All-purpose finite element formulation for arbitrarily shaped crossed-gratings embedded in a multilayered stack.

Area of Science:

• Electromagnetics and Optics
• Computational Physics
• Materials Science

Background:

• Calculating light diffraction by complex structures is computationally challenging.
• Existing methods may lack accuracy or efficiency for arbitrarily shaped gratings in multilayered stacks.
• Understanding energy balance in diffractive optics is crucial for device design.

Purpose of the Study:

• To introduce a novel finite element method (FEM) formulation for vector field diffraction calculations.
• To adapt FEM for arbitrarily shaped crossed-gratings within multilayered stacks under oblique incidence.
• To validate the method's accuracy and analyze its computational performance.

Main Methods:

• Developed a novel FEM formulation for vector field diffraction.
• Applied the method to arbitrarily shaped crossed-gratings in multilayered stacks.
• Calculated complete energy balance (transmission, reflection, losses) from field maps.
• Validated accuracy against independent methods and tested on a torus crossed-grating.

Main Results:

• The proposed FEM formulation accurately calculates diffracted vector fields.
• Complete energy balance was successfully deduced, demonstrating method's completeness.
• Method independence from grating shape was illustrated with a torus crossed-grating.
• Remarkable convergence was observed, even with coarse meshes, indicating efficiency.

Conclusions:

• The novel FEM formulation provides an accurate and efficient tool for analyzing light diffraction by complex gratings.
• The method's robustness and convergence properties make it suitable for various optical applications.
• This work advances the computational capabilities for designing and understanding diffractive optical elements in multilayered systems.