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This study introduces an efficient numerical method for finding diffraction anomalies, which are crucial for manipulating light and electromagnetic waves. The new technique simplifies the discovery of these anomalies by solving nonlinear eigenvalue problems.

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Area of Science:

  • Electromagnetism
  • Optics
  • Computational Physics

Background:

  • Diffraction anomalies occur when outgoing waves in certain channels vanish upon interaction with periodic structures.
  • Examples include zero reflection, zero transmission, and perfect absorption, which are valuable for controlling electromagnetic waves and light.
  • Finding these anomalies is challenging due to their dependence on specific frequencies, wave vectors, and material parameters, often requiring difficult numerical searches.

Purpose of the Study:

  • To develop an efficient numerical method for computing diffraction anomalies.
  • To overcome the difficulties associated with standard numerical and iterative methods in finding these anomalies.
  • To provide a systematic approach for identifying all diffraction anomalies within a given frequency range.

Main Methods:

  • The study employs nonlinear eigenvalue formulations for scattering anomalies.
  • Nonlinear eigenvalue problems are solved using a contour-integral method.
  • The method is demonstrated with numerical examples using periodic arrays of cylinders.

Main Results:

  • An efficient numerical method for computing diffraction anomalies has been successfully developed.
  • The contour-integral method effectively solves the nonlinear eigenvalue problems associated with anomalies.
  • The presented numerical examples validate the efficacy of the new method.

Conclusions:

  • The developed method offers an efficient way to compute diffraction anomalies.
  • This advancement facilitates the discovery and utilization of anomalies for wave manipulation.
  • The technique is applicable to various periodic structures, including arrays of cylinders.