Abstract

The interaction between light and mesoscopic mechanical degrees of freedom has been investigated under various perspectives, from spectroscopy in condensed matter, optical tweezer particle trapping, and long-haul optical fiber communication system penalties to gravitational-wave detector noise. In the context of integrated photonics, two topics with dissimilar origins—cavity optomechanics and guided wave Brillouin scattering—are rooted in the manipulation and control of the energy exchange between trapped light and mechanical modes. In this tutorial, we explore the impact of optical and mechanical subwavelength confinement on the interaction among these waves, coined as Brillouin optomechanics. At this spatial scale, optical and mechanical fields are fully vectorial and the common intuition that more intense fields lead to stronger interaction may fail. Here, we provide a thorough discussion on how the two major physical effects responsible for the Brillouin interaction—photoelastic and moving-boundary effects—interplay to foster exciting possibilities in this field. In order to stimulate beginners into this growing research field, this tutorial is accompanied by all the discussed simulation material based on a widespread commercial finite-element solver.

Highlights

  • To give an overview of the tutorial’s scope, we show in Fig. 1 several structures where forward and backward Brillouin optomechanics have already been demonstrated, divided into fiber-based and integrated waveguides and axisymmetric cavities

  • III, we explore in detail Brillouin scattering in circular dielectric waveguides — a silica glass rod suspended in air

  • Before we discuss some general aspects of the phase-matching in confined photonic structures, we explore how Brillouin scattering in axisymmetric optical cavities share similarities with their waveguide counterparts

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Summary

Context and brief history

When the phase of a propagating light field is disturbed by a spatially periodic modulation, the direction of light propagation is shifted as determined by momentum conservation. If such a spatial modulation is periodic in time, the Doppler effect takes place and energy conservation implies that the scattered light is frequencyshifted. Despite its weak thermal-noise origin, the phase noise induced by GAWBS was identified as a major source of noise in fiber-based quantum noise squeezing experiments.10 These guided mechanical waves can be stimulated by light through electrostriction forces and may lead to cross talk and long range interaction among short-pulses propagating in optical fibers. In the last ten years, following the growth and availability of advanced top-down nanofabrication tools, a series of research breakthroughs occurred in this field within the classical and quantum realm.62–67 The advancement of these integrated photonic structures impacted backward Brillouin scattering, especially after the landmark demonstration of on-chip SBS by Pant et al., which sparked a convergence of the traditional waveguide-based Brillouin concepts with the cavity optomechanics ones. In light of this convergence, in this tutorial, we will use the term Brillouin optomechanics to encompass the whole spectra of experiments involving trapped light and mechanical waves

Scope of this tutorial
Dispersion relation and phase-matching
Intramodal scattering
Intermodal scattering
Photoelasticity and moving boundary perturbations
Waveguides
Cavities
Cavities vs waveguides
Boundary and volume overlap integrals
BRILLOUIN COUPLING IN A SILICA GLASS ROD
Confined mechanical modes vs plane mechanical waves
Confined optical modes
Brillouin optomechanical coupling
Moving boundary effect
Photoelastic effect
BRILLOUIN COUPLING IN AXISYMMETRIC MICROCAVITIES
Optical and mechanical radial confinement
Silicon microdisk cavity
Dispersion relation of a silicon microdisk
Brillouin optomechanical coupling in a silicon microdisk
Backward Brillouin scattering in other microcavities
Bullseye cavity
PERSPECTIVES AND CONCLUSIONS
Full Text
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