On the Question of Radiative Losses in the Frame of Classic and Quantum Formalism

  • Arkadi ChipoulineEmail author
  • Franko Küppers
Part of the Springer Series in Optical Sciences book series (SSOS, volume 211)


The classical consideration of the radiative losses for a free dipole (with dynamics described by in the frame of harmonic oscillator (HO) equation) leads to a well-known extra term in the dynamic equation proportional to the third time derivative.


  1. 1.
    L. Novotny, B. Hecht, Principles of Nano-optics (Cambridge University Press, New York, 2006)CrossRefGoogle Scholar
  2. 2.
    A. Poddubny, P. Belov, Y. Kivshar, Phys. Rev. B 87, 035136 (2013)CrossRefGoogle Scholar
  3. 3.
    M. Decker, I. Staude, I. Shishkin, K. Samusev, P. Parkinson, V. Sreenivasan, A. Minovich, A. Miroshnichenko, A. Zvyagin, C. Jagadish, D. Neshev, Y. Kivshar, Dual-channel spontaneous emission of quantum dots in magnetic metamaterials. Nat. Commun. 4, 2949 (2013)CrossRefGoogle Scholar
  4. 4.
    C. Sauvan, J.P. Hugonin, I.S. Maksymov, P. Lalanne, Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators. PRL 110, 237401 (2013)CrossRefGoogle Scholar
  5. 5.
    M. Agio, D. Cano, The Purcell factor of nanoresonators. Nat. Photon. 7 (2013) CrossRefGoogle Scholar
  6. 6.
    M. Stockman, The spaser as a nanoscale quantum generator and amplifier. J. Opt. 12, 024004 (2010)CrossRefGoogle Scholar
  7. 7.
    U. Fano, Description of states in quantum mechanics by density matrix and operator techniques. Rev. Modern Phys. 29, 74 (1957)CrossRefGoogle Scholar
  8. 8.
    V.M. Fain, Quantum Radio Physics, Vol. 1: Photons and Nonlinear Media (Sovetskoe Radio, Moscow, 1972) (in Russian)Google Scholar
  9. 9.
    V. Akulin, N. Karlov, Intensive Resonance Interaction in Quantum Electronics (Nauka, Moscow, 1987) (in Russian)Google Scholar
  10. 10.
    V. Pustovit, T. Shahbazyan, Phys. Rev. B 82, 075429 (2010)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Microwave Engineering and PhotonicsTechnical University of DarmstadtDarmstadtGermany
  2. 2.Department of Electrical Engineering and Information TechnologiesTechnical University of DarmstadtDarmstadtGermany

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