Structure-Adaptive Topology Optimization Framework for Photonic Band Gaps with TE-Polarized Sources

TL;DR

This paper introduces a structure-adaptive topology optimization framework for designing two-dimensional photonic crystals with photonic band gaps for TE polarization, utilizing both $ ext{Γ}$-point and full Brillouin zone integration schemes.

Contribution

It extends previous TM polarization methods to TE polarization, employing scalar magnetic and vector electric field formulations for comprehensive photonic crystal design.

Findings

Successfully recovers 2D photonic crystals for TE polarization.

Supports frequency-dependent optical response and targeted optimization.

Encourages inherently binarized designs.

Abstract

Leveraging our structure-adaptive topology optimization framework based on the integration of the photonic density of states over a frequency window for the TM polarization of light [see A. Bahulikar et al., arXiv:2411.09165 (2025)], we show that the $\Gamma$-point and full Brillouin zone integration schemes can also recover two-dimensional photonic crystals for TE polarization. For the $\Gamma$-point formalism, we employ the scalar magnetic field formulation of the electromagnetic wave equation with independent sources polarized in the x and y directions. For the full Brillouin zone formalism, we employ the vector electric field formulation of the electromagnetic wave equation, again with independent sources polarized in the x and y directions. This work can simultaneously treat frequency-dependent optical response, allow for targeted optimization for a given frequency and reciprocal lattice vector pair, and inherently encourage binarized designs.