Fresnel's Formulas in Time Domain

Abstract

A time-spatial representation of Fresnel's formulas is obtained that permits description of the interaction of complex electromagnetic signals with a flat interface between dielectric media to be made in the time domain. This description is made by means of integral equations and includes the case when the boundary is nonstationary, for example, if it is created at some instant in time. The solutions of these equations give the transmitted and reflected signals by virtue of resolvent integral operators that take into account the structure of the field polarization. These three-dimensional (3-D) operators are derived for the case when the medium in one of the two half-spaces changes its permittivity and acquires a conductivity. The weight factors in the kernels of these operators are simply the analogues of Fresnel's formulae. The oblique incidence of a plane, monochromatic, wave on the flat boundary of the medium whose permittivity changes abruptly in time is also considered. It is shown that the transient accompanies the transformed field in contrast to the case of the normal incidence, when the transformed field only consists of the monochromatic secondary waves.Index Terms-Integral equation method, nonstationary electromagnetism, time-varying medium.

Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media

“…Finally, another type of Fresnel's formulae accounting for a time-dependent spatial reflection of waves from nonstationary interfaces are derived in Refs. [49,57]. Using relations (13), we can establish the energy balance between the transformed waves (9) and the medium if we, without loss of generality, assume that the dielectric permittivity (or the refractive index) suffer an abrupt change at the time t s = 0.…”

Role of boundary in electomagnetic transients caused by medium time-varyation

“…The phenomenon becomes more complex when the time varying medium has boundaries. The transformation of a plane wave on a plane boundary acquires new features, especially in the case of an inclined incidence of the initial wave onto the medium boundary [4]. Naturally, the boundary shape plays an essential role in these phenomena.…”

Investigation of 2-D electromagnetic transients in a circular cylinder with time discontinuity in permittivity via the resolvent method

“…The TDVIE approach is an established and fully explicit method that is well suited for the analysis of ultra-short electromagnetic pulse transients in media with time-varying properties. Since its introduction (Nerukh and Khizhnyak 1991) the TDVIE method has been significantly enhanced and developed (Nerukh et al 2001Fedotov et al 2003;Nerukh 2004). However to date the TDVIE method has predominantly been applied to structures with parallel planar boundaries.…”