## arXiv Analytics

### arXiv:2206.11879 [physics.optics]AbstractReferencesReviewsResources

#### Topological directed amplification

Published 2022-06-23Version 1

A phenomenon of topological directed amplification of certain initial perturbations is theoretically revealed to emerge in a class of asymptotically stable skin-effect photonic lattices described by nonnormal Toeplitz operators $H_g$ with positive numerical ordinate $\omega(H_g)>0$. Nonnormal temporal evolution, even in the presence of global dissipation, is shown to exhibit a counterintuitive transient phase of edge-state amplification--a behavior, drastically different from the asymptote, that spectral analysis of $H_g$ fails to directly reveal. A consistent description of the effect is provided by the general tool of pseudospectrum, and a quantitative estimation of the maximum power amplification is provided by the Kreiss constant. A recipe to determine an optimal initial condition that will attain maximum amplification power is given by singular value decomposition of the propagator $e^{-i H_g t}$. Finally, it is predicted that the interplay between nonnormality and nonlinearity in a skin-effect laser array can exponentially enhance stable-emission power compared to a normal laser array.