Qaisar Abbas Naqvi

ELECTROMAGNETIC SCATTERING FROM A PERFECT ELECTROMAGNETIC CONDUCTOR CYLINDER BURIED IN A DIELECTRIC HALF-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.

THE WAVE EQUATION AND GENERAL PLANE WAVE SOLUTIONS IN FRACTIONAL SPACE

This work presents the analytical solution of vector wave equation in fractional space. General plane wave solution to the wave equation for flelds in source-free and lossless media is obtained in fractional space. The obtained solution is a generalization of wave equation from integer dimensional space to a non-integer dimensional space. The classical results are recovered when integer-dimensional space is considered.

PLANAR SLAB OF CHIRAL NIHILITY METAMATERIAL BACKED BY FRACTIONAL DUAL/PEMC INTERFACE

Fields inside the chiral nihility slab which is backed by perfect electric conductor are determined. It is noted that both electric and magnetic fields exist inside the grounded chiral nihility slab when it is excited by a plane wave. Electric field inside the slab disappears for excitation due to an electric line source. Magnetic field inside the slab disappears when geometry changes to corresponding dual geometry. Dual geometry means chiral nihility slab backed by perfect magnetic conductor and excited by a magnetic line source. Using fractional curl operator, fields are determined for fractional order geometries which may be regarded as intermediate step between the two geometries which are related through principle of duality. Discussion is extended for chiral nihility slab which is backed by perfect electromagnetic conductor (PEMC).

Analysis of the Fields in Three Dimensional Cassegrain System

High frequency field expressions are derived around feed point of a three dimensional Cassegrain system using the Maslov’s method. Maslov’s method is a systematic procedure for predicting the field in the caustic region. It combines the simplicity of ray theory and generality of the transform method. Numerical computations are made for the analysis of field pattern around the caustic of a Cassegrain system.

AN EXACT SOLUTION OF THE CYLINDRICAL WAVE EQUATION FOR ELECTROMAGNETIC FIELD IN FRACTIONAL DIMENSIONAL SPACE

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.

Differential Electromagnetic Equations in Fractional Space

In this chapter a novel generalization of differential electromagnetic equations in fractional space is provided. Firstly, basic vector differential operators are generalized in fractional space and then using these fractional operators Maxwell’s, Laplace’s, Poisson’s and Helmholtz’s equations have been worked out in fractional space. The differential electromagnetic equations in fractional space, established in this chapter, provide a basis for application of the concept of fractional space in practical electromagnetic wave propagation and scattering problems in fractal media.

Waves in Fractional Dual Planar Waveguides Containing Chiral Nihility Metamaterial

Field expressions for guided waves in three-layered fractional dual planar waveguides are derived by virtue of fractional curl operator. Fractional dual waveguides may be regarded as intermediate steps of the two waveguides which are related through principle of duality. All layers are parallel to the walls of the guide. Middle layer of the waveguide is filled with air however other two layers are filled with chiral nihility metamaterial. Parameter α describes the order of the fractional curl operator. No electric field exists in the chiral nihility layers of the waveguide for α = 0, whereas no magnetic field exists in the chiral nihility layers for α = 1. That is, power flow is confined to only air region of the waveguide for integer values of fractional parameter and corresponding situations have been previously discussed in a published work. In present work, it is noted that, for 0 < α < 1, neither electric field and nor magnetic field is zero inside chiral nihility layers of the fractional dual waveguides. By varying the values of order of the fractional curl operator, one can observe how situation dealing with no electric field changes to situation dealing with no magnetic field. Behavior of fields and power flow in different regions of the fractional waveguides is discussed. It is concluded that, even for fractional dual waveguides, real part of power flow is zero in chiral nihility regions of the waveguides.

Diffraction of Electromagnetic Wave by Disk and Circular Hole in a Perfectly Conducting Plane

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 Maxwells 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.

FRACTIONAL CURL OPERATOR AND FRACTIONAL WAVEGUIDES

Fractional curl operator has been utilized to study the fractional waveguide. The fractional waveguide may be regarded as intermediate step between the two given waveguides. The two given waveguides are related through the principle of duality. Behavior of field lines in fractional waveguides are studied with respect to fractional parameter α.

On electromagnetic wave propagation in fractional 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.