Skin solitons.

Recently, the concept of skin effect has gained considerable attention in the context of non-Hermitian photonics. The experimental realization of Hatano-Nelson systems in optical coupled cavities has provided the opportunity to consider the effect of optical nonlinearity. In this work, we probe the interplay between Kerr nonlinearity and non-Hermiticity in a Hatano-Nelson lattice. In particular, we examine the relation between self-focusing and the skin effect under single-channel excitation. Moreover, we numerically identify skin soliton solutions, which exhibit power threshold and spatial asymmetry.

Higher order exceptional points in infinite lattices.

One of the hallmarks of non-Hermitian photonics is the existence of unique degeneracies, the so-called higher order exceptional points (HEPs). So far, HEPs have been examined mostly in finite coupled systems. In this paper, we present a systematic way to construct infinite optical waveguide lattices that exhibit exceptional points of higher order. The spectral properties and the sensitivity of these lattices around such points are investigated by employing the method of pseudospectra.

Equal-intensity waves in non-Hermitian media.

A novel type of waves is examined in the context of non-Hermitian photonics. We can identify a class of complex guided structures that support localized paraxial solutions whose intensity distribution is exactly the same as the intensity of a corresponding solution in homogeneous media (free or bulk space). In other words, intensity-wise the two solutions are identical and their phase is different by a factor exp[iθ(x,y)]. The non-Hermitian potential is determined by the phase θ, as well as the amplitude and phase of the bulk space solution that contributes to the imaginary and real part of the potential, respectively. That way we can connect the plane waves and Gaussian beams of free space to constant-intensity waves and what we call the equal-intensity waves (EI waves) in non-Hermitian media. Such a relation allows us to study three different physical problems: Propagating EI waves inside random media, interface lattice solitons, and moving solitons in photonic waveguide structures with free-space characteristics. The relation of EI waves to unidirectional invisibility and Bohmian photonics is also examined.