Complex coordinate stretching as a generalized absorbing boundary condition

W. C. Chew, J. M. Jin, E. Michielssen

Research output: Contribution to journalArticlepeer-review


By complex coordinate stretching and a change of variables, it is shown simply that PML is reflectionless for all frequencies and all angles. Also, Maxwell's equations for PML media reduce to ordinary Maxwell's equations with complex coordinate systems. Many closed-form solutions for Maxwell's equations map to corresponding closed-form solutions in complex coordinate systems. Numerical simulations with the closed-form solutions show that metallic boxes lined with PML media are highly absorptive. These closed-form solutions lend a better understanding to the absorptive properties of PML media. For instance, they explain why a PML medium is absorptive when a dielectric or metallic interface extends to the edge to a simulation region where PML media reside. More importantly, the complex coordinate stretching method can be generalized to non-Cartesian coordinate systems, providing absorbing boundary conditions in these coordinate systems.

Original languageEnglish (US)
Pages (from-to)363-369
Number of pages7
JournalMicrowave and Optical Technology Letters
Issue number6
StatePublished - Aug 20 1997


  • Absorbing boundary condition
  • Complex coordinate system
  • Perfectly matched layer

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Electrical and Electronic Engineering

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