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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Advanced Mathematical Methods for Scientists and Engineers

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Introduction To Electrodynamics

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

/pdf/a-review-of-definitions-for-fractional-derivatives-and-1i2f6bcvo4.pdf

A Review of Definitions for Fractional Derivatives and Integral

https://theory.sinp.msu.ru/~tarasov/PDF/AP2008.pdf

Fractional vector calculus and fractional Maxwell’s equations

Electromagnetic Fields and Waves in Fractional Dimensional Space

An analytical solution is presented for the electromagnetic scattering from a perfect electromagnetic conducting circular cylinder, embedded in the dielectric half-space. The solution utilizes the spectral (plane wave) representations of the fields and accounts for all the multiple interactions between the buried circular cylinder and the dielectric interface separating the two half spaces.

https://www.jpier.org/PIER/pier78/03.07081601.A.Naqvi.pdf

Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space

The wave equation has very important role in many areas of physics. It has a fundamental meaning in classical as well as quantum field theory. With this view, one is strongly motivated to discuss solutions of the wave equation in all possible situations. The wave equation in fractional space can effectively describe the wave propagation phenomenon in fractal media. In this chapter, exact solutions of different forms of wave equation in \(D\)-dimensional fractional space are provided, which describe the phenomenon of electromagnetic wave propagation in fractional space.

On electromagnetic wave propagation in fractional space

The scattering of electromagnetic plane wave by a perfectly conducting disk is formulated rigorously in a form of the dual integral equations (abbreviated as DIE). The unknowns are the induced surface current (or magnetic field) and the tangential components of the electric field on the disk. The solution for the surface current is expanded in terms of a set of functions which satisfy Maxwell's equation for the magnetic field on the disk and the required edge condition. At this step we have used the method of the Kobayashi potential and the vector Hankel transform. Applying the projection solves the rest of a pair of equations. Thus the problem reduces to the matrix equations for the expansion coefficients. The matrix elements are given in terms of the infinite integrals with a single variable and these may be transformed into infinite series that are convenient for numerical computation. The numerical results are obtained for far field patterns, current densities induced on the disk, transmission coefficient through the circular aperture, and radar cross section. The results are compared with those obtained by other methods when they are available, and agreement among them is fairly well.

/pdf/diffraction-of-electromagnetic-wave-by-disk-and-circular-1kh5e4oyh3.pdf

Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane

This work deals with an exact solution of cylindrical wave equation for electromagnetic fleld in fractional dimensional space. The obtained fractional solution is a generalization of the cylindrical wave equation from integer dimensional space to a fractional dimensional space. The resulting theoretical framework can be used to study the phenomenon of electromagnetic wave propagation in any fractal media because fractal media can be described as an ordinary media in a fractional dimensional space. The classical results are recovered from fractional solution when integer dimensional space is considered.

/pdf/an-exact-solution-of-the-cylindrical-wave-equation-for-1dltwnf33i.pdf

Qaisar Abbas Naqvi

Papers

Electromagnetic Fields and Waves in Fractional Dimensional Space

Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space

On electromagnetic wave propagation in fractional space

Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane

An Exact Solution of the Cylindrical Wave Equation for Electromagnetic Field in Fractional Dimensional Space