{
  "id": "2206.11879",
  "version": "v1",
  "published": "2022-06-23T17:41:30.000Z",
  "updated": "2022-06-23T17:41:30.000Z",
  "title": "Topological directed amplification",
  "authors": [
    "Bikashkali Midya"
  ],
  "categories": [
    "physics.optics",
    "cond-mat.mes-hall"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-23T17:41:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological directed amplification",
      "enhance stable-emission power",
      "attain maximum amplification power",
      "normal laser array",
      "skin-effect laser array"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}