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

TL;DR

This paper proposes a method to measure the Bogoliubov dispersion relation of optical excitations in nonlinear waveguides using pump-probe phase shift techniques, combining theoretical analysis and experimental design.

Contribution

It introduces a novel pump-and-probe optical phase shift method to quantitatively probe the Bogoliubov dispersion in nonlinear waveguides, supported by theoretical and experimental proposals.

Findings

Derived the Bogoliubov dispersion relation for optical waves in nonlinear waveguides.

Analyzed effects of one- and two-photon losses on dispersion.

Proposed an experimental setup using four-wave mixing and interference spectroscopy.

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.