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 -