Topological directed amplification
arXiv:2206.11879 · doi:10.1103/PhysRevA.106.053513
Abstract
A phenomenon of topological directed amplification of certain initial perturbations is revealed theoretically to emerge in a class of asymptotically stable skin-effect lattices described by nonnormal Toeplitz operators with positive ``numerical ordinate" . Nonnormal temporal evolution, even in the presence of global dissipation, is shown to manifest a counterintuitive transient phase of edge-state amplification -- a behavior, drastically different from the asymptote, that spectral analysis of 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 {\it 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 . It is further predicted that the interplay between nonnormality and nonlinearity in a skin-effect laser array can facilitate narrow-emission spectra with scalable stable-output power.
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