Analytic Solution for Cylinder Waves

Abstract

The two field strengths E_ix and H_iy of Eq.(2.1-31) in a point z = 0, y excite cylinder waves—or rather half-cylinder waves—in medium 1 and 2 according to Fig.2.2-5 and 2.2-7,The coordinates of cylinder waves are usually denoted r,ϕ, z but the cylinder axes in Fig.2.2-5 are in the direction of the x-axis rather than the z-axis, which calls for the coordinates r,ϕ, x. A further notational problem is caused by the letter r that was used for ‘reflected’, as in E _rx Following common practice the r denoting reflected is set in roman while the r denoting the radial variable is set in italic. Fig3.1-1 shows r,ϕ, x for reflected and transmitted waves. We note that the x-axis points out of the paper plane toward the viewer.