Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1407.5549 · Physical Review Letters

Comment on “Counterintuitive Dispersion Violating Kramers-Kronig Relations in Gain Slabs”

Denis G. Baranov, A. A. Zyablovsky, A. V. Dorofeenko, Alexey P. Vinogradov, Alexander A. Lisyansky

Published Feb 26, 2015• 6 citations
arXivHTMLPDF

Abstract

In this Comment, we refute conclusions made in Phys. Rev. Lett. 112, 233601 (2014) by L.-G. Wang, L. Wang, M. Al-Amri, S.-Y. Zhu, and M. S. Zubairy. These conclusions stem from the use of the linear theory, which is not applicable to systems having poles of the reflection and transmission coefficients in the upper half of the complex frequency plane.

DOI
10.1103/physrevlett.114.089301

Related papers

Comment on "Counterintuitive Dispersion Violating Kramers-Kronig Relations in Gain Slabs" Reply

Shi-Yao Zhu, Lin Wang, Li‐Gang Wang +2 more

Physical Review Letters•Jan 1, 2015•3 citations

Counterintuitive Dispersion Violating Kramers-Kronig Relations in Gain Slabs

Li‐Gang Wang, Lin Wang, M. Al-Amri +2 more

We demonstrate the counterintuitive dispersion effect that the peaks (dips) in the gain spectrum correspond to abnormal (normal) dispersion, contrary to the usual Kramers-Kronig point of view. This effect may also lead to two unique features: a broadband abnormal dispersion region and an observable Hartman effect. These results are explained in terms of interference and boundary effects. Finally, two experiments are proposed for the potential experimental verification.

Physical Review Letters•Jun 11, 2014•20 citations

Comments on “Study of the Complex Atomic Susceptibility of Erbium-Doped Fiber Amplifiers”

Jean-Fran�ois Bisson, Dmitrii Kouznetsov

This comment aims to report and correct a mistake in the paper by Desurvire (J. Lightw. Technol., vol. 8, no. 10, pp. 1517-1527, Oct. 1990) with regard to the expression of the complex susceptibility of quasi-three-level laser systems. The derived susceptibility formula contradicts the assumption of thermal equilibrium between sublevels within each manifold and leads to the wrong conclusion that the real and imaginary parts of the susceptibility of saturated materials do not verify the Kramers-Kronig relations (KKR). The corrected formula for the susceptibility is hereby proposed. The poles of the susceptibility obtained with the new formula are all located in the upper half plane of the complex plane, in accordance with the principle of causality. Hence, the KKR should be valid in the saturated regime.

Journal of Lightwave Technology•Jan 1, 2008•1 citation

Comment on “Relative phase between quantum transmission and reflection amplitudes in one dimension” by Y. Fu

Massimiliano Sassoli de Bianchi

Physics Letters A•Aug 1, 1996•0 citations

Comment on “Photonic tunneling times"

Aephraim M. Steinberg

In [1], some misleading statements were made about [2] and “zero-time" tunneling. We criticize these claims.

Journal de Physique I•Dec 1, 1994•12 citations

Dispersion Relations Across the Unitarity Boundary

Kejun Liu

Kramers-Kronig (KK) relations rest on a binary premise: a response function is either analytic in the upper half-plane or it is not. We show that a single reduced-state transform organizes both outcomes into a sharp dichotomy controlled by microscopic unitarity. One closed-form function carries, simultaneously, a zero and a pole in the upper half-plane; the spectral abscissa alpha of the reduced propagator decides which is realized. For alpha < 0 (unitary reduction) the upper-half-plane object is a protected zero: KK holds, yet the zero is directly measurable from a finite-time coherence record by a damped Fourier transform (no analytic continuation), obeying a closed law Im(zeta) = 0.3092 g. For alpha > 0 (gain-driven non-unitary reduction) the zero is replaced by a genuine pole, the Blaschke winding number jumps from 0 to 1, and KK acquires a Lorentzian residue correction scaling as a power law with negative exponent nu ~ -1.08, peaking at threshold. The protected zero is not inert: any scalar single-channel kernel extraction is forced to reproduce a phantom resonance -- a refractive feature with no absorptive origin, at a protocol-independent frequency -- without any initial system-bath correlation. We give the closed-form criteria, a measurable terahertz signature (31-1391 GHz), and the solvable dimer and Jaynes-Cummings models that realize both sides of the boundary.

quant-pharXiv:2605.00117•May 4, 2026•0 citations
In this Comment, we refute conclusions made in Phys. Rev. Lett. 112, 233601 (2014) by L.-G. Wang, L. Wang, M. Al-Amri, S.-Y. Zhu, and M. S. Zubairy. These conclusions stem from the use of the linear theory, which is not applicable to systems having poles of the reflection and transmission coefficients in the upper half of the complex frequency plane.
This comment aims to report and correct a mistake in the paper by Desurvire (J. Lightw. Technol., vol. 8, no. 10, pp. 1517-1527, Oct. 1990) with regard to the expression of the complex susceptibility of quasi-three-level laser systems. The derived susceptibility formula contradicts the assumption of thermal equilibrium between sublevels within each manifold and leads to the wrong conclusion that the real and imaginary parts of the susceptibility of saturated materials do not verify the Kramers-Kronig relations (KKR). The corrected formula for the susceptibility is hereby proposed. The poles of the susceptibility obtained with the new formula are all located in the upper half plane of the complex plane, in accordance with the principle of causality. Hence, the KKR should be valid in the saturated regime.
Kramers-Kronig (KK) relations rest on a binary premise: a response function is either analytic in the upper half-plane or it is not. We show that a single reduced-state transform organizes both outcomes into a sharp dichotomy controlled by microscopic unitarity. One closed-form function carries, simultaneously, a zero and a pole in the upper half-plane; the spectral abscissa alpha of the reduced propagator decides which is realized. For alpha < 0 (unitary reduction) the upper-half-plane object is a protected zero: KK holds, yet the zero is directly measurable from a finite-time coherence record by a damped Fourier transform (no analytic continuation), obeying a closed law Im(zeta) = 0.3092 g. For alpha > 0 (gain-driven non-unitary reduction) the zero is replaced by a genuine pole, the Blaschke winding number jumps from 0 to 1, and KK acquires a Lorentzian residue correction scaling as a power law with negative exponent nu ~ -1.08, peaking at threshold. The protected zero is not inert: any scalar single-channel kernel extraction is forced to reproduce a phantom resonance -- a refractive feature with no absorptive origin, at a protocol-independent frequency -- without any initial system-bath correlation. We give the closed-form criteria, a measurable terahertz signature (31-1391 GHz), and the solvable dimer and Jaynes-Cummings models that realize both sides of the boundary.