Evolutionary approach in transient electrodynamics problems

Abstract

The approach for handling transient electrodynamics problems based on their description by an integral Volterra equation is presented. The expression for a resolvent of this three‐dimensional space‐time vector equation for the case of a time‐varying dielectric restricted by a plane boundary is derived. Using this approach it is demonstrated that an oblique incidence of a plane monochromatic wave on a boundary of a dielectric whose permittivity changes abruptly in time leads to a formation of a continuous wave spectrum. In the case of a point source of electromagnetic radiation, the presence of a plane boundary leads to a replacement of a convergence point of secondary spherical waves to the mirror symmetrical point. The field in this point has a bounded value, as differentiated from the case of an unbounded medium.

Transient Time-Dependent Electric Field of Dielectric Bodies Using the Volterra Integral Equation in Three Dimensions

“…In principle these modifications can be implemented by merely redefining the functions describing the incident field or the medium polarization [36][37][38][39][40][41]. At each instant of time, the present electric field in (1) is determined via a four-dimensional integral over the spacetime history of the field.…”

“…In theory, the background medium can be of any homogeneous linear non-dissipative material and is chosen here to be free space for convenience. The material considered within the discontinuity region can also be linear, non-linear, dissipative, frequency dependent and/or a combination of them [36][37][38][39][40], however, for simplicity it is considered here to be linear, isotropic and nondissipative of relative permittivity ε 1 . For this case, the associated polarization function is defined by…”

“…In general, the electric field for a 3D volumetric structure satisfies a Volterra integral equation [36][37][38],…”

“…Alternatively, the nodal field sample values can be evaluated in an evolutionary manner, first pioneered by Nerukh et al [36][37][38], and also reported in our previous work for the one-dimensional (1D) [39][40][41][42] and three-dimensional (3D) [43,44] cases. To date, successful investigation of the Volterra TDIE has been demonstrated for the 1D case for various scenarios; illustrating their ability to consider nonlinear, dispersive and plasma-like materials as well as to deal with problems in which the material properties are varying in time [40,41].…”

The transient axially symmetric waves transformation caused by plasma creation in a flat waveguide

“…This problem can be equivalently reduced [l] to the following integral equation for the field 6 E=E,ikE (1) where K is a kemel of integral equation. For the considered problem it is convenient to use the cylindrical coordinates.…”