Introduction

This chapter discusses electromagnetic problems and classification, Maxwell equations, guided waves and transverse or longitudinal decomposition, including two Dimensional Helmholtz's equation, and Fourier Transform, DFT, and FFT. Electromagnetic (EM) problems are classified in terms of the equations describing them, with the equations likely to be differential or integral or both. The solution region is usually open so that a solution advances outward indefinitely from initial conditions while always satisfying specified BCs. The Maxwell equations are four differential equations which show classical properties of EM fields by using electric and magnetic field. Guided wave propagation problems can be solved by using simplified equations obtained from the longitudinal and transverse decomposition of Maxwell equations that yield the transverse electric (TE), transverse magnetic (TM), and transverse electromagnetic (TEM) representations under different polarizations, such as perpendicular or parallel polarizations or horizontal or vertical polarizations in application.