Effect of evanescent modes on the transmission and group delay of a wave

The transmission and group delay are investigated for two kinds of waveguide systems. The systems consist of a middle section with distinct cutoff frequency to model the potential barrier or well in quantum mechanics. The cutoff frequency of the middle section is controlled by either the cross-sectional geometry or the properties of loaded material. Modal analysis is introduced because the electromagnetic waves have their own boundary conditions in virtually three-dimensional waveguide systems. The modal analysis is calculated and the results are compared with the simulations using a full wave solver. In the oversized/undersized waveguides case, the calculated results converge quickly as the number of modes of consideration is increased. The higher-order modes which are generally evanescent modify the phase of the fundamental mode and subsequently affect the wave characteristics. The underlying physics is manifested using a multiple-reflection model. This study shows that the evanescent modes are critical for a microwave system with geometrical discontinuity and suggests that it might also play an important role in quantum mechanics.