A note on eigenvectors of Maxwell’s equations in cylindrical coordinates with regard to constructing cylindrical FDTD schemes utilizing the spectral domain methodology

Abstract

In this paper, we discuss the form of eigenvectors and functions of cylindrical Maxwell’s equations and their related cylindrical wave equations, respectively. We begin our discussion by briefly presenting the well-known forms of these entities, when Cartesian coordinates are used. This way we establish a frame of reference for the introduction of the eigenvectors and functions of Maxwell’s equations and their related wave equations when written in cylindrical coordinates. We derive the expressions for the eigenvectors and functions using separation of variables applied to both the wave equations and Maxwell’s equations. We discuss 1D and 2D cases. The need to lay down one of the basic prerequisites for using the spectral domain methodology, that is the knowledge of the spectral equations of Maxwell’s and the wave equations, is what prompted this discussion.

Keywords:

• cylindrical coordinates
• Maxwell’s equations
• wave equation
• eigenvectors
• FDTD
• spectral domain
• higher order schemes
• nonstandard FDTD