The sharpness-induced mode stopping and spectrum rarefication in waveguides with periodically corrugated walls

Abstract

Starting from the rigorous excitation equation, the propagation of waves through a 2D waveguide with the periodically corrugated finite-length insert is examined in detail. The corrugation profile is chosen to obey the property that its amplitude is small as compared to the waveguide width, whereas the sharpness of the asperities is arbitrarily large. With the aid of the method of mode separation, which was developed earlier for inhomogeneous-in-bulk waveguide systems [Waves Random Media 10, 395 (2000)], the corrugated segment of the waveguide is shown to serve as the effective scattering barrier whose width is coincident with the length of the insert and the average height is controlled by the sharpness of boundary asperities. Due to this barrier, the mode spectrum of the waveguide can be substantially rarefied and adjusted so as to reduce the number of extended modes to the value arbitrarily less than that in the absence of corrugation (up to zero), without changing considerably the waveguide average width.

Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic

“…For this reason the impact of randomly (as well as regularly, see Ref. [30]) rough boundaries 14 upon electron transport in wires of finite cross section is much more intricate and strong as compared with the influence of bulk irregularities. In further analysis, along with function (34) which is defined within the conductor rough segment, the trial Green function will be required with the "source" point (z ′ ) positioned at one end of the interval L whereas the observation point (z) on the other.…”

“…Yet, some kind of localization was revealed in Ref. [30], though its nature is notably different from the localization of Anderson origin. The essence of localization disclosed in Ref.…”

“…The essence of localization disclosed in Ref. [30] is that the modes extended in the infinite terminals of the wave-guiding system on strengthening their scattering within the modulated segment are sequentially transformed to the evanescent-type modes, thus being excluded from the set of those modes the energy is transported through. As the boundary corrugation profile is sharpened, the wave conductance of such systems is reduced in modulated-step fashion, where on each of the plateaus the conductance is subject to oscillations of Fabry-Pérot (FP) origin.…”

“…Such a reduction may be regarded as a particular "separation of variables" for systems that were for long believed to be non-integrable. Recent applications of this technique to the problem of wave transport through a waveguide segment with periodically modulated side walls [30] made it possible to ascertain that, firstly, in systems with corrugated boundaries the prevailing mechanism of corrugation-induced wave scattering is the gradient mechanism, the intensity of which is determined by the asperity sharpness rather than by their amplitude. Secondly, the technique applied in Ref.…”

“…Secondly, the technique applied in Ref. [30] has allowed us to describe purely analytically the scattering caused by asperities of any sharpness, not by smooth asperities only. This, in turn, permitted us to discover the peculiar sharpness-induced mode cut-off effect, whose essence consists in that all extended modes of the side-modulated waveguide are sequentially transformed into the modes of evanescent type on sharpening the modulation profile, thus becoming localized right at the entrance to the waveguide rippled section.…”