Full-vectorial finite element method based eigenvalue algorithm for the analysis of 2D photonic crystals with...

Area of Science:

• Computational physics
• Materials science
• Optics and photonics

Background:

• Two-dimensional (2D) photonic crystals (PCs) exhibit unique optical properties.
• Analyzing anisotropic PCs is challenging due to complex wave mode behavior.
• Standard methods may struggle with arbitrary 3D anisotropy in 2D PCs.

Purpose of the Study:

• To develop a robust numerical algorithm for analyzing 2D PC band structures.
• To address the limitations of mode decoupling in anisotropic photonic systems.
• To provide a tool for accurate simulation of complex photonic crystal designs.

Main Methods:

• A full-vectorial finite element method (FEM) is employed.
• An eigenvalue algorithm is developed, considering all electromagnetic field components.
• The method avoids decoupling wave modes into transverse-electric (TE) and transverse-magnetic (TM) polarizations.

Main Results:

• A full-vectorial matrix eigenvalue equation is derived, using the square of the wavenumber as the eigenvalue.
• The algorithm demonstrates accurate convergence behavior.
• The analysis of 2D PCs with arbitrary anisotropy validates the method's correctness and utility.

Conclusions:

• The developed full-vectorial FEM algorithm accurately analyzes 2D PC band structures with arbitrary 3D anisotropy.
• This approach overcomes limitations of mode decoupling, offering a more comprehensive analysis.
• The algorithm is a valuable tool for theoretical and numerical studies of complex photonic crystals.