Complex Scaling for the Junction of Semi-infinite Gratings

2025/09/03 by Fruzsina J. Agocs, Agocs, Fruzsina J., Tristan Goodwill +3 · 1 citation
Materials Science · Physics and Astronomy · #30B40 #31A10 #35C15 #35P25 #35Q60 #45B05 #65N80 #65R20 #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Optical Coatings and Gratings #Photonic Crystals and Applications

paper · pdf · doi:10.48550/arxiv.2509.02951

openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present and analyze an integral equation method for the scattering of a non-periodic source from a geometry consisting of two semi-infinite, periodic structures glued together in two dimensions. The two structures may involve a periodic wall, several layers of transmission surfaces with a shared period, or periodic sets of obstacles. This integral equation is posed on the infinite interface between the two periodic structures using kernels built out of the Green's function for each structure. To combat the slow decay of the Green's function, we also show that our integral equation can be analytically continued into the complex plane, where it can be truncated with exponential accuracy. A careful analysis of the domain Green's functions far from the periodic structure is then used to prove that the analytically continued equation is Fredholm index zero. Finally, we show that the solution we generate satisfies a radiation condition and demonstrate an efficient and high order solver for this problem.

Citations

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Cited by

• An efficient boundary integral equation solution technique for solving aperiodic scattering problems from two-dimensional, periodic boundaries

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• A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures