Abstract
We have solved the scattering problem of an s-polarized normally incident wave from a periodic grating made of thin perfectly conducting ribbons. Using the Riemann–Hilbert method, we have obtained an infinite system of equations for the Fourier coefficients of the electric and magnetic fields. The truncated system has been solved numerically, and rapid convergence to the exact solution has been demonstrated. We have calculated the transmission coefficients as functions of two dimensionless parameters (ratio of the grating period to the wavelength and the grating area fill factor). We have obtained the local field distribution and refined the literature data of the transmission coefficient.
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REFERENCES
Xu, Y. et al., Adv. Opt. Mater., 2019, vol. 7, no. 9, p. 1801433.
Homola, J., Chem. Rev., 2008, vol. 108, no. 2, p. 462.
Zhao, Y. et al., Biosens. Bioelectron., 2019, vol. 142, p. 111505.
Shalabney, A. and Abdulhalim, I., Laser Photonics Rev., 2011, vol. 5, no. 4, p. 571.
Sarychev, A.K. et al., Phys. Rev. Appl., 2022, vol. 17, p. 044029.
Frumin, L.L. and Shapiro D.A., Opt. Express, 2020, vol. 28, no. 18, p. 26143.
Efremova, E.A., Perminov, S.V., and Vergeles, S.S., Photonics Nanostruct., 2021, vol. 46, p. 100953.
Nemykin, A.I. et al., Quantum Electron., 2015, vol. 45, no. 3, p. 240.
Nemykin, A., Frumin, L., and Shapiro, D., Sensors, 2022, vol. 22, p. 449.
Chandra, V. and Ranjan, R., Opt. Quantum Electron., 2021, vol. 53, p. 457.
Tamagnone, M. et al., Appl. Phys. Lett., 2012, vol. 101, no. 21, p. 214102.
Salakhova, N.S. et al., Phys. Rev. B, 2021, vol. 104, no. 8, p. 085424.
Kaliberda, M. et al., Int. J. Microwave Wireless Technol., 2019, vol. 11, no. 4, p. 326.
Shestopalov, V.P., Metod zadachi Rimana–Gil’berta v teorii difraktsii i rasprostraneniya elektromagnitnykh voln (Method of the Riemann–Hilbert Problem in the Theory of Diffraction and Propagation of Electromagnetic Waves), Kharkov: Izd. Khark. Univ., 1971.
Vorobyov, S.N. and Lytvynenko, L.M., IEEE Trans. Antennas Propag., 2011, vol. 59, no. 6, p. 2169.
Brovenko, A.V. et al., Prog. Electromagn. Res. B, 2010, vol. 23, p. 109.
Gakhov, F.D., Boundary Value Problems, New York: Elsevier, 2014.
Vainshtein, L.A., Elektromagnitnye volny (Electromagnetic Waves), Moscow: Radio i svyaz’, 1988.
Muskhelishvili, N.I., Singulyarnye integral’nye uravneniya. Granichnye zadachi teorii funktsii i nekotorye ikh prilozheniya k matematicheskoy fizike (Singular Integral Equations. Boundary Value Problems of Function Theory and Some of Their Applications to Mathematical Physics), Moscow: Nauka, 1968.
Rautian, S.G., Vvedenie v fizicheskuyu optiku (Introduction to Physical Optics), Moscow: Librokom, 2009.
Sologub, V.G., USSR Comput. Math. Math. Phys., 1972, vol. 12, no. 4, p. 159.
ACKNOWLEDGMENTS
The authors are grateful to O.V. Belai for fruitful discussion of some aspects in interpretation of results.
Funding
This study was supported by the Russian Science Foundation (project no. 22-22-00633).
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Translated by N. Wadhwa
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Nemykin, A.V., Shapiro, D.A. Diffraction on a Perfectly Conducting Ribbon Grating. Bull. Lebedev Phys. Inst. 50 (Suppl 3), S355–S365 (2023). https://doi.org/10.3103/S1068335623150113
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DOI: https://doi.org/10.3103/S1068335623150113