https://doi.org/10.1140/epjd/e2017-80208-5
Regular Article
Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide
1 Laboratoire Kastler-Brossel, UPMC (Sorbonne Université), CNRS, ENS (Université de Recherche PSL), Collège de France, 4 Place Jussieu, 75005 Paris, France
2 Laboratorio di Nanoscienze, Università degli Studi di Trento, CNR, INFM, Via Sommarive 14, 38123 Povo (TN), Italy
3 BEC Center, Università degli Studi di Trento, CNR, INO, Via Sommarive 14, 38123 Povo (TN), Italy
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e-mail: pelarre@yahoo.fr
Received: 24 March 2017
Received in final form: 21 April 2017
Published online: 9 June 2017
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.
Key words: Optical Phenomena and Photonics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2017
