Numerical Analysis of Topological Edge States in Photonic Crystals with Defect Engineering

Abstract

Topological photonics has emerged as an important research area in optical physics because it enables electromagnetic waves to exhibit propagation characteristics associated with topological phases of matter. In particular, topological edge states can provide strongly confined and comparatively robust optical transport along interfaces between photonic structures with different topological properties. This paper presents a numerical framework for investigating topological edge states in two-dimensional photonic crystals and examines how deliberately engineered structural defects modify their spectral and spatial properties.

A two-dimensional dielectric photonic crystal is considered as the basic platform. The photonic band structure is obtained by solving the frequency-domain Maxwell eigenvalue problem using a plane-wave expansion or finite-element formulation. Topological characteristics are evaluated through Berry curvature and an appropriate topological invariant, while an interface between two photonic domains with different topological phases is introduced to generate localized edge states. Defects are subsequently introduced by modifying the radius, position, refractive index, or arrangement of selected dielectric elements near the interface. The resulting structures are analyzed in terms of band dispersion, localization length, transmission, field intensity, and sensitivity to structural perturbations.

The analysis predicts that the unperturbed interface supports modes inside the projected bulk band gap. Moderate defect engineering can shift the edge-state frequency, alter its localization length, and generate mode splitting or hybridization without necessarily destroying the bulk gap. Defects that preserve the relevant topological protection are expected to produce substantially smaller backscattering than conventional non-topological waveguide defects, whereas perturbations that break the protecting symmetry or couple counter-propagating states can significantly degrade robustness. Recent numerical and experimental studies support the use of defects as a means of tuning topological photonic states rather than treating defects solely as unwanted imperfections. The proposed framework provides a basis for designing tunable topological waveguides, compact optical filters, sensors, and robust photonic integrated circuits.