The Investigation of Surplus of Energy and Signal Propagation at Time-Domain Waveguide Modes

Abstract

Classical waveguide theory has been developed bearing on Bernoulli's product method which results in separation of space and time variables in Maxwell's equations. The time-harmonic waveguide modes have been stated mathematically for transmitting signals along the waveguides. As a starting point, present studies on transverse-electric (TE) and transversemagnetic (TM) waveguide modes with previous results are taken and exhibited in an advanced form. They have been obtained within the framework of an evolutionary approach to solve Maxwell's equations with time derivative. As a result every modal field is obtained in the form of a product of vector functions of transverse coordinates and modal amplitudes. The modal amplitudes which are the functions of axial coordinate z and time t are the central matter of this study. The amplitudes are generated by a potential which is governing by Klein-Gordon equation (KGE). The KGE has remarkable properties of symmetry which has great importance in our analytical studies of the transient modes. Ultimately, in this study, a time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are shown for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via Airy functions.