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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 15 — Jul. 21, 2008
  • pp: 11376–11392

The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers

Ardavan F. Oskooi, Lei Zhang, Yehuda Avniel, and Steven G. Johnson  »View Author Affiliations

Optics Express, Vol. 16, Issue 15, pp. 11376-11392 (2008)

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Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).

© 2008 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(160.5298) Materials : Photonic crystals

ToC Category:
Diffraction and Gratings

Original Manuscript: May 6, 2008
Revised Manuscript: May 29, 2008
Manuscript Accepted: May 29, 2008
Published: July 14, 2008

Ardavan F. Oskooi, Lei Zhang, Yehuda Avniel, and Steven G. Johnson, "The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers," Opt. Express 16, 11376-11392 (2008)

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