Computing diffraction anomalies as nonlinear eigenvalue problems

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.