Resolvent Convergence and Patch Approximation for Subwavelength Guided Modes in Non-Periodic Systems of High-Contrast Resonators
This work provides a computationally efficient and rigorously justified approach for simulating guided modes in non-periodic high-contrast resonator systems, which is important for researchers and engineers working with such materials.
This paper presents a fast algorithm for computing guided modes in non-periodic high-contrast resonator systems, where traditional Floquet-Bloch theory is not applicable. The method reduces the continuous spectral problem to a discrete eigenvalue problem and introduces a patch approximation for efficient computation, validated through various examples.
This paper develops, analyzes, and validates a fast algorithm for computing guided modes within bent interfaces and non-periodic defects in high-contrast resonator crystals, where the Floquet--Bloch theory is not applicable. We first establish the resolvent convergence of the governing continuous operator to the discrete capacitance operator. This result rigorously justifies the reduction of the continuous spectral problem to a discrete eigenvalue problem. Then, we develop a truncation scheme of the discrete operator, named the patch approximation, and derive a rigorous error estimate for the patch approximation. Finally, we validate the accuracy and efficiency of our scheme through various examples. Our framework provides a general, computationally efficient, and rigorously justified approach to simulate guided modes in non-periodic systems of high-contrast resonators.