Special functions in transferring of energy; a specific case: Airy function

Abstract

Analysis of transferring of transient signals along time-harmonic waveguide modes consists of two main parts. The first one is a modal basis problem. The second one is a modal amplitude problem. Surplus of energy could be observed in process of the signal transferring. In this study, time-domain waveguide modes' surplus of energy is represented. Surplus of energy for the waveguide time-domain waveguide modes are presented via Airy function. The previous works are reviewed for energy and surplus of energy of time-domain modes in the waveguides.