Bound-state evolution of Dirichlet waveguide with Neumann window(s) in transverse electric fields

The influence of electric field on a straight Dirichlet waveguide with Neumann window(s) of arbitrary length L is studied theoretically for 2D and 3D geometries. The energy spectrum for the corresponding bound states was obtained and their dependence on was analysed. At low , the boundary of the window(s) influenced the properties of the particle contrary to the high case, where the energies and localization of particle were seen similar in all the geometries. The critical lengths Lcr, at which higher excited state emerges into the continuum, at different were found and their behavior was explained qualitatively. It was found that at high , the critical lengths of Dirichlet-Neumann boundary window approach the Neumann-Neumann boundary window. This is due to the increase in the fundamental propagation threshold of transverse modes in the wall and window region. On the other hand, the Neumann-Dirichlet boundary window showed an opposite behavior. Furthermore, the polarization of ground state was obtained for different geometries. It was proved that at small L, the polarization reduces to its 1D case. A mathematical treatment and semi classical explanation was provided. Comparative analysis of the 2D and 3D geometries reveals their qualitative similarity and quantitative differences.