Improved Dirichlet-to-Neumann map method for scattering by circular cylinders on a lattice

Area of Science:

• Photonics
• Computational Electromagnetics
• Condensed Matter Physics

Background:

• Two-dimensional photonic crystals are crucial for manipulating light.
• Analyzing wave scattering in these structures is computationally intensive.
• Existing methods like FEM and multipole methods have limitations.

Purpose of the Study:

• To develop a more efficient numerical method for analyzing wave scattering in 2D photonic crystals.
• To improve the Dirichlet-to-Neumann (DtN) map method for lattice-based structures.
• To enhance computational efficiency by leveraging the inherent symmetry of photonic crystals.

Main Methods:

• Development of an improved Dirichlet-to-Neumann (DtN) map method.
• Construction of specialized DtN maps for boundary and corner unit cells.
• Utilizing the method of fictitious sources for enhanced DtN map computation.

Main Results:

• The improved DtN map method demonstrates enhanced efficiency compared to traditional methods.
• The method effectively analyzes wave scattering in 2D photonic crystal devices.
• Specialized DtN maps reduce computational load by avoiding internal cell computations.

Conclusions:

• The enhanced DtN map method provides a computationally efficient approach for photonic crystal analysis.
• This method is particularly advantageous for structures with underlying lattice periodicity.
• The technique offers a valuable tool for the design and simulation of photonic devices.