Spectral element boundary integral method with periodic layered medium dyadic Green's function for multiscale...

Area of Science:

• Computational electromagnetics
• Nano-optics
• Numerical methods

Background:

• Accurate simulation of electromagnetic phenomena in nano-optical devices is crucial.
• Conventional methods often struggle with efficiency and accuracy for layered media.
• Need for advanced numerical solvers to handle multiscale problems in nanophotonics.

Purpose of the Study:

• To propose a novel numerical solver for efficient and accurate simulation of nano-optical applications.
• To combine the spectral element-boundary integral (SEBI) method with a matrix-represented periodic layered medium dyadic Green's function.
• To implement surface integral equations (SIEs) as radiation boundary conditions for domain truncation.

Main Methods:

• Formulation of the periodic layered medium dyadic Green's function in matrix representation.
• Implementation of SIEs for radiation boundary conditions on top and bottom computation domains.
• Discretization of the interior computation domain using vector wave equations and Bloch periodic boundary conditions with mixed-order Gauss-Lobatto-Legendre basis functions in the SEBI method.

Main Results:

• The proposed SEBI method avoids discretization of top and bottom layered media, significantly improving efficiency over conventional techniques.
• Numerical results demonstrate fast convergence across the entire computation domain.
• The solver exhibits good performance for typical multiscale nano-optical applications.

Conclusions:

• The developed numerical solver offers a highly efficient and accurate approach for nano-optical simulations.
• The combination of SEBI and the specialized Green's function provides a robust method for complex layered structures.
• This work advances computational capabilities for designing and analyzing next-generation nanophotonic devices.