Topological reorganization of near-field energy flow governing scattering transitions in subwavelength rectangular grooves

TL;DR

This work addresses how near-field energy transport shapes the concave-to-convex far-field scattering transition in subwavelength rectangular grooves. It employs a rigorous TM modal formulation to analyze the complex field and the time-averaged Poynting vector $\langle \mathbf{S} \rangle$, revealing a topological reorganization of near-field energy flow. In the subwavelength regime, the emergence and migration of Poynting-vector singularities, particularly dominant vortices, steer energy toward the groove axis and produce convex far-field patterns. The study provides a robust, topology-based framework for understanding and engineering nanoscale energy transport in plasmonic and nanoantenna structures, with implications for metasurfaces and sensing platforms.

Abstract

The scattering of electromagnetic waves by subwavelength rectangular grooves has been extensively studied, yet its physical interpretation has largely relied on field-intensity distributions. Here we demonstrate that the transition from concave to convex scattering profiles observed as the groove width approaches the wavelength is governed by a topological reorganization of the near-field energy flow. Using a rigorous modal formulation for TM-polarized fields, we analyze the complex electromagnetic field and the associated time-averaged Poynting vector. We show that reducing the groove width induces the creation, migration, and annihilation of Poynting-vector singularities, including vortices and saddle points, leading to a qualitative restructuring of electromagnetic energy transport. This topological transition redirects the local energy flux and manifests as a convex scattering profile in the far field. The results establish a direct link between near-field energy topology and far-field scattering, providing a unified physical interpretation of subwavelength groove scattering.

Figures (5)

• Figure 1: Schematic of the rectangular groove geometry and definition of parameters.
• Figure 2: Comparison between intensity-based and energy-flow descriptions in the near field.
• Figure 3: Topological transition of the near-field energy flow as a function of normalized groove width.
• Figure 4: Evolution of the near-field energy-flow topology as a function of the normalized groove width $w/\lambda$. The diagram summarizes the number and type of Poynting-vector singularities observed in the near field, revealing discrete topological regimes separated by the emergence or annihilation of vortex--saddle pairs.
• Figure 5: Connection between near-field energy-flow topology and far-field scattering. (a) Normalized near-field Poynting vector $\langle \mathbf{S} \rangle/S_0$ in the vicinity of the groove aperture (spatial coordinates normalized to the wavelength), illustrating the redirection of energy toward the groove axis in the subwavelength regime. (b) Corresponding far-field scattering pattern shown as normalized angular intensity $I(\theta)/I_{\max}$, exhibiting a convex profile as a direct consequence of the near-field energy-flow reorganization. .