Quantum vacuum emission from a refractive-index front

Maxime Jules Roland Jacquet, Friedrich Ernst Wilhelm Koenig

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21 Citations (Scopus)
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A moving boundary separating two otherwise homogeneous regions of a dielectric is known to emit radiation from the quantum vacuum. An analytical framework based on the Hopfield model, describing a moving refractive-index step in 1+1 dimensions for realistic dispersive media has been developed by S. Finazzi and I. Carusotto [Phys. Rev. A 87, 023803 (2013)]. We expand the use of this model to calculate explicitly spectra of all modes of positive and negative norms. Furthermore, for lower step heights we obtain a unique set of mode configurations encompassing black-hole and white-hole setups. This leads to a realistic emission spectrum featuring black-hole and white-hole emission for different frequencies. We also present spectra as measured in the laboratory frame that include all modes, in particular a dominant negative-norm mode, which is the partner mode in any Hawking-type emission. We find that the emission spectrum is highly structured into intervals of emission with black-hole, white-hole, and no horizons. Finally, we estimate the number of photons emitted as a function of the step height and find a power law of 2.5 for low step heights.
Original languageEnglish
Article number023851
Number of pages9
JournalPhysical Review. A, Atomic, molecular, and optical physics
Publication statusPublished - 28 Aug 2015


  • Fiber optics
  • Hawking effect
  • Event horizon
  • Parametric amplification


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