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Accelerated algorithm for calculating spectra of aperiodic gratings
L.L. Frumin 1, A.E. Chernyavsky 1,2

1 Institute of Automation and Electrometry SB RAS,
630090, Russia, Novosibirsk, Academician Koptyug Avenue, 1;
2 Novosibirsk State University,
630090, Russia, Novosibirsk, Pirogov Street, 2

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DOI: 10.18 287/2412-6179-CO-1594

Страницы: 573-578.

Язык статьи: English.

Аннотация:
To compute the spectrum of aperiodic Bragg gratings, we address a direct scattering problem for the Helmholtz equation. Numerically, this problem necessitates the calculation of transfer matrix products, which involves multiple multiplications of matrix elements – polynomials that depend on the spectral parameter of the problem. We propose an accelerated algorithm to solve the scattering problem with second-order accuracy. This algorithm leverages the integral approach for discretization, a duplication strategy, the convolution theorem, and the fast Fourier transform. The computational complexity of this approach is asymptotically O(N log2N) arithmetic operations (multiplications) for a discrete grid of size N. Numerical simulations corroborate the algorithm’s second-order accuracy and its high computational speed, in accordance with the estimates obtained.

Ключевые слова:
aperiodic gratings, scattering problem, algorithm, transfer matrix.

Благодарности
This work was supported by the Russian Science Foundation (project No. 24-22-00183). The authors are grateful to Professor D.A. Shapiro and Professor V.P. Il’in for their interest in the work and useful discussions.

Citation:
Frumin LL, Chernyavsky AE. Accelerated algorithm for calculating spectra of aperiodic gratings. Computer Optics 2025; 49(4): 573-578. DOI: 10.18 287/2412-6179-CO-1594.

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