Gate controlled resonant widths in double-bend waveguides: Bound states in the continuum

We consider quantum transmission through double-bend $\Pi$- and $Z$-shaped waveguides controlled by the finger gate potential. Using the effective non-Hermitian Hamiltonian approach we explain the resonances in transmission. We show a difference in transmission in the short waveguides that is the result of different chirality in $Z$ and $\Pi$ waveguides. We show that the potential selectively affects the resonant widths resulting in the occurrence of bound states in the continuum.