Light-Sound Interaction in Nanoscale Silicon Waveguides

This thesis studies the interaction between near-infrared light and gigahertz sound in nanoscale silicon waveguides. Chapter 2 introduces photon-phonon coupling and its theoretical description, describing basic mechanisms and developing a quantum field theory of the process. Chapter 3 explores the dynamical effects in both waveguides and cavities. It also proves a connection between the Brillouin gain coefficient and the vacuum coupling rate. Chapter 4 deals with the observation of Brillouin scattering in nanoscale silicon waveguides. The waveguides tightly confine $193 \, \text{THz}$ light and $10 \, \text{GHz}$ acoustic vibrations. The acoustic quality factor remains limited to about $300$ because of leakage into silica substrate. These waveguides are optically transparent in a narrow band of frequencies at a pump power of $25 \, \text{mW}$. Besides this amplification, we translate a $10 \, \text{GHz}$ microwave signal across $1 \, \text{THz}$. Chapter 5 extends the experimental work of chapter 4 by fabricating a cascade of fully suspended nanowires held by silica anchors. This enhances the mechanical quality factor from $300$ to $1000$, enabling the observation of Brillouin amplification exceeding the propagation losses in silicon. The amount of amplification is mostly limited by a rapid drop in acoustic quality as the number of suspensions increases. We propose a mechanism to cancel this inhomogeneous broadening. Chapter 6 looks at the potential of narrow silicon slot waveguides to enhance the optomechanical coupling. For certain dimensions, these waveguides support opto-acoustic modes with an interaction efficiency simulated an order of magnitude above those of single-nanobeam systems.Comment: PhD thesis defended at Ghent Universit

Unifying Brillouin scattering and cavity optomechanics

So far, Brillouin scattering and cavity optomechanics were mostly disconnected branches of research -- although both deal with photon-phonon coupling. This begs for the development of a broader theory that contains both fields. Here, we derive the dynamics of optomechanical cavities from that of Brillouin-active waveguides. This explicit transition elucidates the link between phenomena such as Brillouin amplification and electromagnetically induced transparency. It proves that effects familiar from cavity optomechanics all have traveling-wave partners, but not vice versa. We reveal a close connection between two parameters of central importance in these fields: the Brillouin gain coefficient and the zero-point optomechanical coupling rate. This enables comparisons between systems as diverse as ultracold atom clouds, plasmonic Raman cavities and nanoscale silicon waveguides. In addition, back-of-the-envelope calculations show that unobserved effects, such as photon-assisted amplification of traveling phonons, are now accessible in existing systems. Finally, we formulate both circuit- and cavity-oriented optomechanics in terms of vacuum coupling rates, cooperativities and gain coefficients, thus reflecting the similarities in the underlying physics.Comment: published manuscript, minor change

Analysis of enhanced stimulated Brillouin scattering in silicon slot waveguides

Stimulated Brillouin scattering has attracted renewed interest with the promise of highly tailorable integration into the silicon photonics platform. However, significant Brillouin amplification in silicon waveguides has yet to be shown. In an effort to engineer a structure with large photon-phonon coupling, we analyzed both forward and backward Brillouin scattering in high-index-contrast silicon slot waveguides. The calculations predict that gradient forces enhance the Brillouin gain in narrow slots. We estimate a currently feasible gain of about $10^{5} \, \text{W}^{-1}\text{m}^{-1}$, which is an order of magnitude larger than in a stand-alone silicon wire. Such efficient coupling could enable a host of Brillouin technologies on a mass-producible silicon chip

Controlling phonons and photons at the wavelength-scale: silicon photonics meets silicon phononics

Radio-frequency communication systems have long used bulk- and surface-acoustic-wave devices supporting ultrasonic mechanical waves to manipulate and sense signals. These devices have greatly improved our ability to process microwaves by interfacing them to orders-of-magnitude slower and lower loss mechanical fields. In parallel, long-distance communications have been dominated by low-loss infrared optical photons. As electrical signal processing and transmission approaches physical limits imposed by energy dissipation, optical links are now being actively considered for mobile and cloud technologies. Thus there is a strong driver for wavelength-scale mechanical wave or "phononic" circuitry fabricated by scalable semiconductor processes. With the advent of these circuits, new micro- and nanostructures that combine electrical, optical and mechanical elements have emerged. In these devices, such as optomechanical waveguides and resonators, optical photons and gigahertz phonons are ideally matched to one another as both have wavelengths on the order of micrometers. The development of phononic circuits has thus emerged as a vibrant field of research pursued for optical signal processing and sensing applications as well as emerging quantum technologies. In this review, we discuss the key physics and figures of merit underpinning this field. We also summarize the state of the art in nanoscale electro- and optomechanical systems with a focus on scalable platforms such as silicon. Finally, we give perspectives on what these new systems may bring and what challenges they face in the coming years. In particular, we believe hybrid electro- and optomechanical devices incorporating highly coherent and compact mechanical elements on a chip have significant untapped potential for electro-optic modulation, quantum microwave-to-optical photon conversion, sensing and microwave signal processing.Comment: 26 pages, 5 figure

Net on-chip Brillouin gain based on suspended silicon nanowires

The century-old study of photon-phonon coupling has seen a remarkable revival in the past decade. Driven by early observations of dynamical back-action, the field progressed to ground-state cooling and the counting of individual phonons. A recent branch investigates the potential of traveling-wave, optically broadband photon-phonon interaction in silicon circuits. Here, we report continuous-wave Brillouin gain exceeding the optical losses in a series of suspended silicon beams, a step towards selective on-chip amplifiers. We obtain efficiencies up to $10^{4} \, \text{W}^{-1}\text{m}^{-1}$, the highest to date in the phononic gigahertz range. We also find indications that geometric disorder poses a significant challenge towards nanoscale phonon-based technologies.Comment: 14 pages, 8 figure

The group of dyadic unitary matrices

We introduce the group DU(m) of m x m dyadic unitary matrices, i.e. unitary matrices with all entries having a real and an imaginary part that are both rational numbers with denominator of the form 2(p) (with p a non-negative integer). We investigate in detail the finite groups DU(1) and DU(2) and the discrete, but infinite groups DU(3) and DU(4). We further introduce the subgroup XDU(m) of DU(m), consisting of those members of DU(m) that have constant line sum 1. The study of XDU(2) and XDU(4) leads to conclusions concerning the synthesis of quantum computers acting on one and two qubits, respectively

Thermal Brillouin noise observed in silicon optomechanical waveguide

Stimulated Brillouin scattering was recently observed in nanoscale silicon waveguides. Surprisingly, thermally-driven photon-phonon conversion in these structures had not yet been reported. Here, we inject an optical probe in a suspended silicon waveguide and measure its phase fluctuations at the output. We observe mechanical resonances around 8 GHz with a scattering efficiency of $10^{-5} \, \text{m}^{-1}$ and a signal-to-noise ratio of 2. The observations are in agreement with a theory of noise in these waveguides as well as with stimulated measurements. Our scheme may simplify measurements of mechanical signatures in nanoscale waveguides and is a step towards a better grasp of thermal noise in these new continuum optomechanical systems.Comment: 11 pages, 4 figure