Journal of Nanotechnology and Materials Science | Volume 2 | Issue 2 | 2015-09-03

ANALYTICAL STUDY OF ELECTROMAGNETIC WAVE BEHAVIOUR IN FCC LATICE PERIODIC MATERIAL: BLOCH TH EOREM OF MAXWELL’S EQUATION

Emmanuel I. Ugwu

Abstract

In this work, we studied the behaviour of electromagnetic wave as it propagates through face centered cubic(fcc) lattice material with periodic structure using Bloch theorem which was analyzed by one dimensional wave equation solved by method of separation of variables. Bloch theorem was linearised and superposed on the wave function as a modulator to the free wave function constituting real part and imaginary part. The phonon dispersion relation within the long wave limit and the implication of the imposed Bloch function on the free electron model was analyzed for different wavelength such as, ultraviolent, visible and infrared wavelengths within the first Brilouin zone in conjunction with the real and imaginary part of the wave function respectively coupled with the behaviour of the dispersion relation.

Keywords: Electromagnetic wave, Bloch theorem, dispersion Periodic material, Analysis, Brilouin zone, Wave propagation, Wavelength, Free electron