Transmission resonances and zeros in quantum waveguide systems with attached resonators

Use of transmission and reflection complex time delays to reveal scattering matrix poles and zeros: Example of the ring graph

We identify the poles and zeros of the scattering matrix of a simple quantum graph by means of systematic measurement and analysis of Wigner, transmission, and reflection complex time delays. We examine the ring graph because it displays both shape and Feshbach resonances, the latter of which arises from an embedded eigenstate on the real frequency axis. Our analysis provides a unified understanding of the so-called shape, Feshbach, electromagnetically induced transparency, and Fano resonances on the basis of the distribution of poles and zeros of the scattering matrix in the complex frequency plane. It also provides a first-principles understanding of sharp resonant scattering features and associated large time delay in a variety of practical devices, including photonic microring resonators, microwave ring resonators, and mesoscopic ring-shaped conductor devices. Our analysis involves use of the reflection time difference, as well as a comprehensive use of complex time delay, to analyze experimental scattering data.

A pressure-based transfer matrix method and measurement technique for studying resonances in flutes and other open-input resonators

This paper provides an alternative formulation of a transfer matrix method (TMM) long used for modeling the passive resonances of wind instruments. In the conventional, impedance-based TMMs, the quantities being evaluated are the acoustic pressure P and the acoustic flow U; in the present pressure-based TMM (a variation of the Heavens matrix method developed for thin film optics), the quantities being evaluated are the amplitudes of the forward-going and backward-going pressure waves, P⁺ and P^-. Power spectra (|P⁺+P^-|² vs frequency) for several types of branched and non-branched open-input resonators are computed and then compared to experimental spectra obtained from a Fourier analysis of the acoustic pressure at a position inside the resonator recorded during excitation by a localized sound source placed just outside the resonator. Agreement is good for both one-end-closed polyvinyl chloride chimney pipes and a modern flute set up with a variety of lip, keywork, and open/closed tonehole configurations, although fits for very short straight tubes appeared to require unphysically high wall losses. Input impedance derived from the computed values of P⁺ and P^- at the flute's embouchure hole appears consistent with directly measured input impedance data in the literature.

Zero-conductance resonances due to flux states in nanographite ribbon junctions

Electronic transport properties through junctions in nanographite ribbons are investigated using the Landauer approach. In the low-energy regime ribbons with zigzag boundary have a single conducting channel of edge states. The conductance as a function of the chemical potential shows a rich structure with sharp dips of zero conductance. Each zero-conductance resonance is connected with a resonant state which can be interpreted as the superposition of two degenerate flux states with Kekule-like current patterns. These zero-conductance dips are connected with a pronounced negative magnetoresistance.