Vertical mode expansion method for numerical modeling of biperiodic structures

Area of Science:

• Photonics and Nanophotonics
• Computational Electromagnetics
• Materials Science

Background:

• Periodic photonic structures are crucial in optics and photonics.
• Fabrication often results in structures with material properties varying along one spatial dimension.
• Analyzing light scattering in these structures requires efficient computational methods.

Purpose of the Study:

• To present two variants of the vertical mode expansion method (VMEM) for biperiodic structures.
• To adapt VMEM for structures containing cylindrical objects with circular or general cross sections.
• To enhance the analysis of light scattering in complex periodic photonic systems.

Main Methods:

• Utilizing cylindrical wave expansions and boundary integral equations.
• Formulating the three-dimensional problem into two-dimensional (2D) Helmholtz equations.
• Developing techniques to address challenges related to periodicity in biperiodic structures.

Main Results:

• Successfully applied VMEM to biperiodic structures with cylindrical components.
• Demonstrated the method's ability to handle general cross sections.
• Achieved efficient and accurate 2D formulations for light scattering analysis.

Conclusions:

• The presented VMEM variants offer a simplified yet powerful approach for analyzing specific photonic structures.
• The method is computationally efficient and accurate, making it competitive for practical applications.
• This work advances the simulation capabilities for periodic photonic devices with cylindrical elements.