Journal of Radio Electronics. eISSN 1684-1719. 2026. ¹3
Full text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2026.3.15
Self-consistent equation method
for weak scattering analysis
on two-dimensional lattices of dielectric spheres
A.Yu. Vetuzhsky
Institute of Physical Materials Science of the Siberian Branch of the RAS,
670047, Russia, Ulan-Ude, Sakhyanovoy st., 6
The paper was received February 27, 2026.
Abstract. The article proposes and provides a detailed analysis of a self-consistent equations method designed for studying the diffraction of electromagnetic waves on photonic crystal structures, which are a periodic two-dimensional lattice of dielectric spheres. The modeling was performed within the scalar approximation, which significantly simplified the mathematical formalism for systems characterized by weak dielectric constant contrast and subwavelength sizes of scattering particles (sphere radius smaller than the incident radiation wavelength). A key advantage of the developed approach is the explicit accounting of multiple scattering effects between all lattice elements. This ensures efficient determination of scattered wave amplitudes in the far-field zone and allows for the analysis of conditions for the formation of photonic band gaps (stopbands and passbands). To validate the theoretical model, a detailed comparison of calculated spectral characteristics, particularly transmission coefficients, with the results of rigorous numerical modeling performed by the finite element method was conducted. It is shown that the self-consistent equations method provides high accuracy in the long-wavelength part of the spectrum, when the radiation wavelength exceeds the structure period, as well as in the case of small values of the dielectric constant of the sphere material. Furthermore, this method imposes no restrictions on the ratios between the period of element arrangement in the lattice and the sphere radius and remains functional even with very dense structure packing. The work defines the limits of the method's applicability, associated with an increase in refractive index contrast and a decrease in the wavelength-to-lattice-period ratio, providing clear criteria for its use. The developed approach can be successfully applied for rapid preliminary analysis, parameter optimization, and design of flat photonic crystal structures and metasurfaces based on dielectric spheres, especially under conditions of weak scattering and moderate contrast of optical properties, which are of practical interest for modern optical devices.
Key words: photonic crystals, sphere diffraction, self-consistent equation method, subwavelength particles, refractive index.
Financing: The work was carried out within the framework of the state assignment of the Institute of Physical Materials Science of the Siberian Branch of the Russian Academy of Sciences No. FWSF-2024-0008
Corresponding author: Vetluzhsky Alexander Yurievich, vay@ipms.bscnet.ru
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For citation:
Vetluzhsky A.Yu. Self-consistent equation method for weak scattering analysis on two-dimensional lattices of dielectric spheres. // Journal of Radio Electronics. – 2026. – ¹. 3. https://doi.org/10.30898/1684-1719.2026.3.15 (In Russian)