On normal congruence of surfaces and position vector of optical fiber by electromagnetic wave vectors

Abstract

The present paper gives an extraordinary view of the normal congruence of surfaces including the s−lines and b−lines in terms of electromagnetic wave vectors in ordinary space. Frenet–Serret frame of given a space curve are described in E3 in terms of anholonomic coordinates which includes eight parameters. Using the expression the Frenet frames and electromagnetic wave vectors on the curve with a linear transformation in terms of each other, the changes of t⃗, E⃗ and B⃗ between any two points in the tangential and binormal direction along with the curved path σ=σ(s,n,b) are obtained in terms of geometric phase β, respectively. Moreover, the solution of the systems of differential equations of optical fiber with position vector is obtained. Intrinsic geometric properties of this normal congruence of surfaces are obtained in terms of electromagnetic wave vectors. The conditions under which electromagnetic and magnetic vectors satisfy Maxwell’s equations given electric charge and current densities are investigated. Finally, an application is stated to investigate a normal congruence of surfaces by using electromagnetic wave vectors. Also, illustrations of polarization and magnetic field vector of EM wave are given.