Bound states and resonances in waveguides and quantum wires

Abstract

We present experimental and theoretical results on bound states in quantum wires (narrow, twodimensional quantum channels). We study rectangular systems of constant width, varying the bend angle. This system is realized by propagation of TE-mode microwaves in flat rectangular waveguides; resonant frequencies for absorption of power are measured for various bend angles, and compared with theoretical results for bound-state (resonant) eigenvalues.

Weakly bound states in heterogeneous waveguides

“…In particular, Exner and Seba [5] have proved that the existence of a bound state for an electron confined to a planar waveguide, with curvature decaying at infinity and obeying Dirichlet boundary conditions at the border; Goldstone and Jaffe [6] have proved that an electron confined to an infinite tube of constant cross section, in two or more dimensions, has always a bound state, when the tube is not perfectly straight. The effect of bound states in infinite non-straight waveguides has been studied in [7,8,9,10,11,12]. It is worth mentioning a recent pedagogical article by Londergan and Murdock [13], that illustrates different numerical methods for the solutions of confined systems, in particular two-dimensional waveguides.…”

Manifestations of vortices during ultracold-atom propagation through waveguides

“…The direct experimental observation of a resonant dip in the wave transmission that was observed using bent electromagnetic waveguides [29] would be virtually impossible to observe in the propagation of clouds of atoms through a microstructured waveguide bend. Our interest was driven by whether the dramatic local phase characteristics seen in plane-wave calculations across resonance energies would leave a measurable signature on a wave packet.…”

Confined modes in two-dimensional tubes

“…27 Carini et al 16,17 subsequently solved this by mode-matching methods which we review here; they also carried out experimental studies of modes in bent waveguides and found the confined mode below threshold frequency, using the exact analogy between confined modes in a 2D tube and modes in a bent waveguide of the same shape.…”

“…Remembering the exact analogy between tubes and waveguides, this also implies that bent waveguides will possess a confined mode below the cutoff frequency. Carini et al 16,17 demonstrated that a waveguide in the form of an L-shaped tube possessed a confined mode below the cutoff frequency, at just the location predicted by numerical calculations.…”