Bound states in waveguides and bent quantum wires. I. Applications to waveguide systems

It has been shown that in quantum wires which contain bends there will be one or more bound states for electrons placed in such systems. Bound states have been observed in quantum wires, but detailed mapping of such states is difficult. However, there is a one-to-one correspondence between wave functions of free electrons in two-dimensional (2D) systems, and electric fields of TE modes in rectangular waveguides with the same cross section as the 2D system. We therefore construct bent waveguides, find the frequencies at which confined EM fields occur, and map out the electromagnetic energy density there. We compare the experimental results with theoretical predictions of bound state energies and eigenfunctions. The geometry has been chosen to correspond to two-dimensional systems for which quantum wire experiments have been carried out. In such systems, we can predict the number and location of the bound states in the system; in addition, we can predict the electric and magnetic fields for the confined TE modes in this system. We show very good agreement between our predictions and experiment for bent waveguides in this geometry.