Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8351Research ArticleThe Simplest Geometrization of Maxwell’s EquationsKulyabovD STelecommunication Systems Departmentdharma@sci.pfu.edu.ruKorolkovaA VTelecommunication Systems Departmentakorolkova@sci.pfu.edu.ruSevastyanovL ATelecommunication Systems Departmentleonid.sevast@gmail.comPeoples’ Friendship University of Russia15022014211512508092016Copyright © 2014,2014For research in the field of transformation optics and for the calculation of optically inhomogeneous lenses the method of geometrization of the Maxwell equations seems to be perspective. The basic idea is to transform the coefficients of constitutive equations, namely the dielectric permittivity and magnetic permeability into the effective geometry of space-time (and the vacuum Maxwell equations). This allows us to solve the direct and inverse problems, that is, to find the permittivity and magnetic permeability for a given effective geometry (paths of rays), as well as finding the effective geometry on the base of dielectric permittivity and magnetic permeability. The most popular naive geometrization was proposed by J. Plebanski. Under certain limitations it is quite good for solving relevant problems. It should be noted that in his paper only the resulting formulas and exclusively for Cartesian coordinate systems are given. In our work we conducted a detailed derivation of formulas for the naive geometrization of Maxwell’s equations, and these formulas are written for an arbitrary curvilinear coordinate system. This work is a step toward building a complete covariant geometrization of the macroscopic Maxwell’s equations.Maxwell’s equationsconstitutive equationsMaxwell’s equations geometrizationRiemann geometrycurvilinear coordinatesPlebanski’s geometrizationуравнения Максвелламатериальные уравнения Максвеллагеометризация уравнений Максвеллариманова геометриякриволинейные координатыгеометризация Плебанского