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

Abstract

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. Interestingly, we discover a nonlinearity-induced point-gap topological phase transition accompanied by a reversal of the skin mode localization, which is distinct from previous nonlinearity-induced line-gap topological phases. 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. Our results open a new route towards nonlinear topological physics in non-Hermitian systems and are promising for reconfigurable topological wave manipulation.

Figures (4)

• Figure 1: Nonlinear Hatano-Nelson model.a Schematic of the nonlinear Hatano-Nelson model and nonlinearity-induced reversal of skin localization. Here, the $t_{\text{r}(\text{l})}$ represents the rightward (leftward) coupling, which is nonlinear (linear). b,c Plot of the average position of all OBC eigenvectors as functions of intensity $I$ and $\theta$ (and $t_0$), with a fixed $t_0=2.05$ ($\theta=-0.9\pi$). The black dashed line denotes the point-gap closing points obtained from PBC spectra. d-f Plots of eigenvalues on the complex plane under PBC (dots) and OBC (crosses) for the three intensity values highlighted by the blue (d), black (e), and red (f) star makers in b and c. g-i The corresponding OBC eigenvectors for d-f. In all calculations, we take $f_0=-2.5i$, $\kappa_\text{l}=1$, $t_{\infty}=0.2$ and $t_\text{c}=1$.
• Figure 2: Implementation of microwave nonlinear nonreciprocal couplings.a Photograph of a sample consisting of two coupled microwave resonators (labeled "1" and "2"). The lower panel shows the details of the coupling region. b Simulated eigenmode profile of a single microwave resonator. c Simplified tight-binding model for the setup in a. d Experimentally measured (circles) and numerically calculated (curves) response spectra for the setup in a. e Experimentally measured (circles) and numerically calculated (curves) magnitude and phase as a function of input power at 1.056 GHz. The source and probe are at resonators 1 and 2, respectively.
• Figure 3: Observation of nonlinearity-induced reversal of the NHSE via port measurements.a Photograph of a sample composed of 11 identical resonators. The source is connected to the lower ports, whereas the probe is affixed to the upper ports. b-d Measured field distributions at $P=-25$ dBm (b), $P=-4$ dBm (c), and $P=11$ dBm (d). e-g Simulated field distributions at $P=-25$ dBm (e), $P=-4$ dBm (f), and $P=11$ dBm (g). h Calculated PBC (circles) and OBC (crosses) eigenfrequencies and eigenmodes (insets) for the three cases in b-d. Experimentally measured electric field distributions at 1.013 GHz ($|E_z|$ component) with $P=-25$ dBm (i), $P=-5$ dBm (j), and $P=11$ dBm (k).
• Figure 4: Observation of harmonic signals produced by the skin modes.a Measured output spectrum at site 11 under input power $P_{\rm in}=-25$ dBm. b Maximum output power among all sites at fundamental ($f_{\rm in}$) and third ($3f_{\rm in}$) harmonics as a function of increasing input power $P_{\rm in}$. c,d Field localization behavior of fundamental and third harmonics, measured at $P_{\rm in}=-25~\rm{dBm}$ and $P_{\rm in}=25 ~\rm{dBm}$.