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Accelerated algorithm for calculating spectra of aperiodic gratings. / Frumin, L. L.; Chernyavsky, A. E.

In: Computer Optics, Vol. 49, No. 4, 6, 07.2025, p. 573-578.

Research output: Contribution to journal › Article › peer-review

Harvard

Frumin, LL & Chernyavsky, AE 2025, 'Accelerated algorithm for calculating spectra of aperiodic gratings', Computer Optics, vol. 49, no. 4, 6, pp. 573-578. https://doi.org/10.18287/2412-6179-CO-1594

APA

Frumin, L. L., & Chernyavsky, A. E. (2025). Accelerated algorithm for calculating spectra of aperiodic gratings. Computer Optics, 49(4), 573-578. [6]. https://doi.org/10.18287/2412-6179-CO-1594

Vancouver

Frumin LL, Chernyavsky AE. Accelerated algorithm for calculating spectra of aperiodic gratings. Computer Optics. 2025 Jul;49(4):573-578. 6. doi: 10.18287/2412-6179-CO-1594

Author

Frumin, L. L. ; Chernyavsky, A. E. / Accelerated algorithm for calculating spectra of aperiodic gratings. In: Computer Optics. 2025 ; Vol. 49, No. 4. pp. 573-578.

BibTeX

@article{221b8352111e45d39de5750fd997e6d9,
title = "Accelerated algorithm for calculating spectra of aperiodic gratings",
abstract = "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{\textquoteright}s second-order accuracy and its high computational speed, in accordance with the estimates obtained.",
keywords = "algorithm, aperiodic gratings, scattering problem, transfer matrix",
author = "Frumin, {L. L.} and Chernyavsky, {A. E.}",
note = "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. 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{\textquoteright}in for their interest in the work and useful discussions.",
year = "2025",
month = jul,
doi = "10.18287/2412-6179-CO-1594",
language = "English",
volume = "49",
pages = "573--578",
journal = "Computer Optics",
issn = "0134-2452",
publisher = "Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS",
number = "4",

}

RIS

TY - JOUR

T1 - Accelerated algorithm for calculating spectra of aperiodic gratings

AU - Frumin, L. L.

AU - Chernyavsky, A. E.

N1 - 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. 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.

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.scopus.com/record/display.uri?eid=2-s2.0-105009014977&origin=inward&txGid=ad47023a49b65d8f735a8b8cb26c1ec9

UR - https://www.mendeley.com/catalogue/28871fb8-d82c-38eb-a849-9104056775fe/

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

M1 - 6

ER -

ID: 68178044