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Weak Coupling, Strong Coupling, Critical Coupling and Fano Resonances: A Unifying Vision

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Book cover Fano Resonances in Optics and Microwaves

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 219))

Abstract

The transversal concepts of weak, strong and critical coupling, and of Fano resonances, are analyzed within a unified framework which relies on a simple classical model of driven-dissipative coupled oscillators. A careful exploration of the system’s parameter space has led to the emergence of certain intriguing phenomena, which we named lineshape inheritance, universal absorption lineshape, and strong critical coupling. These concepts may be of relevance when attempting to understand the response of a diversity of systems, especially in the fields of (quantum) light-matter coupling, and of solid-state nanophysics, where the basic scheme of multi-oscillator dissipative resonances is often encountered.

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Notes

  1. 1.

    The following expressions are the most general ones that fulfill the constraints given in (23.2), and generalize both [27] and [43].

  2. 2.

    Reflectance behaves similarly.

  3. 3.

    We anticipate that the parameter \(\xi \) does not affect the line shapes.

  4. 4.

    Specifically it holds \(\tan \delta = \left( \rho _2 \sin \psi _2 + \rho _1 \sin \psi _1 \right) / \left( \rho _2 \cos \psi _2 - \rho _1 \cos \psi _1 \right) \), where \(\rho _{1,2}\) and \(\psi _{1,2}\) are the amplitudes and phases of the reflection coefficients \(s_{11}\) and \(s_{22}\), respectively.

  5. 5.

    This fact is interesting since the product \(r \xi \) is directly connected with the cavity-exterior coupling coefficients \(\kappa \) (see Sect. 23.2).

  6. 6.

    Notice, however, that the curve which separates the single- from the double-peak region of reflectance and transmittance spectra is different. See also [50] for a discussion on this topic.

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Acknowledgements

The author acknowledges very insightful discussions with Dr. Raffaele Colombelli, Lorenzo Baldacci, and Prof. Alessandro Tredicucci.

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  1. NEST, Istituto Nanoscienze - CNR and Scuola Normale Superiore, 56127, Pisa, Italy

    Simone Zanotto

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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beersheba, Israel

    Eugene Kamenetskii

  2. Federal Research Center KSC SB RAS, Kirensky Institute of Physics, Krasnoyarsk, Russia

    Almas Sadreev

  3. School of Engineering and Information Technology, University of New South Wales, Canberra, ACT, Australia

    Andrey Miroshnichenko

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Zanotto, S. (2018). Weak Coupling, Strong Coupling, Critical Coupling and Fano Resonances: A Unifying Vision. In: Kamenetskii, E., Sadreev, A., Miroshnichenko, A. (eds) Fano Resonances in Optics and Microwaves. Springer Series in Optical Sciences, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-99731-5_23

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