The solution is obtained for determining electric and magnetic field energy densities formed by a twodimensional array of spherical particles located in a light-absorbing medium near their surface, at normal incidence of a plane electromagnetic wave. It is based on the statistical description of spatial distribution of particles in an array using the radial distribution functions, quasi-crystalline approximation of the theory of multiple scattering of waves, and multipole expansion of fields and tensor Green’s function in terms of vector spherical wave functions. The amplification of fields in such a system is considered relative to their values in the medium without introducing an array of particles. The influence of the absorption index of the medium and the type of spatial ordering of the array on this effect was investigated. The calculation results are in excellent agreement with the data from numerical simulation using the finite element method.

1. Lalanne P., Chen M., Rockstuhl C., Sprafke A., Dmitriev A., Vynck K. Disordered optical metasurfaces: basics, properties, and applications. Advances in Optics and Photonics, 2025, vol. 17, no. 1, pp. 45–113. https://doi.org/10.1364/aop.537175

2. Novotny L., Hecht B. Principles of Nano-Optics. Cambridge, Cambridge University Press, 2012. 564 p. https://doi.org/10.1017/cbo9780511794193

3. Loiko N. A., Miskevich A. A., Loiko V. A. Scattering and absorption of light by a monolayer of spherical particles under oblique illumination. Journal of Experimental and Theoretical Physics, 2020, vol. 131, pp. 227–243. https://doi.org/10.1134/s1063776120060060

4. Loiko N. A., Miskevich A. A., Loiko V. A. Optical characteristics of a monolayer of identical spherical particles in an absorbing host medium. Journal of the Optical Society of America A, 2023, vol. 40, no. 4, pp. 682–691. https://doi.org/10.1364/josaa.476765

5. Loiko V. A., Miskevich A. A., Hubarevich A., Loiko N. A. Statistical method to describe the electromagnetic field on the surface of spherical particle of a 2D array. Journal of the Optical Society of America A, 2025, vol. 42, no. 3, pp. 334–343. https://doi.org/10.1364/josaa.538231

6. Lax M. Multiple scattering of waves. II. The effective field in dense systems. Physical Review, 1952, vol. 85, art. 621. https://doi.org/10.1103/physrev.85.621

7. Loiko V. A., Miskevich A. A., Loiko N. A. Disorder effect in a 2D array of spherical particles on the electromagnetic field on their surface. Journal of the Optical Society of America A, 2025, vol. 42, no. 12, pp. 1890–1899. https://doi.org/10.1364/josaa.565216

8. Ziman J. M. Models of Disorder: the Theoretical Physics of Homogeneously Disordered Systems. Cambridge, 1979. 525 p.

9. Ivanov A. P., Loiko V. A., Dick V. P. Propagation of Light in Densely Packed Disperse Media. Minsk, 1988. 191 p. (in Russian).

10. Miskevich A. A., Loiko V. A. Coherent transmission and reflection of a two-dimensional planar photonic crystal. Journal of Experimental and Theoretical Physics, 2011, vol. 113, pp. 1–13. https://doi.org/10.1134/s1063776111050153

11. Loiko N. A., Miskevich A. A., Loiko V. A. Polarization of light scattered by a two-dimensional array of dielectric spherical particles. Journal of the Optical Society of America B, 2021, vol. 38, no. 9, pp. C22–C32. https://doi.org/10.1364/josab.424426

12. Jin Y., Puckett J. G., Makse H. A. Statistical theory of correlations in random packings of hard particles. Physical Review E, 2014, vol. 89, art. 052207. https://doi.org/10.1103/physreve.89.052207

13. Babenko V. A., Astafyeva L. G., Kuzmin V. N. Electromagnetic Scattering in Disperse Media: Inhomogeneous and Anisotropic Particles. Berlin, 2003. 434 p.

14. Palik E. D., ed. Handbook of Optical Constants of Solids. San Diego, 1985, vol. 1. 804 p.

15. Loiko N. A., Miskevich A. A., Loiko V. A. Resonant absorption of light by a two-dimensional imperfect lattice of spherical particles. Journal of the Optical Society of America A, 2022, vol. 39, no. 12, pp. C36–C44. https://doi.org/10.1364/josaa.469733