Spectral points and stop-pass effects in waveguides with obstacles

The blocking and passing effects are analyzed and discussed based on integral-equation mathematical models for elastic waveguides with different nature obstacles. Since the mathematical background of various wave phenomena is, generally, the same, the results obtained should be of interest for electromagnetic and coupled piezo-elastic wave propagation as well. The resonance effects take place in the course of guided wave diffraction by local obstacles. These phenomena, which are also known as trapping-mode effects, are usually accompanied by a sharp stopping of the wave energy flow along the waveguide and, consequently, in deep and narrow gaps in the frequency plots of transmission coefficients. Those effects are closely connected with the allocation of nearly real natural frequencies (resonance poles) in the complex frequency plane, which are, in fact, the spectral points of the related boundary value problems. With several obstacles, the number of such poles increases in parallel with the number of defects. On the other hand, a resonance wave passing in narrow bands associated with the poles is also observed. Thus, while a resonance response of a single obstacle in a two-dimensional (2D) waveguide works as a blocker, the waveguide with several obstacles becomes opened in narrow vicinities of nearly real spectral poles, just as it is known for one-dimensional (1D) waveguides with a finite number of scatterers.