A Tight-binding Approach for Computing Subwavelength Guided Modes in Crystals with Line Defects

In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an eigenvalue problem for the Helmholtz equation with high-contrast parameters. By employing layer potential theory on unbounded domains, we characterize the subwavelength frequencies via the quasi-periodic capacitance matrix. Our main contribution is the proof of exponential decay of the off-diagonal elements of the associated full and quasi-periodic capacitance matrices. These decay properties provide error bounds for the banded approximation of the capacitance matrices, thereby enabling a tight-binding approach for computing the spectral properties of subwavelength resonators with non-compact defects. Various numerical experiments are presented to validate the theoretical results, including applications to topological interface modes.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-12-05

• Fields of study

  Mathematics, Physics

• Identifiers
  arXiv 2512.05370
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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