Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide

  • Pierre-Élie Larré
  • Stefano Biasi
  • Fernando Ramiro-Manzano
  • Lorenzo Pavesi
  • Iacopo Carusotto
Regular Article

Abstract

We theoretically investigate the dispersion relation of small-amplitude optical waves superimposing upon a beam of polarized monochromatic light propagating along a single-mode channel waveguide characterized by an instantaneous and spatially local Kerr nonlinearity. These small luminous fluctuations propagate along the waveguide as Bogoliubov elementary excitations on top of a one-dimensional dilute Bose quantum fluid evolve in time. They consequently display a strongly renormalized dispersion law, of Bogoliubov type. Analytical and numerical results are found in both the absence and the presence of one- and two-photon losses. Silicon and silicon-nitride waveguides are used as examples. We finally propose an experiment to measure this Bogoliubov dispersion relation, based on a stimulated four-wave mixing and interference spectroscopy techniques.

Graphical abstract

Keywords

Optical Phenomena and Photonics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Pierre-Élie Larré
    • 1
  • Stefano Biasi
    • 2
  • Fernando Ramiro-Manzano
    • 2
  • Lorenzo Pavesi
    • 2
  • Iacopo Carusotto
    • 3
  1. 1.Laboratoire Kastler-Brossel, UPMC (Sorbonne Université), CNRS, ENS (Université de Recherche PSL), Collège de FranceParisFrance
  2. 2.Laboratorio di Nanoscienze, Università degli Studi di Trento, CNR, INFMPovo (TN)Italy
  3. 3.BEC Center, Università degli Studi di Trento, CNR, INOPovo (TN)Italy

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