Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach

Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help of an effective potential approach the occurrence of bound states in sharply bent quantum wires. In particular, we compute the bound states, study the features of the transition from a bound to an unbound state caused by the variation of the bending angle and determine the critical bending angles at which such a transition takes place. The predictions are confirmed by calculations based on a conventional numerical method as well as experimental measurements of the spectra and electric field intensity distributions of electromagnetic waveguides

Bound states in open coupled asymmetrical waveguides and quantum wires

The behavior of bound states in asymmetric cross, T and L shaped configurations is considered. Because of the symmetries of the wavefunctions, the analysis can be reduced to the case of an electron localized at the intersection of two orthogonal crossed wires of different width. Numerical calculations show that the fundamental mode of this system remains bound for the widths that we have been able to study directly; moreover, the extrapolation of the results obtained for finite widths suggests that this state remains bound even when the width of one arm becomes infinitesimal. We provide a qualitative argument which explains this behavior and that can be generalized to the lowest energy states in each symmetry class. In the case of odd-odd states of the cross we find that the lowest mode is bounded when the width of the two arms is the same and stays bound up to a critical value of the ratio between the widths; in the case of the even-odd states we find that the lowest mode is unbound up to a critical value of the ratio between the widths. Our qualitative arguments suggest that the bound state survives as the width of the vertical arm becomes infinitesimal.Comment: 11 pages, 19 figures, 3 table