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 -