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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

A theoretical investigation is made for the problem of electromagnetic field focussing by wide angle spherical reflector receiving obliquely incident plane waves of linearly polarized monochromatic radiation. The Maslov's method has been applied to determine the electromagnetic fields in the caustic region of the reflector. High frequency field expression which contains caustic region is converted into caustic free field expression by transforming the situation into hybrid domain. The high-frequency field solution that contains the caustic region is obtained from geometrical optics. The defect in high frequency solution due to geometrical optics is overcome by Maslov's method. Two cases of polarization of the incident wave have been considered, namely, (1) with the field parallel and (2) perpendicular to the meridional plane of incidence. The numerical computations are made to study the behavior of field intensity in caustic region using Maslov's method. The analytical and numerical results obtained from Maslov's method are also compared with method of angular spectrum which are in agreement.

Electromagnetic field in the caustic region of a spherical reflector under oblique incidence using Maslov's method

Diffraction of an electromagnetic plane wave from a slit in an impedance plane placed at the interface of two different media, has been formulated rigorously. Both the principal polarizations are considered. The method of analysis is Kobayashi Potential (KP). To determine the unknown weighting functions, boundary conditions are imposed which resulted into dual integral equations (DIEs). These DIEs are solved by using the discontinuous properties of Weber- Schafheitlin's integrals. The resulting expressions are then expanded in terms of Jacobi's polynomials. The problems are then, reduced to matrix equations with infinite number of unknowns whose elements are expressed in terms of infinite integrals. These integrals are hard to solve analytically. The integrals contain poles for particular values of surface impedance and are solved numerically. Illustrative computations are given for far diffracted fields and other physical quantities of interest. To check the validity of our work, we compared the far field patterns with those of obtained through Physical Optics (PO). The agreement is good.

/pdf/diffraction-from-a-slit-in-an-impedance-plane-placed-at-the-11n0um5o11.pdf

Diffraction from a slit in an impedance plane placed at the interface of two semi-infinite half spaces of different media

Quasi-static analysis of electromagnetic scattering from a chiral sphere placed in another chiral medium is presented in this manuscript. Several special cases, for host medium and/or sphere, are also addressed. Expressions of electric and magnetic fields for inside and outside the space occupying the sphere are derived and discussed.

Quasi-static analysis of scattering from a chiral sphere in chiral medium

The focusing of electromagnetic waves from a quartic inhomogeneous chiro-slab is examined, using Maslov’s method. Analytic field expressions are derived for the transmission coefficients at the interfaces and numerical computations are made to determine the field behavior around the caustic point of the chiro-slab. The effects of chirality parameter, permittivity and permeability on the intensity of the field around caustic point of the chiro-slab are also discussed. The results obtained through this method are shown to be in good agreement with those obtained from Huygens Kirchhoff’s integral.

Qaisar Abbas Naqvi

Papers

Electromagnetic field in the caustic region of a spherical reflector under oblique incidence using Maslov's method

Diffraction from a slit in an impedance plane placed at the interface of two semi-infinite half spaces of different media

Quasi-static analysis of scattering from a chiral sphere in chiral medium

Focusing of Electromagnetic Wave from Quartic Inhomogeneous Chiro-Slab

Scattering from a topological insulator circular cylinder coated with DNG/MNG/ENG metamaterials