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Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations

by T. Dohnal and T. Hagstrom

(Report number 2006-12)

Abstract
Extending the general approach for first-order hyperbolic systems developed in [5], we construct PML equations for the mixed-type system governing propagation of optical wave packets in both 1D and 2D Bragg resonant photonic waveguides with a cubic nonlinearity, i.e. the Coupled Mode Equations. We prove that the layer equations are stable, absorbing, and perfectly matched. A number of numerical experiments are performed to assess the layer's performance in both the linear and nonlinear regimes.

Keywords:

@Techreport{DH06_361,
  author = {T. Dohnal and T. Hagstrom},
  title = {Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2006-12},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2006/2006-12.pdf },
  year = {2006}
}

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