I am interested in ``quantum wires'', very narrow 2-dimensional structures in which electrons can move freely. One can prove that a quantum wire with a bend must generally have at least one bound state. We have calculated the properties of such bound states in quantum wires.
Electrons in quantum wires have exactly the same properties as EM fields in rectangular waveguides. If a quantum wire contains a bound state, a waveguide of the same shape will have "confined" electric fields, localized EM modes which exist below the cutoff frequency for the waveguide.
With John Carini (IU) and Dave Murdock (Tenn Tech),
we have done experiments to study the properties of confined
EM fields in bent waveguides. These states had never been
seen before, despite many decades of research on waveguide
The plot shows experimental (upper) and theoretical (lower) graphs of the EM energy density for a "confined" EM mode in a waveguide with two bends. What is plotted is the frequency shift of this confined state, as a small metal ball is moved around the waveguide.