Observation of localization reversal and harmonic generation in nonlinear non-Hermitian skin effect

The interplay between band topology and material nonlinearity gives rise to a variety of novel phenomena, such as topological solitons and nonlinearity-induced topological phase transitions. However, most previous studies fall within the Hermitian regime, leaving the impact of nonlinearity on non-Hermitian topology seldom explored. Here, we investigate the effects of nonlinearity on the non-Hermitian skin effect, a well-known non-Hermitian phenomenon induced by the point-gap topology unique to non-Hermitian systems. We discover a nonlinearity-induced point-gap topological phase transition accompanied by a reversal of the skin mode localization. This phenomenon is experimentally demonstrated in a nonlinear microwave metamaterial, where electromagnetic waves are localized around one end of the sample under a low-intensity pump, whereas at a high-intensity pump, the waves are localized around the other end. We also observe third harmonic generation signal induced by the skin modes, whose spatial distribution consistently shows the localization reversal. Furthermore, we extend our setup to build a nonlinear non-Hermitian Su-Schrieffer-Heeger model with both nonlinearity-induced point-gap and line-gap phase transitions. Our results open a new route towards nonlinear topological physics in non-Hermitian systems and are promising for reconfigurable topological wave manipulation and frequency conversion.