Use of Transmission and Reflection Complex Time Delays to Reveal Scattering Matrix Poles and Zeros: Example of the Ring Graph

Abstract

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 is the first use of reflection time difference, as well as the first comprehensive use of complex time delay, to analyze experimental scattering data.

22 pages, 18 figures

References in corpus (18)

• Topological nature of bound states in the radiation continuum
• Coherent Perfect Absorbers: Time-reversed Lasers
• Light fields in complex media: mesoscopic scattering meets wave control
• Classical Analogue of Electromagnetically Induced Transparency with a Metal-Superconductor Hybrid Metamaterial
• Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
• Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption
• Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
• Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers
• Transmission zeros and ultrasensitive detection in complex systems
• Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
• Sensing Small Changes in a Wave Chaotic Scattering System
• Sensor Based on Extending the Concept of Fidelity to Classical Waves
• Quantifying Volume Changing Perturbations in a Wave Chaotic System
• Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
• Experimental observation of the avoided crossing of two $S$-matrix resonance poles in an ultracold atom collider
• Delay-time distribution in the scattering of time-narrow wave packets (II) - Quantum Graphs
• Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks
• Transmission through a noisy network

Cited by in corpus (9)

• Reflectionless Programmable Signal Routers
• A Physical Interpretation of Imaginary Time Delay
• Bound states in the continuum induced via local symmetries in complex structures
• Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
• Asymmetric Transmission Through a Classical Analogue of the Aharonov-Bohm Ring
• Multiple-Order Singularity Expansion Method
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities
• Local perfect chirality at reflection-zeros away from exceptional points in optical whispering gallery microcavity