A general transmission line model of Maxwell´s equations in cylindrical co-ordinates

From Maxwell´s equations we present a fundamental work which allows the exact synthesis of a transformation method for modeling Maxwell´s equations in cylindrical coordinates of a uniform cylindrical dielectric thin layer to a set of transmission line equations. The equations are exact and general and do not require the assumption of exponential variation in time or in z directions. This concept allows the use of circuit theory in determining the electromagnetic properties of many wave phenomena. In many cases use of circuit theory is more convenient and offers well understood analogies than direct application of Maxwell´s equations. This transformation models a dielectric waveguide which can be described by a series of successive coaxial cylindrical layers by a succession of connected T-circuits. As an example, the guided modes of a waveguide can be found by determining the resonance frequency of the circuits. What is new in this work is the general analysis which allows also determination of the response of the waveguide to arbitrary wave shape axial excitation. The variation of the Electric field across the cylindrical waveguide due to this excitation can also be derived from knowledge of the refractive index distribution. Inversely, the synthesis of the refractive index profile can be obtained from knowledge of the radial Electric field of the waveguide. This inversion is made particularly easy with this analysis. Other very important waveguide properties such as mode dispersion can easily be obtained with this technique, without the need for curve fitting and numerical differentiation. This method offers direct use of analytic equations for determining the dispersion recursively directly from the mode propagation constant. The method is powerful and has application potential in many other fields such as in antennas, and in physics.