Brillouin cooling in a linear waveguide

Yin-Chung Chen,Gaurav Bahl,Seunghwi Kim

doi:10.1088/1367-2630/18/11/115004

Yin-Chung Chen, Gaurav Bahl + Show 1 more

Open Access

https://doi.org/10.1088/1367-2630/18/11/115004

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Abstract

Brillouin scattering is not usually considered as a mechanism that can cause cooling of a material due to the thermodynamic dominance of Stokes scattering in most practical systems. However, it has been shown in experiments on resonators that net phonon annihilation through anti-Stokes Brillouin scattering can be enabled by means of a suitable set of optical and acoustic states. The cooling of traveling phonons in a linear waveguide, on the other hand, could lead to the exciting future prospect of manipulating unidirectional phonon fluxes and even the nonreciprocal transport of quantum information via phonons. In this work, we present an analysis of the conditions under which Brillouin cooling of phonons of both low and high group velocities may be achieved in a linear waveguide. We analyze the three-wave mixing interaction between the optical and traveling acoustic modes that participate in forward Brillouin scattering, and reveal the key regimes of operation for the process. Our calculations indicate that measurable cooling may occur in a system having phonons with spatial loss rate that is of the same order as the spatial optical loss rate. If the Brillouin gain in such a waveguide reaches the order of 105 m−1 W−1, appreciable cooling of phonon modes may be observed with modest pump power of a few mW.

Highlights

Spontaneous Brillouin scattering of light from acoustic phonons [1, 2] results in creation of photons at both higher and lower (Stokes) energies than the pump
In this paper we address the question of whether Brillouin cooling of traveling phonons of arbitrary group velocity can be achieved in a linear waveguide
We have investigated the anti-Stokes Brillouin scattering process in linear waveguides for the possibility of achieving phonon annihilation and cooling

Summary

Introduction

Spontaneous Brillouin scattering of light from acoustic phonons [1, 2] results in creation of photons at both higher (anti-Stokes) and lower (Stokes) energies than the pump. The solution to the fundamental challenge of achieving net phonon annihilation lies in engineering the Stokes vs anti-Stokes scattering probabilities through the photonic density of states of the system [8,9,10]. Light exits a local region of a waveguide considerably faster than phonons do, suggesting that the local, apparent phonon lifetime is considerably longer than the photons Addressing this question effectively requires an analysis of both high and low group velocity phonons, since these spatial relationships can result in different conclusions. We aim to fill this gap in knowledge by studying the Brillouin cooling of large group velocity traveling phonon modes inside a waveguide, with the inclusion of Langevin noise force and determination of the resulting phonon spectrum. Our analysis here presents the conditions under which appreciable cooling could potentially be achieved and hopes to help direct further experimental studies on linear waveguides

Coupled wave equations for anti-Stokes Brillouin scattering

Low group velocity acoustic modes at thermal equilibrium

High group velocity acoustic modes at thermal equilibrium

Solution with non-depleted optical pumping

Practical considerations for observing Brillouin cooling in linear waveguides

Conclusions