitudes, unidirectional invisibility and cloaking, coherent absorption and more. For systems that are non-Hermitian due to nonreciprocity,

the wave propagation is usually amplified in one direction and attenuated in the other. This inherent unidirectional dynamics is

related to the celebrated skin effect, which leads to accumulation of modes at the lattice boundary. Recently, it was shown by the authors

that peculiar wave dynamics can be supported at the intersection of Hermitian and non-Hermitian lattices. Specifically, a tunneling-like

phenomenon occurs when connecting two non-Hermitian chains with mirrored nonreciprocity. A wave that hits the non-Hermitian interface

boundary completely disappears from the entire interface, and reemerges on its opposite side. In this work, we derive this non-Hermitian

tunneling phenomenon for nonlinear wave propagation in a metamaterial, both quantum and classical, with cubic nonlinearity. We explore

whether solitons can be tunneled through the non-Hermitian interface similarly to the linear system wavepackets.