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<p>We use two methods to study the properties of cylindrical lenses formed by a limited photonic crystal formed by dielectric cylinders. The first method calculates phase velocities in a threedimensional photonic crystal. The effective refractive index is determined. The diffraction field of a homogeneous lens with the found refractive index is investigated. The second method finds a rigorous numerical-analytical solution to the problem of diffraction by a limited photonic crystal. Both the methods are based on the numerical-analytical solution of volumetric integro-differential equations for an unknown field strength inside a dielectric. The applicability of the first approximate method is estimated. The properties of lenses are investigated in a wide frequency range, including the opacity region of the photonic crystal.</p>

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Electrodynamic Analysis of Cylindrical Focusing Devices Made of a Photonic Crystal Formed by Dielectric Cylinders

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • A. M. Lerer,
  • I. V. Donets,
  • S. M. Tsvetkovskaya,
  • M. Danelyan

摘要

We use two methods to study the properties of cylindrical lenses formed by a limited photonic crystal formed by dielectric cylinders. The first method calculates phase velocities in a threedimensional photonic crystal. The effective refractive index is determined. The diffraction field of a homogeneous lens with the found refractive index is investigated. The second method finds a rigorous numerical-analytical solution to the problem of diffraction by a limited photonic crystal. Both the methods are based on the numerical-analytical solution of volumetric integro-differential equations for an unknown field strength inside a dielectric. The applicability of the first approximate method is estimated. The properties of lenses are investigated in a wide frequency range, including the opacity region of the photonic crystal.