Transmission resonances and zeros in quantum waveguide systems with attached resonators

Transmission phenomena in quantum waveguide structures are studied by examining the transmission amplitude in the complex-energy plane. We find that, similar to double-barrier resonant tunneling, there are transmission poles in the complex-energy plane for quantum waveguide structures which contain quasibound states in attached t-stub resonators. In contrast to double-barrier resonant tunneling, however, we find that the quantum-wire networks also possess transmission zeros (antiresonances), which always occur on the real-energy axis. The existence of transmission zeros is a characteristic feature of a quantum waveguide system with attached resonators, but is absent for double-barrier resonant tunneling, which contains the resonant cavity as part of the transmission channel. We demonstrate that each quasibound state of the resonantly coupled quantum waveguide system leads to a zero-pole pair of the transmission amplitude in the complex-energy plane. The previously noted resonance-antiresonance behavior of the transmission probability, which leads to its sharp variation as a function of energy, can be understood in terms of these zero-pole pairs.