Statistics of Complex Wigner Time Delays as a Counter of 
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-Matrix Poles: Theory and Experiment

Chen, Lei; Anlage, Steven M.; Fyodorov, Yan V.

doi:10.1103/physrevlett.127.204101

Cited by 19 publications

(10 citation statements)

References 66 publications

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“…Zeros of scattering coefficients that lie on the real frequency axis lead to phase singularities and anomalously long diverging delay times (7,25,(46)(47)(48)(49). The interpretation and statistical properties of complex Wigner time delays in subunitary (and possibly overmoded) scattering systems, as well as their relation to the singularities (poles and zeros) of the associated wave transport matrix, is currently an active area of research (26,(48)(49)(50)(51). In general, away from such singularities, it is well established that longer dwell times increase the sensitivity to minute perturbations, with important implications for precision sensing (52,53).…”

Section: Reflectionless Wavelength Demultiplexermentioning

confidence: 99%

Reflectionless programmable signal routers

et al. 2023

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We demonstrate experimentally that reflectionless scattering modes (RSMs), a generalized version of coherent perfect absorption, can be functionalized to perform reflectionless programmable signal routing. We achieve versatile programmability both in terms of operating frequencies and routing functionality with negligible reflection upon in-coupling, which avoids unwanted signal power echoes in radio frequency or photonic networks. We report in situ observations of routing functionalities like wavelength demultiplexing, including cases where multichannel excitation requires adapted coherent input wavefronts. All experiments are performed in the microwave domain based on the same irregularly shaped cavity with strong modal overlap that is massively parametrized by a 304–element-programmable metasurface. RSMs in our highly overdamped multiresonance transport problem are fundamentally intriguing because the simple critical coupling picture for reflectionless excitation of isolated resonances fails spectacularly. We show in simulation that the distribution of damping rates of scattering singularities broadens under strong absorption so that weakly damped zeros can be tuned toward functionalized RSMs.

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Section: Reflectionless Wavelength Demultiplexermentioning

confidence: 99%

Reflectionless programmable signal routers

et al. 2023

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“…(7) and (8) and the random matrix predictions for the distribution of Γ n . [38] We can define the scattering matrix as S = R T T R in terms of the reflection sub-matrix R and transmission sub-matrix T [20, 21, 96, 97]. For a system with uniform absorption, the determinant of the transmission sub-matrix can be written as:…”

Section: Complex Time Delays and Scattering Poles And Zerosmentioning

confidence: 99%

“…[24][25][26][27][28][29][30][31][32][33][34][35] Recently, a complex generalization of time delay that applies to sub-unitary scattering systems was introduced, and this quantity turns out to be much richer than its lossless counterpart. [36][37][38] It has been demonstrated that complex Wigner-Smith time delay is sensitive to the locations and statistics of the poles and zeros of the full scattering matrix. One of the goals of this paper is to extend the use of complex Wigner-Smith time delay (τ W , the sum of all partial time delays) to the transmission (τ T ), reflection (τ…”

Section: Introductionmentioning

confidence: 99%

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

Chen,

Anlage

2022

Preprint

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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 an 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.

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“…[2,8,[10][11][12] for reviews of that activity. In particular, statistics of resonance poles of widths Γ n ∼ ∆ (∆ being the mean level spacing) and related objects has been thoroughly studied along these lines [13][14][15][16][17][18][19], and some of theoretical predictions subsequently verified in experiments in microwave chaotic scattering from cavities [20,21] and graphs [22] or accurate numerical simulations in realistic models [23][24][25]. It is appropriate also to mention an alternative line of research going back to [26] and relying upon semiclassical methods to address resonances in quantum chaotic systems [27][28][29][30].…”

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confidence: 99%

“…( 4) is provided in the Supplemental Material [54]. Here we only mention that it combines two essential ingredients: (i ) recently discovered relation [22] between the density ρ(y) and a complex-valued generalization [55] of the standard Wigner time delay [56] and (ii ) a relation [57] between the OPF and the mean density of complex eigenvalues K c of the so-called Wigner K-matrix related to S-matrix as S = (1 − iK)/(1 + iK). The latter generalizes a wellknown relation between the OPF and the joint probability density P(u, v) of real u and complex v parts of the local Green's function G(x, x, E + iη) = u − iv [58,59].…”

mentioning

confidence: 99%