On beautiful analytic structure of the S-matrix

Moroz, Alexander; Miroshnichenko, Andrey E.

doi:10.1088/1367-2630/ab484b

Cited by 9 publications

(7 citation statements)

References 28 publications

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“…One should not omit another important condition: resonant states must also fulfill the continuity condition at the surface of the scatterer. A resonant states analysis of light-scattering involves a pole expansion of the S-matrix coefficients [8,16,49,59,62] that yields the following expression (8) where Expressions of poles and residues can also be derived analytically. We first consider even modes [8] S e (𝜔) = r(𝜔)…”

Section: Pole Expansion Of the S-matrix In The Harmonic Domainmentioning

confidence: 99%

Derivation of the Transient and Steady Optical States from the Poles of the S‐Matrix

Soltane

Colom

Stout

et al. 2022

Laser & Photonics Reviews

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The electromagnetic response of optical systems can be described by scattering operators, S, that link the incoming fields onto the system to the outgoing fields emerging from it. Considerable efforts have been devoted to retrieve the spectral response of the optical systems by expanding the S‐matrix in terms of its singularities. Here a planar optical cavity that allows to derive analytical expressions of poles (in the case of lossless materials) and residues, and reflection/transmission Fresnel coefficients in the harmonic domain is considered. This singularity expansion is used to derive the impulse response function (IRF) of the cavity with respect to the poles of the S‐matrix. The singular expression of the IRF consists of contributions oscillating at the excitation frequency and exponentially decaying contributions that impact signals only during the transient regimes. The convergence of this approach is thoroughly discussed in the case of a dispersive and metallic slab. The convergence is achieved by increasing the number of poles in the singularity expansion. It can also be achieved by considering only the poles within the spectral range of interest plus a fictive resonant term encapsulating the contribution of the singularities outside this spectral range.

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Section: Pole Expansion Of the S-matrix In The Harmonic Domainmentioning

confidence: 99%

Derivation of the Transient and Steady Optical States from the Poles of the S‐Matrix

Soltane

Colom

Stout

et al. 2022

Laser & Photonics Reviews

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“…An interpretation of an anti-bound or virtual state is that if the interaction were a bit stronger, the anti-bound state would become a bound state. 7,8 In Sec. IV A we will illustrate this transition for the potential well.…”

Section: S-matrixmentioning

confidence: 99%

Illustrations of loosely-bound and resonant states in atomic nuclei

Dassie,

Gerdau,

Gonzalez

et al. 2021

Preprint

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Using the one-dimensional potential well with realistic parameters for atomic nuclei, we illustrate the movement of the poles of the S-matrix, and the transmission coefficient when the well supports an anti-bound state. We calculate the phase shift of the atomic nuclei 5 He using the three-dimensional potential well, and compare it with the experimental one. The paper gives a glance of some of the properties found in realistic loosely and resonant nuclear systems, using equations at the level of undergraduate students.

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“…In the limit x −→ −∞, we have to take into account the relation (13), so as to obtain the following asymptotic forms:…”

Section: Scattering Wave Functionsmentioning

confidence: 99%

“…Very recently, Moroz and Miroshnichenko [12,13] had exhaustively studied the analytic behavior of the scattering matrix S(k) corresponding to the radial Schrödinger equation with potential…”

Section: Introductionmentioning

confidence: 99%

Redundant poles of the $S$-matrix for the one dimensional Morse potential

Gadella

Hernández-Ortega

Kuru

et al. 2020

Preprint

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We analyze the structure of the scattering matrix, S(k), for the one dimensional Morse potential. We show that, in addition to a finite number of bound state poles and an infinite number of anti-bound poles, there exist an infinite number of redundant poles, on the positive imaginary axis, which do not correspond to either of the other types. This can be solved analytically and exactly. In addition, we obtain wave functions for all these poles and ladder operators connecting them. Wave functions for redundant state poles are connected via two different series. We also study some exceptional cases.

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On beautiful analytic structure of the S-matrix

Cited by 9 publications

References 28 publications

Derivation of the Transient and Steady Optical States from the Poles of the S‐Matrix

Derivation of the Transient and Steady Optical States from the Poles of the S‐Matrix

Illustrations of loosely-bound and resonant states in atomic nuclei

Redundant poles of the $S$-matrix for the one dimensional Morse potential

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