Mode Analysis of the Optical and the Microwave Waveguides Using Electromagnetic Energy Flow Lines

Abstract

Planar optical waveguides are the key devices in construction of integrated optical circuits and semiconductor lasers. In microwave engineering practice the most common type of waveguide for high power transmission is the microwave rectangular waveguide. The analysis of the physical processes in these waveguides, which determine their behavior, is necessary for their purposeful use. The usual and the most common approach in the analysis of optical and microwave waveguides is the use of a rigorous numerical treatment of the equations derived from Maxwell’s equations and corresponding boundary conditions [1, 2]. The numerical results are usually obtained from commercially available software (such as [3]), and it is relatively easy to produce a large amount of numerical data. Although such results are most often very precise, the drawback of this method is that it does not supply simple and transparent interpretation of the results obtained and of their physical meaning. This is especially evident if one wants to see the space energy distribution in the modes of various characters. This drawback can be diminished by construction of energy flow lines for a specific problem we are trying to solve. The method of electromagnetic (EM) flow lines has been used in [4] in the context of interpretation of two slit diffraction of a planar EM wave. EM flow lines were suggested recently in [5] as photon paths in analogy with the massive particle trajectories in Bohmian quantum mechanics. In this paper we construct the EM energy flow lines with the help of the Poynting vector, obtained from the analytical expression for electric and magnetic fields for two cases, namely the optical slab waveguide and the microwave rectangular waveguide.