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L’ubomír Šumichrast

Abstract

Scalar and vector potential as well as the electromagnetic field of a moving point charge is a nice example how the application of symbolic functions (distributions) in electromagnetics makes it easier to obtain and interpret solutions of otherwise hardly solvable problems.

Open access

L’ubomír Šumichrast

In the circuit theory the concept of the impulse response of a linear system due to its excitation by the Dirac delta function δ(t) together with the convolution principle is widely used and accepted. The rigorous theory of symbolic functions, sometimes called distributions, where also the delta function belongs, is rather abstract and requires subtle mathematical tools [1-4]. Nevertheless, the most people intuitively well understand the delta function as a derivative of the (Heaviside) unit step function 1(t) without too much mathematical rigor. In the previous part [5] the concept of the impulse response of linear systems was approached in a unified manner and generalized to the time-space phenomena in one dimension (transmission lines). Here the phenomena in more dimensions (static and dynamic electromagnetic fields) are treated. It is shown that many formulas in the field theory, which are often postulated in an inductive way as results of the experiments, and therefore appear as “deux ex machina” effects, can be mathematically deduced from a few starting equations.

Open access

L’Ubomír Šumichrast

In the circuit theory the concept of the impulse response of a linear system due to its excitation by the Dirac delta function ƍ(t) together with the convolution principle is widely used and accepted. The rigorous theory of symbolic functions, sometimes called distributions, where also the delta function belongs, is rather abstract and requires subtle mathematical tools [1], [2], [3], [4]. Nevertheless, the most people intuitively well understand the delta function as a derivative of the (Heaviside) unit step function 1(t) without too much mathematical rigor. The concept of the impulse response of linear systems is here approached in a unified manner and generalized to the time-space phenomena in one dimension (transmission lines), as well as in a subsequent paper [5] to the phenomena in more dimensions (static and dynamic electromagnetic fields).

Open access

L’ubomír Šumichrast

Abstract

Some aspects of the numerical modeling of the electromagnetic waves propagation using the “complex-envelope” finitedifferences formulation in the one-dimensional case are here reviewed and discussed in comparison with the standard finitedifferences in time-domain (FDTD) approach. The main focus is put on the stability and the numerical dispersion issues of the “complex envelope” explicit and implicit methods

Open access

L’ubomír Šumichrast and Jaroslav Franek

Abstract

Propagation of a two-dimensional spatio-temporal electromagnetic beam wave is analysed. In parabolic (paraxial) approximation the exact analytical results for a spatio-temporal Gaussian impulse can be obtained. For solution of the full wave equation the numerical simulation has to be used. The various facets of this simulation are discussed here.

Open access

L’ubomír Šumichrast and Rastislav Dosoudil

Abstract

In the recently published short paper author deals with the derivation of the scalar potential pertaining to the point charge as well as of the vector potential pertaining to the point current. He shows his alternative approach and compares it to the ”traditional” methods commonly used in textbooks. Here we want to show that use of the generalised functions (symbolic functions, distributions) in the domain of electromagnetic field theory provides more straightforward and more rigorous approach to the problem.

Open access

Jozefa Červeňová, Rastislav Dosoudil, Jaroslav Franek and L’ubomír Šumichrast

Abstract

The total internal reflection of a beam wave on planar dielectric boundary in presence of a nearby dielectric slab is thoroughly investigated together with its influence on the Goos-Hänchen shift and on the beam-wave-profile deformation.

Open access

L’ubomír Šumichrast, Jaroslav Franek, Rastislav Dosoudil and Jozefa Červeňová

Abstract

Total internal reflection of plane waves is a well-known phenomenon. Some new aspects of the numerical treatment of the total internal reflection phenomena, concerning the beam-wave, are discussed.