Projection operator method for biperiodic diffraction gratings with anisotropic/bianisotropic generalizations.

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Materials Science

Background:

• Simulating optical diffraction from biperiodic gratings is crucial for various photonic applications.
• The normal-vector method, while useful, faces challenges with sign reversals and discontinuities.
• Developing robust numerical methods is essential for accurate grating analysis.

Purpose of the Study:

• To introduce a novel "projection operator" method for simulating optical diffraction.
• To address and overcome the limitations of the conventional normal-vector method.
• To provide a more versatile and easily implementable approach for grating simulations.

Main Methods:

• A projection operator, defined by the normal vector, is interpolated over the grating volume.
• This approach avoids direct interpolation of the normal vector, mitigating issues like sign reversals.
• The method is designed for straightforward implementation and extensibility.

Main Results:

• The projection operator method successfully simulates optical diffraction from biperiodic gratings.
• It effectively circumvents the sign reversal and discontinuity problems of the normal-vector method.
• Numerical examples demonstrate the method's accuracy and applicability to various grating geometries.

Conclusions:

• The projection operator method offers a significant advancement in simulating optical diffraction from biperiodic gratings.
• This technique provides a more robust and flexible alternative to existing methods.
• The method's extensibility to anisotropic and bianisotropic materials broadens its potential applications.