Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Accelerated algorithm for calculating spectra of aperiodic gratings. / Frumin, L. L.; Chernyavsky, A. E.
в: Computer Optics, Том 49, № 4, 07.2025, стр. 573-578.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Accelerated algorithm for calculating spectra of aperiodic gratings
AU - Frumin, L. L.
AU - Chernyavsky, A. E.
N1 - 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. Frumin L. L., Chernyavsky A. E. Accelerated algorithm for calculating spectra of aperiodic gratings. / L. L. Frumin, A. E. Chernyavsky // Computer Optics. - 2025. - Т. 49. - № 4. - С. 573 - 578. DOI: 10.18 287/2412-6179-CO-1594.
PY - 2025/7
Y1 - 2025/7
N2 - 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.
AB - 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.
KW - algorithm
KW - aperiodic gratings
KW - scattering problem
KW - transfer matrix
UR - https://www.mendeley.com/catalogue/28871fb8-d82c-38eb-a849-9104056775fe/
UR - https://computeroptics.ru/?ysclid=mcledr4zb9388169277
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105009014977&origin=inward&txGid=ad47023a49b65d8f735a8b8cb26c1ec9
U2 - 10.18287/2412-6179-CO-1594
DO - 10.18287/2412-6179-CO-1594
M3 - Article
VL - 49
SP - 573
EP - 578
JO - Computer Optics
JF - Computer Optics
SN - 0134-2452
IS - 4
ER -
ID: 68178044