c© 2014 Kewen Han

MANUFACTURING AND AEROSTATIC TUNABILITY OFOPTO-MECHANO-FLUIDIC RESONATOR AND ITS APPLICATION

IN VISCOSITY SENSING

BY

KEWEN HAN

THESIS

Submitted in partial fulfillment of the requirementsfor the degree of Master of Science in Mechanical Engineering

in the Graduate College of theUniversity of Illinois at Urbana-Champaign, 2014

Urbana, Illinois

Adviser:

Assistant Professor Gaurav Bahl

ABSTRACT

1 2 Cavity optomechanics experiments parametrically couple the phonon

modes and photon modes in microresonators and various optical systems

have been investigated. However, because of the increased acoustic radiative

losses during direct liquid immersion of optomechanical devices, almost all

published optomechanical experiments have been performed in solid phase.

The high acoustic losses during direct liquid immersion limits the biosens-

ing applications of optomechanical devices. This thesis discusses a recently

introduced hollow opto-mechano-fluidic resonator (OMFR), which by design

are equipped for microfluidic experiments. By confining liquids inside the

capillary resonator, high mechanical- and optical- quality factors are simul-

taneously maintained. Unlike optofluidics biosensing, because the optical

modes don’t interact with the liquids directly, the optomechanical biosensing

doesn’t have any requirement of the optical properties of the fluids and bio-

analytes. Detailed methodology is provided to fabricate these ultra-high-Q

microfluidic resonators, perform optomechanical testing, and measure radi-

ation pressure-driven breathing mode (10–20 MHz) and SBS-driven (10–12

GHz) whispering gallery mode vibrations. We also experimentally investi-

gate aerostatic tuning of these hollow-shell oscillators, enabled by geometry,

stress, and temperature effects. We demonstrate for the first time the si-

multaneous actuation of RP-induced breathing mechanical modes and SBS-

induced whispering gallery acoustic modes, through a single pump laser.

In addition, we show that fluid viscosity can also be determined through op-

tomechanical measurement of the vibrational noise spectrum of the resonator

1This thesis includes the author’s previously published material [1–4]. The copyrightowners have provided permission to reprint.

2 [2] was published in Optics Express and is made available as an electronic reprint withthe permission of OSA. The paper can be found at the following URL on the OSA website:http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-2-1267. Systematic or multi-ple reproduction or distribution to multiple locations via electronic or other means isprohibited and is subject to penalties under law.

ii

mechanical modes. A linear relationship between the spectral linewidth and

root-viscosity is predicted and experimentally verified in the low viscosity

regime. Our result is a step towards completely self-referenced optomechani-

cal sensor technologies and multi-frequency measurement of viscoelasticity of

arbitrary fluids and bioanalytes, without sample contamination, using highly

sensitive optomechanics techniques.

iii

To my parents, for their love and support.

iv

ACKNOWLEDGMENTS

I would like to express my profound appreciation to Prof. Bahl for giving me

the opportunity to be part of this project and his assistance in the preparation

of this manuscript. I would also like to thank my colleague, JunHwan Kim,

for giving his help during some of my experiments. In addition, I would like

to acknowledge stimulating discussions and guidance from Prof. Tal Carmon,

Prof. Xudong Fan, Prof. William P. King, Prof. Randy Ewoldt, Prof. Taher

Saif, Prof. Rashid Bashir, Prof. Kimani Toussaint, Prof. Lynford Goddard,

Prof. David Saintillan, and Sandeep Anand.

v

TABLE OF CONTENTS

CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . 11.1 Whispering gallery Microresonators . . . . . . . . . . . . . . . 31.2 Microresonator light coupling . . . . . . . . . . . . . . . . . . 41.3 Radiation pressure induced optomechanical oscillation . . . . . 61.4 Stimulated Brillouin scattering induced optomechanical os-

cillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 Experimental setup and measurement . . . . . . . . . . . . . . 13

CHAPTER 2 MANUFACTURING OF OMFRS AND MEASUR-ING THE OPTOMECHANICAL OSCILLATIONS . . . . . . . . . 152.1 Fabrication of OMFR . . . . . . . . . . . . . . . . . . . . . . . 152.2 Experimental setup for optomechanical testing . . . . . . . . . 192.3 Measuring optomechanical vibrations . . . . . . . . . . . . . . 22

CHAPTER 3 AEROSTATICALLY TUNABLE OPTOMECHAN-ICAL OSCILLATORS . . . . . . . . . . . . . . . . . . . . . . . . . 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Setup and working principle . . . . . . . . . . . . . . . . . . . 263.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 313.4 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

CHAPTER 4 OPTO-MECHANO-FLUIDIC VISCOMETER . . . . . 364.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2 Setup and working principle . . . . . . . . . . . . . . . . . . . 374.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4 Influence of the shell thickness . . . . . . . . . . . . . . . . . . 424.5 Comparison with other MEMS viscometers . . . . . . . . . . . 434.6 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

CHAPTER 5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . 44

APPENDIX A MEASUREMENT OF THE GEOMETRY OF THEOMFR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

APPENDIX B MATERIALS’ LIST FOR THE FABRICATIONOF OMFR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

vi

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

vii

CHAPTER 1

INTRODUCTION

1 Optomechanical microresonators enable strong-coupling between their pho-

ton modes and phonon modes through photothermal effects [6–8], radiation

pressure (RP) force [9–15], optical gradient force [16–19], and electrostric-

tion mechanisms [5, 20–25]. This capability has been harnessed for many

fundamental experiments including optomechanical cooling [10–12, 24], in-

duced transparency [26, 27], and dark modes [28]. Efforts have also been

made towards sensing applications such as accelerometers [29,30], mass sen-

sors [31,32], and force sensors [33,34]. However, almost all reported optome-

chanics experiments are with solid phases of matter. This is because direct

liquid immersion of the optomechanical devices results in greatly increased

radiative acoustic loss because of the higher impedance of liquids compared

against air. In addition, in some situations dissipative loss mechanisms in

liquids may exceed the radiative acoustic losses. The low mechanical Q limits

the optomechanical application in biosensing.

Recent technological advances in optofluidics [35] have enabled biochemical

sensors that employ many different optical techniques such as refractive

index measurement [36–38], fluorescence [39], and surface enhanced Raman

spectroscopy [40]. Many different optofluidic structures have been explored,

including ring resonators [41–44], liquid core capillaries [36], microtoroids

[45], bubbles [46–48], droplets [49, 50], photonic crystals [51, 52], liquid core

waveguides [53], surface plasmon resonance devices [54]. These structures

enable sensitive detection of DNAs, proteins, viruses, cells, and bacteria down

to the level of single molecules or particles [45, 51]. In addition, optical

nanoparticle sizing and sorting [37, 55] as well as flow control [56, 57] have

also been achieved.

Recently, the opto-mechano-fluidic resonators (OMFRs) were introduced

1This chapter includes Dr. Bahl’s previous publication [5]. The copyright owner hasprovided permission to reprint.

1

[5,46,58,59], and which by design are equipped for microfluidic experiments.

The OMFR is fabricated by heating a glass capillary preform CO2 laser radi-

ation and drawing out the heated capillary linearly. The diameter of this cap-

illary is modulated along its length to form multiple bottle resonators that si-

multaneously confine optical whispering-gallery resonances [60] as well as me-

chanical resonant modes [61]. Multiple families of mechanical resonant modes

participate, including breathing modes, wine-glass modes, and whispering-

gallery acoustic modes. The wine-glass (standing-wave) and whispering-

gallery acoustic (traveling-wave) resonances are formed when a vibration

with integer multiple of acoustic wavelengths occurs around the device cir-

cumference. Light is evanescently coupled into the optical whispering-gallery

modes of these bottles by means of a tapered optical fiber [62]. Confinement

of the liquid inside [63, 64] the capillary resonator, as opposed to outside it,

enables high mechanical- and optical- quality factors simultaneously, which

allows the optical excitation of mechanical modes by means of both RP and

stimulated Brillouin scattering (SBS). As has been shown, these mechanical

excitations are able to penetrate into the fluid within the device [5,58], form-

ing a shared solid-liquid resonant mode, thus enabling an opto-mechanical

interface to the fluidic environment within.

There are multiple advantages of the OMFR in biosensing applications.

First, unlike in the optofluidics sensing applications, the optical field does

not directly interact with the bioanalytes. The optical Q is preserved and

the power consumption is very low. Meanwhile, mechanical interaction with

liquids doesn’t contaminate the fluid with dispersed particles. The high me-

chanical quality factor is ideal for high resolution frequency tracking [31]. Be-

sides, OMFR operational frequencies extend from a few MHz to the 11 GHz

regime, presenting an opportunity to study dynamics over broad timescales

and spacial scales. For example, when the frequency is high, the viscoelastic

nature of the fluid becomes prominent. In fact, the transmission and re-

flection of acoustic waves shorter than the dimensions of a cell can serve in

revealing details on the membrane stiffness and cytoskeleton that cannot be

observed by conventional microscopy. OMFRs can thus provide a novel path

towards high-resolution analysis of the viscoelastic properties of fluids and

bioanalytes. In addition,

In this thesis we first describe, in detail, the basic concepts, the fabrica-

tion, RP and SBS actuation for this novel optomechanical system. Then we

2

experimentally investigate the aerostatic tuning of these OMFR devices and

we show the simultaneous actuation and tuning of multiple modes and mech-

anisms of optomechanical oscillation. Furthermore, we demonstrate the first

experimental system for optomechanically measuring the dynamic viscosity,

µ, of various test fluids using sample volumes in the nanoliter regime.

1.1 Whispering gallery Microresonators

Whispering gallery mode (WGM) optical resonator is a well known type of

miniaturized optical resonator [65]. Unlike traditional bulk optical resonator,

in a whispering gallery mode optical resonator, light is confined in a circular

shape dielectric structure by total internal reflection, like shown in Fig. 1.1.

Such optical mode is called optical whispering gallery mode.

Dielectric

Figure 1.1: Ray of light propagation in a circular dielectric. Light isconfined inside the whispering-gallery mode by total internal reflection.

The optical resonances in a whispering gallery resonator are dependent on

the radius of the structure, a, and the refractive index of the dielectric, n.

Since light circulates inside and close to the surface of the resonator, and the

traveling distance can be approximated as 2πa per round. If the traveling

distance is exactly equal to multiple integer wavelengths in the dielectric , a

constructive interference happens. In other words, the resonance condition

is,

2πa = lλ/n. (1.1)

Here, l is an integer and λ is the wavelength in vacuum. Otherwise, the

destructive interference happens, as shown in Fig. 1.2, and the resonator is

off resonance.

3

Figure 1.2: Constructive interference happens when the the resonator isexactly on resonance. Destructive interference happens when the resonatoris off resonance.

Since the reflection losses are very small, when the material absorption

is minimized, whispering gallery resonator can reach extraordinarily high

quality factor, up to 1011 [66]. Thus very high energy density can be achieved

in WGM and it makes the WGM resonator a great candidate for sensing

applications.

1.2 Microresonator light coupling

Efficient coupling of light into/out a microresonator from a waveguide relies

on the evanescent wave. When total internal reflection happens at the in-

terface between two dielectric media, an evanescent wave exists outside the

dielectric in which light travels and exponentially decays over a short distance

from the boundary. As shown by Fig. 1.3, since the evanescent field dies out

very fast, when two optical waveguides are far away from each other, there is

no propagating wave generated in the right waveguide. However, when these

two optical waveguides are close enough, the evanescent field can generate a

propagating wave in the right waveguide.

Multiple evanescent coupling methods have been developed, for example,

prism coupling [67], polished optical fiber coupling [68], and tapered fiber

coupling [69]. In this thesis, tapered fiber coupling is used to couple light to

an OMFR as shown in Fig. 1.4. The fabrication of tapered optical fiber and

taper-coupling to WGM are discussed in detail in Chap. 2. The coupling

efficiency is maximized when the critical distance is reached between the

4

(a)

(b)

Distance

Field

strength

Figure 1.3: (a) Light cannot be coupled into the waveguide on the righthand side since the evanescent field dies out when the gap between twowaveguides is large. (b) The evanescent field does not decay much before itreach the waveguide on the right hand side, resulting in a propagative modein the right waveguide.

5

waveguide and resonator [70]. However, as discussed later, sometimes we do

want the tapered fiber to be in contact with the resonator (over-coupled) for

improved resilience to ambient vibration and geometry change.

Tapered fiber

coupler

WGM

resonator

Figure 1.4: Light is evanescently coupled into the WGM resonator througha tapered fiber.

1.3 Radiation pressure induced optomechanical

oscillation

Centrifugal radiation pressure induced optomechanical oscillations (OMOs)

were first described in [9,71,72]. In order to understand this phenomenon in

detail, we first consider a simple Fabry-Perot cavity as shown in Fig. 1.5 (a).

A Fabry-Perot cavity consists of a pair of highly reflective mirrors, separated

by a distance L. The optical resonance for such Fabry-Perot cavity happens

at angular frequency

ωr = mπc/L. (1.2)

Here, m is an integer, c is speed of light. Because of the resonance, the

intensity of light inside the Fabry-Perot cavity (I) depends on the wavelength

of the incoming light. The relationship between the intensity and wavelength

(intensity transfer function) has a familiar Lorentzian shape (Fig. 1.5 (b)),

6

characterized by the equation,

I(ω) =1

π

Γ/2

(ω − ωr)2 + (Γ/2)2. (1.3)

Here, ω is the pump laser frequency, ωr is the resonant frequency, and Γ is

the linewidth of the resonance peak (Fig. 1.5(b)). We note that, the laser

detuning, ∆ω, is defined as:

∆ω = ωr − ω. (1.4)

A signal with a smaller frequency than the resonance frequency is called

red detuned (ω < ωr); a signal with a larger frequency than the resonance

frequency is called blue detuned (ω > ωr). Now, we park the pump laser near

𝜔 Frequency

𝜔𝑚

Γ =Full-Width at Half-Maximum

(FWHM)

𝐼(𝜔)

Intensity

(𝑎)

(𝑏)

Incoming light

𝜔

Light field inside the Fabry-Perot

with intensity 𝐼

Figure 1.5: (a) Fabry-Perot cavity. (b) Light inside the Fabry-Perot cavityhas intensity I.

resonance and we keep the left mirror fixed while moving the right mirror

sinusoidally. When the right mirror moves, the cavity length changes and

the resonance shifts. If we keep our laser parked at the same place, the

intensity inside the Fabry-Perot varies with the boundary movement (Fig.

1.6). Remember, every time when a photon is bounced off from a mirror,

it transfers two times its linear momentum to the mirror. Therefore, the

radiation pressure of the circulating light induces the expansion of the cavity.

7

𝐼(𝜔)

Intensity

Figure 1.6: Moving boundary of the Fabry-Perot cavity can cause theintensity inside the cavity to vary.

Consider now laser signal is blue detuned, while the right mirror is deformable

but is not intensionally moved (Fig. 1.7, note that the resonance is plotted in

wavelength in this figure). After the light is coupled in, the radiation pressure

of light causes the expansion of the cavity (right mirror moves to the right).

The expansion of the Fabry-Perot, in turn, shifts the resonance to a longer

wavelength (Eq. 1.3) and thus reduces the intensity inside the cavity. The

lowered radiation pressure cannot sustain the boundary deformation anymore

and the cavity collapses. Once the mechanical deformation is restored, the

process resumes. This leads to a self-sustained oscillation. This radiation

pressure induced instability is termed “parametric oscillation” by Braginsky

[73]. When the oscillation happens, the resonator is effectively an optical

modulator – during the expansion, circulating light experiences a red Doppler

shift; during the shrinking, circulating light experiences a blue Doppler shift.

Modulation of the device geometry at mechanical frequency Ω generates both

upper and lower optical sidebands of the pump light at ωp ± Ω. A detailed

discussion can be found in [74].

Although the first study about parametric instability talks about Fabry-

Perot cavity of the Laser Interferometer Gravitational Wave Observatory

(LIGO) [73], the similar process can happen in the WGM resonator. The

8

Figure 1.7: Illustration of the parametric instability of the Fabry-Perotcavity.

much higher quality factor of the optical WGM allows the amplification of

radiation pressure inside the resonator, enhancing the mutual coupling be-

tween the optical and mechanical modes significantly. When the input optical

power is larger than the threshold power, radiation pressure induced para-

metric instability generates mechanical oscillations (standing waves), which

can take various modeshapes. An example is shown in Fig. 1.8. The vibrat-

ing resonator can then be treated as the optical modulator: changing optical

path length modulates input laser, resulting in a pair of sidebands (Fig. 1.9).

Breathing mode

8 MHz

Figure 1.8: FEM simulation of a 8 MHz breathing mode on a 150 µmOMFR.

9

Resonator

surface

Radiation

pressure

𝜔𝑝 𝜔𝑝

Optical

WGM

Tapered fiber coupler

Mechanical

modes

Radiation

pressure

Tapered fiber coupler

𝜔𝑝 − 𝛺

𝜔𝑝 𝜔𝑝 + 𝛺

𝜔𝑝

Phase and amplitude

modulation Optical

WGM

Mechanical

modes

(a) (b) (c)

Figure 1.9: (a) High quality factor of the optical whispering gallery modesamplifies radiation pressure. (b) Radiation pressure induced parametricinstability generates mechanical oscillations at Ω . (c) Changing opticalpath length modulates input laser, resulting in a pair of sidebands at bothωp ± Ω.

1.4 Stimulated Brillouin scattering induced

optomechanical oscillation

Stimulated Brillouin scattering (SBS) is an acousto-optical nonlinearity [75–

78] that has been recently used for generating high frequency acoustic waves

in various resonant and nonresonant systems [1,5,20–25,61,79,80]. Brillouin

scattering is the scattering of light from propagating acoustic waves [77]. We

know that light scattering originates from the fluctuations in any of the op-

tical properties of the medium [77]. Indeed, propagating thermal acoustic

noises of the material can cause light scattering since the acoustic wave mod-

ifies the density of the medium, and thus the refractive index. As a result,

light can either be Stokes scattered, with scattering of light from a retreat-

ing acoustic wave, or it can be anti-Stokes scattered, with the scattering of

light from an oncoming acoustic wave. In the case of SBS, the incident light

with frequency ωL is at first Stokes scattered to a lower frequency, ωS (Fig.

1.10), by the thermal acoustic phonon. At this moment, the Stokes scatter-

ing happens at frequencies where the SBS gain is the largest [77]. We also

Thermal phonon

ωS, kS

ωL, kL

Figure 1.10: The start of stimulated Brillouin scattering process fromthermal phonon (adapted from [77]).

10

know that dielectric materials tend to be compressed in the presence of an

electric field, due to electrostriction pressure [77]. Indeed, EM waves can also

generate such pressures. The beat note between the incident and scattered

light from thermal phonons results in a pressure wave, which reinforces the

phonon. With stronger acoustic wave, more incident light can scatter off,

which accompanies the Stokes wave. Thus a mutual reinforcement between

the Stokes wave and the acoustic wave is formed through such positive feed-

back loop (Fig. 1.11). This process is governed by both the energy and

Sound ↔ Light

feedback loop

R. Chiao, C. Townes, Phys. Rev. Lett., 12 (12), 1964.

Energy conservation :: ħωL = ħωS + ħΩ

Momentum conservation :: 𝑘𝐿 = 𝑘𝑆 + 𝑘

. 11.3 GHz

Extremely high order

acoustic wave

Silica, 1550 nm

Speed of sound

Electrostriction excitation of sound

ωL, kL ωS, kS

Ω, k

Back

scattered light

Brillouin scattering of light from sound

Sound wave

ωS, kS

ωL, kL

Ω, k

Figure 1.11: Electromagnetic waves can generate constriction of dielectricsvia electrostriction force. The superposition of two optical fields can lead toa pressure wave, traveling at the speed of sound (upper figure). When thissound generation process is coupled with Brillouin scattering, which is thescattering of light from sound waves in a material, we end up getting apositive feedback loop that amplifies the acoustic wave starting from a fewthermal phonons. The bottom left figure uses Brillouin back scattering asan example. This process is governed by both energy and momentumconservation conditions. As shown by the bottom right figure, for silicamaterial for a 1550 nm pump, this phase matching occurs at 11 GHz forbackscattered light.

momentum conservation conditions. Here, the frequency difference between

the incident and scattered light is equal to the frequency of the sound wave.

11

The relationship between them is ( [77]):

ωS = ωL − Ω. (1.5)

In this process, the energy is being transfered from the incident photon to

the acoustic phonon.

We note that the Stokes scattering can happen in any direction. In the

case of WGM resonator, as shown in Fig. 1.12, after light is coupled to the

WGMs of the resonator, it can be scattered both forward and backward. As

an example, in Fig. 1.11, SBS occurs near 11 GHz for a 1550 nm pump laser in

silica material in the backward direction. In contrast, the acoustic frequency

is much lower (less than 1 GHz) in the case of forward scattering. Like

we have discussed above, the resulting acoustic waves are traveling waves,

taking the form of acoustic whispering gallery modes (Fig. 1.13). Since

the acoustic wave always travels unidirectionally with the scattered light,

circulating light only experiences either a red Doppler or a blue Doppler

shift, only one sideband of the pump laser is generated in the SBS process,

which is different to the RP induced modes.

Pump

Acoustic

Stokes

Pump

Acoustic Stokes

Resonator

Resonator

Fo

rwa

rd s

ca

tte

rin

g

Pump

Stokes

Pump

Stokes

Acoustic

Acoustic

Ba

ckw

ard

sca

tte

rin

g

Illustration of WGM interaction

with evanescent coupler

Momentum (k-vector) conservation for

acoustical and optical waves

𝑘

𝑘𝐿

𝑘𝑆

𝑘𝐿

𝑘

𝑘𝑆

Figure 1.12: SBS in WGM resonator (adapted from [5]). Bothforward SBS and backward SBS can happen in a WGM resonator. Themomentum conservation diagrams show that the relative length of theacoustic k-vectors needed in both the forward and backward scattering.

12

277 MHz M = 24

SAW-WGM

Figure 1.13: SBS mode at 277 MHz (adapted from [5])

1.5 Experimental setup and measurement

A typical experimental setup used for this thesis is shown in Fig. 1.14. A

colorized scanning electron micrograph of a OMFR is shown in Fig. 1.15.

Tapered fiber coupler is used to couple 1550 nm light from the tunable laser

into the WGM of an OMFR. The sample optical modes in the cross section

of an OMFR are shown in Fig. 1.16. Photodetector is used to convert

the temporal interference between pump and scattered light to electric RF

signal like shown in Fig. 1.17. The temporal electric signal is analyzed

by an electrical spectrum analyzer through a fast Fourier transform and a

power spectrum of the mechanical vibration is obtained. The spectrum has

a Lorentzian shape with the center frequency at the mechanical vibration

frequency [72].

1550 nm

Laser

Photodetector

Tapered fiber

coupler

Frequency

Counter

Circulator

Electrical

spectrum

analyzer

Photodetector

Electrical

spectrum

analyzer Silica capillary

resonator

(OMFR)

Figure 1.14: 1550 nm laser light is evanescently coupled into the WGMthrough a tapered fiber coupler. Photodetectors are used to convert theoptical transmission to RF signal. Electrical spectrum analyzer andfrequency counter can be used both in the forward and backward directionto analyze the signal.

13

Figure 1.15: Colorized scanning electron micrograph of a hollow-corefused-silica optomechanical resonator (OMFR).

Figure 1.16: FEM simulation of the first several orders of optical WGMs inthe shell of an OMFR (cross section view)

Power spectrum

Photodetector 𝜔𝑝 + 𝛺

𝜔𝑝 − 𝛺

𝜔𝑝 ESA

Electrical signal

Frequency

𝛺

Figure 1.17: The optical pump and the scattered sidebands from aradiation pressure induced vibration are made to interfere on high speedphotodetectors, thus generating beat notes at the mechanical vibrationfrequency. The beat note is then analyzed by the electrical spectrumanalyzer (ESA) and power spectrum (Lorentzian shape)of the mechanicalvibration is generated. The center frequency of the Lorentzian shape is atthe mechanical vibration frequency.

14

CHAPTER 2

MANUFACTURING OF OMFRS ANDMEASURING THE OPTOMECHANICAL

OSCILLATIONS

1 Cavity optomechanics have been demonstrated in many different optical

systems, such as fibers [81], microspheres [21, 82], toroids [9, 83] and crys-

talline resonators [22, 84]. While these previous optomechanics demonstra-

tions have focused on solid state sensors, recent demonstrations of opto-

mechano-fluidic resonators (OMFRs) have enabled applications with liq-

uids [5, 58] and gases [2]. These applications are accomplished by using the

hollow capillary structure of the OMFR, which is very different from previous

optical systems. In this chapter, we will discuss in detail how to manufacture

OMFRs, how to mount the OMFRs for testing, how to build tapered fiber

and couple light to WGM, and how to measure optomechanical vibrations.

2.1 Fabrication of OMFR

The material needed for the fabrication of the OMFR is very simple – a

silica capillary preform. The OMFR is fabricated by heating a glass capillary

preform with approximately 10 watts of CO2 laser radiation at 10.6 microns

wavelength, and drawing out the heated capillary linearly using motorized

translation stages. The silica glass material is a very good absorber to 10.6

micron laser light, making the laser heating possible. Meanwhile, silica glass

is a low loss waveguide for the 1.5 micron laser light, providing the high Q

needed for a strong photon-phonon coupling.

2.1.1 Preparation of capillary manufacturing setup

Fig. 2.1 shows the arrangement of the linear translation stages, the lasers,

and the location of the capillary preform before the pulling process. The two

1All the materials and instruments mentioned in this chapter are listed in Fig. B.1

15

Laser 1

Laser 2

Slow linear stage Fast linear stage

Mirror 2

Mirror 1 Beam block

Beam block

Capillary

Target zone

Figure 2.1: Schematic of the capillary pulling setup. The microfluidicoptomechanical resonators are drawn from a larger capillary preformattached to two linear stages while the glass is heated by the CO2 laser.Both laser beams are carefully aligned to the same spot of the capillary.Moving direction and relative speeds of the linear stages are indicated bythe arrows.

CO2 lasers (for heating) and the two linear stages are simultaneously con-

trolled by programing suitable automation software. The control software

used here is NI LabVIEW. The two linear stages perform the drawing pro-

cess for the laser-heated capillary. One of the linear stages must be fast (e.g.

5 mm/s) for the linear drawing process. More material to the heating zone

is fed with the second, slower linear stage (e.g. 0.5 mm/s) since the capil-

lary preform material gets depleted during the pulling process. The sample

holders are aligned on the linear stages along both vertical and horizontal

axes. Both CO2 laser beams are carefully aligned such that they target the

same spot in space (between the sample holders). A piece of card paper or

heat sensitive paper is useful for this process. Eye protection is used for laser

safety. Beam blocks, fume exhaust, and fire protection are used suitably.

Reasonable parameters are selected for the drawing process. For example,

the following parameters can be used to reliably produce a good capillary

size - 10 mm/s pulling speed, 0.5 mm/s feed-in speed, 3 s preheating time,

4.5 W preheating powers for both lasers, and 5 W heating powers for both

lasers. Modulation of the laser power during pulling can be used to control

the capillary radius lengthwise during the drawing process to form the bottle

resonators. An example is shown in Fig. 2.2(d). The proper modulation

parameters selected here are: 3 Hz frequency, 6 W and 3 W for laser powers,

16

and 50% duty cycle.

(a)

(b)

Laser target spot (glowing)

Pulled capillary

(c)

E shape structure

Plastic tube Resonators

Optical glue Slow stage

Fast stage

(d)

200 um

Figure 2.2: Optomechanical bottle resonator fabrication. (a) Thecapillary preform is pulled at a constant speed while being heated by meansof CO2 laser radiation. Note the glowing region is the laser target spot(where the beams heat the silica). When the required length and diameterare reached, (b) stop the linear stage motion and turn the lasers off. Thepulled capillary is thin, clear, and very flexible. (c) Employ an E shapeglass structure to mount the microcapillary resonator device as described inpart 2.1.3. The optomechanical bottle resonator is now ready to be taken tothe experimental setup and connected to tubing that will provide analytes.(d) Scanning electron micrograph of the fabricated optomechanical bottleresonator. Resonator radius and wall thickness can be varied as needed.

2.1.2 Fabrication of microfluidic optomechanical resonators

A sufficiently long segment (about 2 - 4 centimeters) of fused silica capillary

is first cut such that it can reach the two holders attached to the linear

translation stages. The capillary sample is mounted on the sample holders

such that the laser target zone is roughly in the middle of the capillary. The

capillary is pulled using the parameters as stated above. First the capillary

is preheated for a few seconds (Fig. 2.2(a)), and then it is pulled with or

without laser modulation (parameters in 2.1) as needed. The drawn capillary

(Fig. 2.2(b)) is removed from the sample holder. The sample is handled

with gloves at the two thick ends only, in order not to contaminate the clean

resonator surface. The pulling parameters are varied to fabricate capillaries

with different diameters. Typically outer diameter varies from 30 µm to 200

µm depending on pulling conditions.

17

2.1.3 Mounting the fabricated device for testing

An E shape glass holder (Fig. 2.2(c)) is prepared. Three 1 cm x 0.5 cm and

one 3 cm x 0.5 cm glass pieces are cut from glass slides (Fig. 2.3 (a)). They

are then assembled into an E shape using glass adhesive or superglue. A

length of microfluidic capillary out of the drawn sample is cut. This length

should be longer than the distance between two adjacent glass branches on

the E shape holder (Fig. 2.3 (b)).

The microcapillary device is glued onto the holder using optical adhesive

while making sure to keep a portion hanging uncontaminated between two

branches of the E shape holder (Fig. 2.3 (c)). The optical adhesive is cured

with a LED UV curing light source for 10 seconds. Fig. 2.2(c) and (d)

show the finished product. Both ends of the mounted resonator are carefully

inserted into two slightly larger plastic tubes (e.g. 200 µm in inner diameter)

(Fig. 2.3 (d)). Both ends are glued and cured using ultraviolet light to the

plastic tubes with optical adhesive. The E shape structure is clamped from

the third (free) glass branch to a clamped mounting device for testing (Fig.

2.4). The optical quality factor of the final microfluidic resonator depends

on how well the fabrication lasers were aligned and how stable their power

levels were.

(a) (b)

(c) (d)

Figure 2.3: Assembly of the fabricated device.

18

Figure 2.4: Clamped E shape structure.

2.2 Experimental setup for optomechanical testing

2.2.1 Fabrication of tapered optical fiber

A single mode telecom-band optical fiber is prepared of desired length (e.g.

a few feet). Fiber segment should be long enough to be both mounted in the

tapering area and connected to the setup (Fig. 2.6). The tapering method

explained here is similar to what is suggested and demonstrated in [69]. The

prepared fiber segment is connected to the rest of the experimental setup

using any convenient fiber-splicing method. The spliced fiber segment is

mounted onto two linear pullers that face each other. The fiber jacket is then

stripped off in the center of the mounted fiber fragment to expose cladding

area. This is where taper is fabricated. The stripped area is cleaned with

methanol. The tunable laser is turned on to see real-time transmission on an

oscilloscope. Attenuators are used so that photodetectors are not damaged.

A narrow nozzle hydrogen gas burner is placed immediately underneath the

unjacketed portion of the fiber. All recommended safety procedures must be

followed when working with pressurized flammable gases such as hydrogen.

Other clean burning sources of flame or ceramic heaters could also be used.

Before lighting up the gas, the flow rate is checked so that flame will not be

too large (a 1-2 cm tall flame is adequate). Note that the flame is mostly

invisible but may be seen as a faint bluish-;orange glow in a dark room.

The hydrogen flow rate should be set to a point where lighted flame will

19

adequately soften the glass fiber. As soon as flame is on, the fiber pulling is

started using motorized stages (Fig. ??). Appropriate pulling speed depends

on flow rate of hydrogen gas and vicinity of the flame. Transmission through

the fiber will begin to show temporal oscillation behavior as pulling continues.

This indicates multimode operation. When oscillatory behavior stops and

Pull Pull

Pull Pull

Pull Pull

Single mode

optical fiber

~ 125 um

~ 1 um

Hydrogen flame

~ 2200 C

Figure 2.5: Taper is pulled until the diameter is about 1 µm.

shows an unchanging signal over time, the pulling is stopped and the flame

is turned off immediately. This is when single-mode taper is obtained. The

transmission through the taper is checked then. If transmission is too low,

the procedure is repeated from 2.2.1. with modified gas flow rate, flame

size, and flame location. On occasion, low transmission could be due to bad

alignment at step 2.2.1. or due to contamination of the exposed cladding. If

resultant transmission through the taper is satisfactory, the taper is cooled

down by waiting a few minutes. The taper is inspected under a microscope.

For 1550 nm operational wavelength, typical diameter of the single-mode

taper is in the order of 1 - 2 µm.

20

Tapered fiber

Resonators

Figure 2.6: Coupling light from a fiber to micro resonator. The Eshape structure is mounted just above the tapered fiber so that light can beevanescently coupled into the resonators.

2.2.2 Taper-coupling to WGM and searching for electronicsignals indicating vibration.

The experiment is set up in the configuration shown in Fig. 1.14. Mechanical

vibrations can be generated through both SBS and RP by the same exper-

imental configuration. In order to clearly detect back-scattered signals as

in the case of backward-SBS [21, 85], a circulator is used between taper and

tunable laser (Fig. 1.14). The tunable IR laser is turned on and stabilized.

A function generator is used to sweep the frequency of the input IR laser.

The resonator holder is mounted on a nanopositioning stage. The resonator is

carefully brought close to the tapered fiber in order to obtain evanescent cou-

pling. As the laser frequency is swept, optical resonances will appear as dips

in transmission in the oscilloscope, as in Fig. 2.7. The photodetector output

is connected to an electrical spectrum analyzer (ESA), where the temporal

interference (i.e. beat note) between the input laser light and the scattered

light can be observed if mechanical oscillation takes place. This temporal

interference occurs at the mechanical oscillation frequency. The peak hold

function on the spectrum analyzer is often useful in the initial search for me-

chanical vibrations. Higher input power is used while performing the initial

search for mechanical vibration, especially when liquids are present inside the

device. Typically, input power in the order of 100 µW to the device is suf-

21

Figure 2.7: The transmission (blue line) changes as the laser sweeps(purple line).

ficient to excite mechanical vibration. If mechanical oscillation is observed,

the laser frequency scan is turned off and the laser wavelength is controlled

in CW mode to attempt to lock to the relevant optical mode. Here, both

oscilloscope and spectrum analyzer are useful in tandem. Periodic signals

appear on the oscilloscope when a mechanical mode is present, as seen in

Fig. 2.8 and [23,86].

2.3 Measuring optomechanical vibrations

2.3.1 Optical and electronic signature of radiation pressure(RP) modes.

As described in 2.2.2, mechanical oscillations will be observed when the taper

and device are correctly coupled, the device optical and mechanical modes

have sufficient Q-factors, and sufficient input optical power is provided. If

oscillations in the range of 10MHz - 1GHz are not observed, polarization

is changed to investigate different resonances, the input power from tunable

laser is increased in order to overcome the minimum threshold for oscillation.

When increasing the input power, we make sure not to saturate or damage the

22

photodetectors. Also, as described in [82], coupling distance is a key factor

for exciting different RP modes. If mechanical modes are still not observed,

optical quality factor can be measured. For microfluidic optomechanical res-

onators, results show that optical quality factor of 106 is sufficient to excite

parametric oscillations [58]. Usually, RP modes will manifest as electronic

oscillations on the spectrum analyzer accompanied by their harmonics, as

seen in Fig. 2.8. A scanning Fabry-Perot interferometer or high-resolution

optical spectrum analyzer is used to detect the optical side bands that are

generated due to amplitude and phase modulation, which is in turn induced

by the periodic cavity deformation. An example measurement may be seen

in Fig. 3h of [9].

20 40 60 80-100

-80

-60

-40

-20

0

Frequency, MHz

Po

wer,

dB

m

Photodetector signal Eigenmode of a capillary

24.94MHz

0 0.05 0.1 0.15 0.2 0.25

0.3

0.32

0.34

0.36

Time, s

Dete

cte

d P

ow

er,

a.u

.

(a) (b) (c)

Figure 2.8: Representative results (a) A breathing mechanical mode at24.94 MHz in the microcapillary is excited by centrifugal radiation pressureby light circulating in an optical mode. Modulation of the input light bythis mechanical vibration is observable on an electrical spectrum analyzerthrough beat-note generation on a photodetector placed in theforward-scattering direction (See Fig. 3). (b) An oscilloscope trace of thephotodetector output signal (i.e. transmitted power) shows the periodictemporal interference of the input light and scattered light. (c) Finiteelement simulation for the corresponding breathing mode confirms that theobserved optical modulation corresponds to an eigenmechanical frequency.Colors represent deformation and the simulation is sliced at the capillarymid-point for presentation.

2.3.2 Optical and electronic signature of whispering-galleryacoustic modes

The acoustic frequency of backward-SBS for silica glass is approximately 11

GHz when a 1.5 micron pump laser is used [21, 77]. A circulator to mon-

23

itor the back-scattered light and some small amount of Rayleigh-scattered

pump is used, to observe electronic signals for these vibrational modes. A

high-resolution optical spectrum analyzer is used to resolve the scattered

light. An example measurement is shown in Fig. 2 of [21]. The beat note

is used between forward scattered light and the pump laser to observe lower

frequency (sub-1 GHz) whispering-gallery acoustic modes. Due to the lower

mechanical rigidity in the breathing direction, the signal from SBS is some-

times weaker than the signal from the RP modes. Again, the laser is swept

at slow speed, and peak hold on the spectrum analyzer is used to help in

finding the SBS signal. Note that unlike RP-excited breathing modes, SBS-

excited whispering-gallery acoustic modes do not exhibit harmonics in the

optical and electronic spectra (unless cascaded excitation takes place [21,85]).

Instead only one Stokes sideband appears for SBS modes.

24

CHAPTER 3

AEROSTATICALLY TUNABLEOPTOMECHANICAL OSCILLATORS

3.1 Introduction

We have discussed, in last chapter, how to induce radiation pressure modes

and stimulated Brillouin scattering modes in detail. However, although

individual optomechanical devices can operate at multiple oscillation fre-

quencies [5, 23], these frequencies are discrete and the spectral gaps cannot

easily be filled. Achieving complete spectral coverage with a single device

can provide frequency-on-demand capability that is extremely important for

frequency-hopping and cognitive oscillator applications in communication

systems. Enhanced tuning also helps align optical and mechanical modes

to ‘phase match’ fundamental light-matter interaction processes that employ

optomechanics [24,26–28].

Till date, continuous tuning of the discrete optomechanical oscillation fre-

quencies is primarily achieved through direct temperature control [87] or

by managing the dropped power [79, 88]. However, tuning by means of

temperature is often impractical since low phonon occupation and specific

laser power coupling are often desirable, especially for single-phonon experi-

ments in the quantum regime. For this reason aerostatic tuning, i.e. tuning

through air pressure, is an alternative that can provide improved tuning

capability with greater spectral coverage. Aerostatic tuning has been suc-

cessfully employed with hollow microbubble resonators [48, 89], opto-fluidic

ring resonators (OFRR) [90], and ring resonators on flexible membranes [91].

Another deformation-based strategy involves the use of stretchable polymer

microspheres and achieves THz range tuning [92]. However, these extremely-

tunable devices have not yet been employed for optomechanics, and the tun-

ing of mechanical modes in conjunction with tuning of optical modes has

not been studied previously. In this study, we experimentally investigate the

25

aerostatic tuning of OMFR devices and we show the simultaneous actuation

and tuning of multiple modes and mechanisms of optomechanical oscillation.

3.2 Setup and working principle

As been discussed in Chap. 2, our experimental devices (Fig. 3.1(a)) are

fabricated from fused-silica glass capillary preforms that are drawn under

heating with infra-red laser light from two CO2 lasers [1, 90]. The diameter

of the hollow micro-device can be varied as a function of position by modu-

lating the heating laser power, with the widest region forming a bulb about

135 µm in diameter for example (Fig. 3.1(a)), where acoustic and optical

modes are simultaneously confined. The resonator wall thickness is about 12

µm (Fig. 3.1(a)) in this example. The wall can be made thinner as needed

by using a thin-walled preform, HF etching, and glass-blowing [59]. One end

of the device is sealed using optical glue while the other end is an open port

for pressure control (Fig. 3.1(b)). Pressure inside the capillary is controlled

by means of a syringe pump capable of micro-liter control while the ambient

pressure remains constant at 1 atm (101 kPa). Continuous-wave light from

a 200 kHz linewidth C-band external cavity diode laser (Newport Corpora-

tion TLB-6728) tunable between 1520 – 1570 nm (30 GHz fine-tuning range)

is coupled into the ”bottle” [93] optical whispering-gallery modes (WGMs)

of the device by means of a tapered optical fiber (Fig. 3.1(b)) [69]. The

taper is < 1 µm in diameter at the narrowest point and is single-mode for

the wavelength range used. An oscilloscope is used to monitor the forward

transmission in the tapered fiber and to identify where the optical resonances

occur. RP oscillations are observed on nearly all of the high-Q optical modes.

As described above, SBS oscillations require a more stringent phase matching

condition. Optical resonances that support SBS phase matching are found by

scanning the laser across the optical resonances and measuring resultant os-

cillations on the photodetector. Input laser power in the range of 10 – 20 mW

is used. Frequency-locking between the laser and the optomechanical device

is automatically achieved on the blue-detuned side of the optical resonance

through the well-known thermal self-stability mechanism [94]. Self-stability

is achieved here because of the ultra-high-Q of the optical resonances. In

contrast to most optomechanics experiments, the coupling fiber is placed

26

a

b

1550 nm

Laser

Photodetector

Tapered fiber

coupler

(in contact)

Frequency

Counter

Open port for pressure

control

Sealed

Circulator

Electrical

spectrum

analyzer

Photodetector

RP

Silica

resonator

c d

= 10-20 MHz

RP

Breathe

modeAcoustic

WGMStokes

WGM

11 GHz

Diameter = 135 µm

Thickness = 12 µm

SBS-driven OMO RP-driven OMO

Figure 3.1: Experimental overview (a) Colorized scanning electronmicrograph of a hollow-core fused-silica optomechanical resonator withradius modulated by design. Resonator wall thickness can be varied asneeded. (b) 1.5 µm light is coupled to the ultra-high-Q optical modes bymeans of a tapered fiber placed in contact to minimize vibrational issues.The optical pump and the scattered light are made to interfere on highspeed photodetectors in both forward and backward directions, thusgenerating beat notes at the mechanical vibration frequency. (c) Radiationpressure (RP) drives “breathing mode” optomechanical oscillators (OMOs)that generate both upper and lower sidebands of the input optical signal.(d) Stimulated Brillouin scattering (SBS) excites traveling whisperinggallery acoustic modes (WGAMs) that generate only a single Stokes shiftedsideband in the backscattering direction.

27

in contact with the resonator for improved resilience to ambient vibration

and geometry change. Indeed, the taper does add some damping to the me-

chanical modes but this effect is very small since the mechanical Q-factors

remain high. We observe the excitation of breathing mechanical oscillations

in the 10 – 20 MHz span driven by radiation pressure (Fig. 3.1(c)), and also

whispering-gallery acoustic mode (WGAM) oscillations driven by stimulated

Brillouin scattering [5, 20, 21, 23, 24, 61, 79] (Fig. 3.1(d)). Multimode oper-

ation through simultaneous oscillations of RP and SBS modes is possible,

as we show later. Both modes of operations are tunable by controlling the

aerostatic pressure in the device.

Like discussed in Chap. 1, we measure the radiation pressure induced

optomechanical oscillations (OMOs) at the acoustic frequency ΩRP in the

forward propagation direction on the tapered fiber. By monitoring back-

scattered light through a circulator, we can measure the temporal interference

of the pump laser and the scattered Stokes optical signal which occurs at the

acoustic frequency ΩSBS (Fig. 3.1(d)).

Multiple phenomena can contribute to the pressure response of the RP- and

SBS-driven OMOs in a hollow optomechanical system, namely (1) geometric

effect, (2) stress effect, and (3) temperature effect, as shown in Fig. 3.2.

The deformation of the resonator geometry by the application of differential

pressure between the internal pressure, Pint, and the ambient pressure, Pamb

∆P = Pint − Pamb, (3.1)

will affect the mechanical frequency ΩM directly. This can be modeled via

the resonant frequency equation for the breathing mechanical modes of an

annular resonator [95] of radius R.

ΩM =1

2πR

√E

ρ(3.2)

where, E is the modulus of elasticity and ρ is the mass density. The stiffness

of the resonator decreases as the radius of the annulus increases. For a radius

R of 67.5 µm and a wall thickness of 12 µm (Fig. 3.1(a)), the change of radius

of the resonator with respect to ∆P can be calculated through finite element

28

Pint

Ambient

pressure,

Pamb

Pint

dR Pamb

Radius

increases

Mechanical

frequency

decreases

Mechanical

frequency

increases

Optical

resonance

shift

Less light in T drops

Temperature

drops

Pint Pamb

Stress

builds up S

Pump laser

λ

Figure 3.2: Aerostatic tuning mechanisms: Increasing the internalaerostatic pressure (Pint) causes geometry change (radius, dR) andincreases the stress (S) in the resonator shell, both of which cause themechanical frequency to shift. Geometry and stress effects also modify theoptical modes, which changes the laser power coupling and thus energydissipation in the resonator, modifying the device temperature. Since themechanical modulii of a material are temperature-dependent, this alsoinduces a change in the mechanical frequency of the OMO.

analysis in COMSOL Multiphysics [96] to provide

dR/d∆P = 3.82× 10−12 m/kPa. (3.3)

Similarly, the mechanical frequency due to geometry perturbation can also

be calculated to get

dΩM/dR = −0.19× 1012 Hz/m. (3.4)

Here, we define a new quantity, the pressure coefficient of frequency,

PCf = dΩM/d∆P = dΩM/dR× dR/d∆P = −0.736 Hz/kPa (3.5)

caused by geometry change alone.

Circumferential stress (S) is also developed on the resonator when pressure

is applied. Stress-induced stiffening effects are well-understood, and have

been previously studied in the case of beams as described by equation (5.144)

of [95] and in the case of curved beams and annular resonators in [97]. In

29

general, higher tensile stress (such as that caused due to pressure exerting

an outward force on a hollow tube) causes mechanical resonance frequencies

to increase [97].

Finally, we note that the optical modes also shift in response to the applied

pressure, by the optomechanical coupling coefficient dω/dR. For a fundamen-

tal optical WGM at free-space wavelength λ0 = 1550 nm on our R = 67.5

µm device, the estimated azimuthal wavenumber of the modes is

M = 2πRn/λ0 = 396. (3.6)

Therefore, we can analytically calculate the couping coefficient

dω/dR = −cM/(2πR2n) (3.7)

for this simplified situation, which is estimated at -2.85 GHz/nm for the

considered device. Employing the above analysis for mechanical modes, the

optical mode tuning to applied pressure is estimated as

dω/d∆P = dω/dR× dR/d∆P = -0.011 GHz/kPa. (3.8)

In our ultra-high-Q resonator (Qopt ≈ 108) where the optical losses are ex-

tremely low and the mode linewidth is narrow (≈ 2 MHz), these shifts in

the optical mode can significantly affect power coupling into the device, and

thus affect the optical power being dissipated in the silica. The relationship

between the net heat dissipated to the cavity with the optical resonance shift

and temperature change has been revealed in [94,98], which also examined the

microcavity dynamical thermal behavior in detail. The temperature tuning

of optical modes in silica resonators is known to be 6 ppm/K [94]. Since silica

has a large temperature coefficient of Young’s modulus of 183±29 ppm/K [99]

while the thermal expansion coefficient of silica is about 2.6 ppm/K [99], the

resulting temperature coefficient of mechanical frequency is aaproxiamately

90 ppm/K and is dominated by the Young’s modulus change. Thus a minute

shift of the optical mode can significantly temperature-tune the oscillation

frequency, even when the optical mode is over-coupled due to taper-device

contact. This is challenging to theoretically model as the thermal pathways

in the system are complex. However, we can control the power coupling into

the resonator to be constant by tracking the optical resonance when it shifts

30

under applied pressure. Since the temperature of the resonator is related

to the power dissipated in the resonator, feedback control of the coupled

power maintains a constant temperature in the device and eliminates any

additional temperature-related stress or radius effects.Such feedback control

will successfully arrest the unpredictability of the RP-driven OMO. How-

ever as we explain later, the SBS-driven OMO cannot be controlled in this

way as it depends on two optical modes that typically have slightly different

temperature coefficients.

3.3 Results and discussion

Our experiment is capable of testing over a wide differential pressure range

(∆P = -90 kPa to 1000 kPa). However, in order to avoid optical and me-

chanical mode hopping, we experimentally measure the behavior of the RP-

and SBS-driven OMOs over a smaller pressure range. As described above,

the PCf is the fractional shift of oscillation frequency for a change in ∆P .

As shown in Fig. 3.3, the mechanical vibration frequency is tuned through

internally applied pressure. The sensitivity is measured to be PCf = -3.1

Hz/kPa without any control applied to the coupled optical power. As we de-

scribed above, when pressure is increased inside the resonator, the geometric

deformation and the temperature effect both act to decrease the mechanical

frequency. However, the stress effect simultaneously acts to increase the me-

chanical frequency. A study of these three effects separately is necessary to

verify our hypothesis. However, decoupling the geometric effect and stress

effect is not feasible. Nevertheless, one can apply feedback control on the

coupled optical power in order to at least eliminate the temperature effect.

With such feedback applied (Fig. 3.3), the PCf without the temperature ef-

fect is measured to be +4.4 Hz/kPa. Since the geometrical effect is small as

calculated (PCf = -0.736 Hz/kPa), this positive PCf verifies the strong influ-

ence of the additional stress-tuning effect. The reversed sign of PCf indicates

that the temperature effect is a major influence in determining sensitivity of

this high-Q OMO.

In contrast to the RP-driven OMO, the SBS-driven 11 GHz OMO requires

two optical modes and one acoustic mode that are mutually phase matched

(this can also be understood as a momentum and energy conservation re-

31

100 120 140 160 180 200 220−400

−300

−200

−100

0

100

200

300

400

500

Pint

, kPa

Osc

illat

ion

freq

uenc

y sh

ift, H

z

With feedback control on powerLinear fit (with feedback control)Without feedback control on powerLinear fit (without feedback control)

PCf = +4.4 Hz/kPa

PCf = −3.1 Hz/kPa

Figure 3.3: Aerostatic tuning of a 13.07 MHz RP-driven OMO. Wecharacterize aerostatic tuning of the OMO using a fixed-frequency pumplaser, observing a negative pressure coefficient of frequency (PCf) caused bylowering of the temperature of the device due to the optical mode shift.When feedback control is applied on the laser (to track the shifting opticalmode) the amount of power coupling into the device does not change. Thusthe temperature effect is eliminated and the net positive PCf indicates thatthe OMO frequency is dominated by the increasing stress in the resonatorshell.

quirement) [5, 58]. At such high frequencies, the WGAMs are part of a

continuum, and thus do not restrict a specific operational frequency. As a

result, pressure tuning of SBS-driven OMOs is highly sensitive to the sepa-

ration between the two optical modes involved, which are known to exhibit a

wide variety of slopes in their dispersion behavior [100,101]. Our experimen-

tal data provides evidence for this argument by demonstrating both positive

(Fig. 3.4(a)) and negative (Fig. 3.4(b)) PCf for different 11 GHz OMOs

on the same resonator. We find that for any specific optomechanical cou-

pling mode the SBS-based sensor demonstrates very large absolute pressure

sensitivity (up to | PCf | = 55 kHz/kPa) and is repeatable.

Finally, we note that on a low stiffness shell-type resonator that we ex-

plore here, it is easy to actuate SBS-driven oscillation simultaneously with

RP-driven oscillation. A representative experimental spectrogram demon-

strating such dual-mode operation is shown in Fig. 3.5. The SBS oscillation

(ΩSBS ≈ 11.2 GHz) is modulated by the RP oscillation (ΩRP ≈ 16 MHz)

resulting in sidebands that are separated by ΩRP . This modulation occurs

because the resonator geometry is being modified by the radiation pressure

32

100 120 140 160 180 200-6

-4

-2

0

2

Pint

, kPa

Oscill

ation

frequency s

hift,

MH

z

PCf = -55.1 kHz/kPa

100 200 300 400 5000

2

4

6

8

10

Pint

, kPa

Oscill

ation

frequency s

hift,

MH

z

PCf = +26.6 kHz/kPa

a b

Figure 3.4: Aerostatic tuning of 11.2 GHz SBS-driven OMOs: Both(a) negative and (b) positive PCf are observed in multiple trials, exhibitinglarge absolute pressure sensitivity. The red line is a linear fit to the data.

oscillation, resulting in coupling between the two oscillation modes. As the

internal pressure is changed from 1 atm (∼101 kPa) to 5 atm (∼500 kPa),

both ΩRP and ΩSBS are tuned (Fig. 3.5). The tuning of the two modes

can be quantified accurately by interferometric measurement of the forward

and backward scattered optical signals as explained previously. A represen-

tative result is shown in Fig. 3.6. The frequency shift data are presented in

parts-per-million (ppm) since the absolute sensitivity of the SBS oscillator

is four orders-of-magnitude greater than the RP oscillator. Such multimode

operation enables the future possibility of self-referencing the pressure sensor

without need for additional amplitude or wavelength references.

3.4 Future work

Here we have demonstrated the aerostatical tunability of the optomechan-

ical oscillators driven by both radiation pressure and stimulated Brillouin

scattering. In the future, the thickness of the wall needs to be thinned to

increase the pressure sensitivity when the oscillator is used for pressure sens-

ing. For future optomechanics experiments with liquids infusing inside the

OMFR, understanding the pressure effect accompanied with infusing is im-

portant. We note that this coupled system involves a MHz regime mechanical

oscillator, a GHz regime mechanical oscillator, and a 200 THz regime opti-

cal oscillator. This presents a unique and exciting opportunity to explore

coupled oscillator dynamics over extremely broad timescales, and to study

33

16 MHz 16 MHz

Pint (atm)

1 5

Relative Frequency, MHz

CF =11.2 GHz

16 MHz - ∆𝛺RP 16 MHz - ∆𝛺RP

Figure 3.5: RP and SBS oscillations can be simultaneously actuated on asingle device as evidenced in this spectrogram. Experimentally, the ΩRP =11 GHz oscillation shows multiple sidebands separated by ΩRP = 16 MHz.As internal pressure is changed from 1 atm (∼101 kPa) to 5 atm(∼500 kPa), both the 11 GHz OMO and the 16 MHz OMO are tuned. CF,center frequency.

100 102 104 106 108 110 112 114 116 118−50

0

50

100

150

200

250

Pint

, kPa

Osc

illat

ion

freq

uenc

y sh

ift, p

pm

RP modelinear fit (RP)SBS modelinear fit (SBS)

PCf for RP (15.2 MHz)−0.81 ppm/kpa

PCf for SBS (10.9 GHz)+13.8 ppm/kpa

Figure 3.6: Aerostatic tuning experiment with simultaneous RP (15.2 MHz)and SBS oscillation (11 GHz) on a device. Fractional mechanical frequencyshift is recorded in parts-per-million (ppm) for convenient comparison sincethe SBS OMO absolute sensitivity is four order-of-magnitude higher.

34

the coupling of fields and signals spanning radio-frequency, microwave, and

optical regimes.

35

CHAPTER 4

OPTO-MECHANO-FLUIDICVISCOMETER

4.1 Introduction

The measurement of a shift of a resonators vibrational frequency to infer mass

of a particle has been achieved with fluid infused suspended microchannel

resonators [63]. By confining liquid inside the suspended microchannel res-

onator (SMR) rather than submerging the resonator in the fluid, the aqueous

environment needed for biological applications can be provided to cells and

other bio-particles without performance degradation of the SMR from vis-

cous damping. This method has recently achieved mass detection resolution

as impressive as 0.85 attograms [102]. SMRs have been employed for a wide

range of biological applications, for example, monitoring cell growth [103] and

studying single cell biophysical properties [104]. The impressive capabilities

of SMRs and the ability to overcome fluid dissipation are key inspirations

for OMFRs. Based on this concept, by using acoustic waves shorter than

the dimensions of a cell (or high frequency acoustic waves), the details of

cells, like composition and membrane stiffness, can be revealed that cannot

be observed by conventional microscopy. As a matter of fact, high-frequency

opto-acoustic interaction (Brillouin scattering) has been used to measure

fluid properties [105,106], hydration of biofilms [107], and image mechanical

properties of bioparticles beyond the abilities of optical microscopy [108,109].

The recent introduction of optically-interfaced acoustics into optofluidic

devices [5,58], inspired by lab-on-a-chip mechanical sensors [63], is providing

researchers with a new mechanical degree of freedom by which to perform

such biochemical analyses. In this part we have invoked these opto-mechano-

fluidic techniques to develop the first microfluidic optomechanical sensor of

liquid viscosity.

36

4.2 Setup and working principle

In this work, the device we use has a ∼ 170 µm diameter and ∼ 15 µm wall

thickness. One end of the device is left open while the other end is connected

to a syringe through which analytes can be infused (Fig. 4.1). The sensing

volume contained within is about 20 nl, and can be reduced by changing the

fabrication parameters.

Electrical Spectrum

Analyzer

Photodetector

Tapered fiber

coupler

Pump

Fluid outlet

𝜔𝑝 + 𝛺

𝜔𝑝 − 𝛺

𝜔𝑝

Optomechanofluidic

resonator

Polarizer

𝜔𝑝 1550 nm

Laser

Test

Fluids

Test fluid plugs can be

moved through device

Figure 4.1: Experimental overview: The temporal interference of opticalsignals at the photodetector generates an electronically measurable signal,allowing the mechanical power spectrum to be measured using an electricalspectrum analyzer. Test fluids can be pumped in and out of the resonator,changing the effective mass and stiffness as well as the damping loss rate.

Continuous-wave 1550 nm laser light is coupled into the optical whispering-

gallery modes (Q-factor ∼ 107) of the OMFR by evanescent coupling [69]

through a tapered optical fiber (Fig. 4.1). The taper is not in contact

with the device, which prevents additional damping effects. The radiation

pressure of light is capable of actuating eigenmechanical oscillations through

the optomechanical parametric instability [58] in this device (Fig. 4.2(a)).

Mechanical modulation of the device geometry generates optical sidebands

of the input light. Even when the parametric actuation threshold power is

not reached, stochastic thermal fluctuations (Langevin noise force) provide a

detectable amount of quiescent energy to the mechanical degrees of freedom.

We can electronically measure the noise spectrum of the mechanical mode by

observing the beating between input and scattered light on a photodetector

(Fig. 4.1).

In this work, Ω ≈ 11 MHz, 13 MHz, and 17 MHz vibrational modes are

37

Vibrational frequency

Shell deformation

mode

Fluid pressure

mode

11 MHz

13 MHz

17 MHz

(a)

11 MHz

13 MHz

17 MHz

Frequency, MHz Mec

hani

cal P

ower

Spe

ctru

m, a

.u.

(b)

Figure 4.2: (a) Mechanical power spectrum using above-threshold,continuous-wave laser excitation power shows three mechanical modes. (b)Multiphysical simulations of solid OMFR shell and coupled pressure wavesin fluid for the 11 MHz (high order wineglass mode), 13 MHz (breathingmode), and 17 MHz (high order wineglass mode) vibrational resonances.

selected (Fig. 4.2(a)). According to computational models, these modes are

high-order wineglass modes and a breathing mode, where both fluid and shell

are coupled into a hybrid eigenmode (Fig. 4.2(b)). For a continuously driven

system, the mechanical damping losses in these hybrid shell-fluid modes can

be obtained through optical measurement of the linewidth of the Lorentzian

shaped mechanical noise spectrum as described in Fig. 4.3. Information on

both the mechanical damping rate and the effective mass and stiffness of the

hybrid system are embodied in the vibrational noise spectrum. By measuring

the linewidth of the spectrum, Γ, we can quantify the mechanical damping

rate of the system; by measuring the center frequency of the spectrum, Ω,

we can quantify the oscillator effective mass and stiffness.

Optomechanical self oscillation [58,110], however, narrows the vibrational

linewidth due to amplification, which affects the ability to measure intrinsic

oscillator damping. Here we make sure to employ very low subthreshold

input optical power to avoid amplifying the mechanical motion to the self

oscillation point. Specifically, the typical threshold input optical power for

oscillation for our system is in the range of 10 mW when the OMFR is

loaded with liquids, and we ensured that the input optical power was always

less than 0.5 mW. In such a low-power situation, as described in [111], the

influence of the coupled optical power on the linewidth can be neglected.

This preserves the intrinsic damping and natural linewidth of the vibrational

spectrum, allowing us to quantify intrinsic loss rates.

38

Γ1 = 11971 Hz

Ω1 =16.59 MHz

Γ2 = 47820 Hz

Ω2 =17.68 MHz

Mech

anic

al p

ow

er

spect

rum

Frequency

Change fluid

Theore

tica

l Experi

menta

l

Γ is related to damping.

Ω is related to oscillator effective mass and stiffness.

Ω1

Γ1

Fluid 1:

𝜌1, 𝜇1

Viscosity oil N2:

𝜌1 = 0.76 g/mL

𝜇1 = 2.2 cP

Viscosity oil S20:

𝜌2 = 0.86 g/mL

𝜇2 = 37 cP

Ω2

Γ2

Fluid 2:

𝜌2, 𝜇2

(a)

(b) (c)

Mech

anic

al p

ow

er

spect

rum

, a.u

.

Frequency, MHz Frequency, MHz

Mech

anic

al p

ow

er

spect

rum

, a.u

.

Figure 4.3: (a) Theoretically, the vibrational noise spectrum containsinformation about both the mechanical damping rate and the effective massand stiffness of the hybrid system. The linewidth (-3 dB bandwidth) of thespectrum, Γ, is related to damping; and the vibrational frequency, Ω, isrelated to the oscillator effective mass and stiffness. Example measurementof the vibrational noise spectrum of ∼ 17 MHz mode with (b) N2 viscosityoil, and with (c) S20 viscosity oil. In both cases, there are linewidth andcenter frequency changes.

39

4.3 Results

To calibrate the optomechanical viscometers, we use seven viscosity stan-

dard oils (Cannon Instrument Company – Table 4.1). For each of the three

vibrational modes in Fig. 4.2(a), we plot in Fig. 4.4(a) the density normal-

ized experimentally measured mechanical mode linewidth Γ/√ρ, against the

square root of the viscosity,õ.

Table 4.1: Properties of the calibration viscosity oils

Sample Density (g/mL) Viscosity (cP)N2 0.762 2.2N4 0.787 5.2S6 0.878 10

N10 0.884 21S20 0.863 37N26 0.820 47N35 0.868 75

The results in Fig. 4.4(a) can be understood by considering the nature

of viscous damping in OMFR. The geometry of the resonator is a shell,

which locally resembles the thin plate case discussed in [112]. Because of

liquid entrainment within the resonator, viscous damping, associated with

both shear and normal motion of the fluid relative to the resonator wall,

occurs near the solid-fluid interface. For thin shells or plates, this damping

is dominated by the shear motion of the fluid relative to the resonator wall.

The attenuation rate due to viscous damping is proportional to√ρµ at low

values of viscosity [112]. At high viscosity, attenuation saturates due to the

viscoelastic nature of the fluid. Using Maxwell’s model of a viscoelastic fluid,

a critical viscosity separating low and high viscosity regimes can be defined

by µc = τG∞ at which 2πΩτ = 1, where Ω is the mechanical vibrational

frequency, τ is the viscoelastic relaxation time in the liquid, and G∞ is the

high-frequency elastic rigidity modulus. Assuming a typical G∞ value of 1

GPa [112], the µc for a 10 MHz device is 1.6 × 104 cP, indicating that our

experiment is well within the linear regime. Since the intrinsic losses of the

mechanical modes without liquids are very low (Qm ∼ 103-104 without fluids),

the acoustic energy loss primarily arises from viscous damping associated

with the fluid (Qm ∼ 101-103 with fluids). By electronically measuring the

vibrational noise spectrum of the mechanical mode, the mechanical mode

40

2 4 6 811

12

13

14

15

16

17

18

+,

MH

z

p7,

pcenti poi se

11 MHz mode

13 MHz mode

17 MHz mode

2 4 6 80

0.05

0.1

0.15

0.2

0.25

0.3

!=p

;,

MH

z=p

g=cm

3

p7,

pcenti poi se

(a)

(b)

Densi

ty n

orm

aliz

ed lin

ew

idth

V

ibra

tional

fre

quency

Square root of viscosity

2 4 6 811

12

13

14

15

16

17

18

+,

MH

z

p7,

pcenti poi se

11 MHz mode

13 MHz mode

17 MHz mode

Square root of viscosity

Figure 4.4: (a) Measured linewidth of selected mechancial modes operatingwith viscosity standard oils shows that the damping loss rate Γ increaseslinearly with square root of viscosity

õ. Slope differences between

different modes indicate different modeshapes (Fig. 4.2(b)). Dashed linesare the linear fits. (b) Measured frequency of selected mechanical modesoperating with viscosity standard oils. The three selected modes havesimilar frequency trend. This increasing frequency trend is likely caused byvariation in density and the speed of sound of the test fluids [58].

41

linewidth, Γ, is obtained (Fig. 4.3(b),(c)). Since Γ is proportional to loss

rate, it is also proportional to√ρµ at low values of viscosity. In order to

isolate the effects of viscosity, we normalize the linewidth against√ρ to

obtain Fig. 4.4(a). We note that the linewidth slopes of the 11 MHz and

17 MHz modes are similar, but are lower than that of the 13 MHz mode,

potentially indicating a difference in the mechanical mode families. This

can be intuitively understood as a greater amount of mechanical energy of

the 13 MHz breathing mode is stored in the fluid and is subject to viscous

dissipation.

In addition, the measured relationship between the line center frequency

Ω and√µ is plotted in Fig. 4.4(b). We see that the frequencies of all three

modes are not constant but follow the same increasing trend. We believe

that the frequency shift is correlated with the density and speed of sound

change in the test fluids as has been established previously [58].

4.4 Influence of the shell thickness

We now proceed to analyze how the sensitivity and dynamic range are influ-

enced by the OMFR shell thickness. As discussed in [112], the attenuation

rate is inversely proportional to the plate thickness due to the fact that a

thicker plate can transmit more wave energy compared with the amount lost

in viscous dissipation. Thus, in the OMFR case, a thinner shell should be

used to increase the viscosity sensitivity. In contrast, a thicker shell should

be used to expand the viscosity measurement dynamic range. However, as

revealed by [61], thick shells can prevent the acoustic excitation from inter-

acting with the liquid. So does increasing the mechanical frequency since

it can decrease the radial depth of the acoustic mode. Therefore a suitable

balance between operational frequency and shell thickness must be sought.

Finally, we note that thin-shell resonators are also subject to potentially

undesirable pressure effects [2] generated by pumped liquids (Chap. 3).

42

4.5 Comparison with other MEMS viscometers

Several types of fully-contained microfluidic oscillating microstructures for

measuring fluid viscosity have been developed previously. They employ a

variety of actuation methods, including electromagnetic [113], electrostatic

[114], thermal [115], and piezoelectric [116] techniques. Our viscometer uses

an optical interface, but the principle of viscosity measurement is still the

damping of a vibrational mode. As a result, we expect similar limitations to

dynamic range, noise performance, and sensitivity when compared against

existing MEMS technologies.

4.6 Future work

In the near future, we will need to implement the Pound-Drever-Hall method

[117] to stabilize the laser wavelength and laser power that coupled into

OMFR to stabilize the mechanical vibration and increase the frequency de-

tection resolution. Meanwhile, instead of static measurement, viscosity mea-

surement will be implemented while infusing the liquids into the OMFR.

Besides laser stabilization, such a dynamic measurement also requires con-

stant pressure difference between the inlet and outlet to avoid the pressure

tuning of the resonance [2]. In the long-term, we envision high-throughput

acoustic flow cytometry.

43

CHAPTER 5

CONCLUSIONS

We have fabricated and tested a new device that bridges between cavity

optomechanics and microfluidics by employing high-Q optical resonances to

excite (and interrogate) mechanical vibration. It is surprising that multiple

excitation mechanisms are available in the very same device, which gener-

ate a variety of mechanical vibrational modes at rates spanning 2 MHz to

11300 MHz. Centrifugal radiation pressure supports both wineglass modes

and breathing modes in the 2 MHz – 200 MHz span, forward stimulated Bril-

louin scattering allows mechanical whispering gallery modes in the 50 MHz –

1500 MHz range, and lastly, backward stimulated Brillouin scattering excites

mechanical whispering gallery modes near 11,000 MHz.

The methods that are described in the current work enable the fabrica-

tion of these microfluidic resonators with ultra-high optical quality factors of

about 108. Simultaneously, since liquids are now confined within the device,

acoustic losses are brought under control and the device is able to maintain

a high mechanical quality factor as well.

There are a few practical challenges associated with this fabrication method.

For instance, the capillary material must be a good absorber for the 10.6 mi-

cron CO2 laser radiation so that it can heat up sufficiently for the pulling

process to take place. In this regard, the materials that have been tested for

capillary fabrication are silica and quartz. Furthermore, the circular symme-

try of the capillary is dictated by the relative power balance between the two

lasers that are employed during the pulling step, and by the location of the

capillary in the laser target zone. Since the circular symmetry of the device is

a key parameter for maintaining high optical and mechanical quality factor,

misalignment of the capillary preform in the CO2 laser target zone before

pulling or during pulling can be a concern and care must be taken to keep

this under control.

On the other hand, this fabrication method provides a lot of flexibility

44

in the fabrication of silica-based optomechanical capillary resonators. By

modulating the CO2 laser power, the capillary diameter can be varied quite

easily to suit the application. On demand spacing between adjacent bottle

resonators is possible thanks to the high degree of computer control. Finally,

control of the rate of pulling and the rate of feed in of the capillary preform

provides an easy knob for controlling the capillary diameter.

We have also experimentally demonstrated and characterized the first

aerostatically-tunable optomechanical oscillators driven by both radiation

pressure as well as stimulated Brillouin scattering. Understanding the pressure-

sensitivity of these deformable devices is important for future optomechan-

ics experiments with liquid-phase media such as viscous liquids, bioana-

lytes [5, 58], and superfluids [118]. We note that multimode oscillators with

different coefficients-of-frequency have been employed widely in quartz [119]

and MEMS [120] resonator technology to provide reference-free operation for

timing reference and sensor applications.

In addition, our viscometer result supplements established passive [121,

122] and active [122, 123] microrheological techniques for the optical mea-

surement of fluid viscoelasticity, but does not contaminate the fluid with

dispersed particles.

Potential applications of this system include sensing in extremely harsh

conditions, because the advantage of our all-silica fiber-interfaced device is

the operability in high temperature, remote, and electromagnetically noisy

environments, such as engines, oil wells, and reaction chambers. Finally,

the GHz-regime multifrequency capability of OMFRs [5] can enable high-

frequency probes for mapping viscoelastic properties of fluids and boundary

layers. In the long-term, we envision high-throughput viscoelastic measure-

ments on flowing living cells, essentially enabling a novel acoustic flow cy-

tometry.

45

APPENDIX A

MEASUREMENT OF THE GEOMETRYOF THE OMFR

The measurement of the dimensions of the OMFR is done under the micro-

scope with the help of a camera control software called ToupView. The view

can be seen through the software is shown in Fig. A.1 (a). The red line

can be used to measure the length (in pixels) between two points. Such a

length can be converted to the real length (in µm) after a calibration. The

conversion relation in our case is

length (µm) = 11.1111× pixels/magnification (A.1)

By doing similar measurement, the dimensions (Fig. A.1 (b)) of the OMFR

can be determined, namely, length L, outer diameter at the widest point D1,

inner diameter at the widest point d1, outer diameter at the thinnest point

D2, and inner diameter at the thinnest point d2.

A more accurate way to measure the side wall thickness is to cut the cap-

illary and look at the cross section under microscope. Such method could

avoid the influence of refraction when measuring from the side view. How-

ever, the accuracy of this measurement depends on the observation angle.

In real application, the aspect ratio, which is the ratio of the outer diameter

and inner diameter, can be assumed unchanged from the initial value [124].

Thus during experiments, one can only measure outer diameter, given that

the initial aspect ratio is known.

46

109.88 px

=122 um

77.10 px

=86 um

Magnification = 10x

D1

L

d1 d2 D2

(a)

(b)

Figure A.1: (a) Measurement of the outer and inner diameter of an OMFRfrom the side view. (b) Dimensions of an OMFR.

47

176 px

= 49 um

148 px

= 39 um

Figure A.2: (a) Measurement of the outer and inner diameter of an OMFRfrom the cross section view.

48

APPENDIX B

MATERIALS’ LIST FOR THEFABRICATION OF OMFR

Figure B.1: Materials’ list for the fabrication of OMFR.

49

REFERENCES

[1] K. Han, K. H. Kim, J. Kim, W. Lee, J. Liu, X. Fan, T. Carmon,and G. Bahl, “Fabrication and testing of microfluidic optomechanicaloscillators.” Journal of visualized experiments, no. 87, p. e51497, Jan.2014.

[2] K. Han, J. H. Kim, and G. Bahl, “Aerostatically tunableoptomechanical oscillators.” Optics Express, vol. 22, no. 2, pp.1267–76, Jan. 2014.

[3] K. Han, K. Zhu, and G. Bahl, “Opto-mechano-fluidic viscometer,”Applied Physics Letters, vol. 105, no. 1, p. 014103, July 2014.

[4] K. Zhu, K. Han, T. Carmon, X. Fan, and G. Bahl, “Opto-Acoustic Biosensing with Optomechanofluidic Resonators,” 2014.arXiv: 1405.5282.

[5] G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon,“Brillouin cavity optomechanics with microfluidic devices,” Nat.Commun., vol. 4, no. May, p. 1994, Jan. 2013.

[6] J. Mertz, O. Marti, and J. Mlynek, “Regulation of a microcantileverresponse by force feedback,” Appl. Phys. Lett., vol. 62, no. 19, pp.2344–2346, 1993.

[7] C. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature,vol. 432, no. 7020, pp. 1002–1005, Jan 2004.

[8] C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Kar-rai, and F. Marquardt, “Self-induced oscillations in an optomechanicalsystem driven by bolometric backaction,” Phys. Rev. Lett., vol. 101, p.133903, Sep 2008.

[9] T. Carmon, H. Rokhsari, L. Yang, T. Kippenberg, and K. Vahala,“Temporal behavior of radiation-pressure-induced vibrations of an op-tical microcavity phonon mode,” Phys. Rev. Lett., vol. 94, no. 22, p.223902, 2005.

50

[10] O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann,“Radiation-pressure cooling and optomechanical instability of a mi-cromirror,” Nature, vol. 444, no. 7115, pp. 71–74, Nov 2006.

[11] S. Gigan, H. Bohm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg,K. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, “Self-coolingof a micromirror by radiation pressure,” Nature, vol. 444, no. 7115, pp.67–70, Nov 2006.

[12] D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a mi-cromechanical resonator,” Nature, vol. 444, no. 7115, pp. 75–78, Nov2006.

[13] J. Thompson, B. Zwickl, A. Jayich, F. Marquardt, S. Girvin, andJ. Harris, “Strong dispersive coupling of a high-finesse cavity to a mi-cromechanical membrane,” Nature, vol. 452, no. 7183, pp. 72–75, Mar2008.

[14] J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause,S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of ananomechanical oscillator into its quantum ground state,” Nature, vol.478, no. 7367, pp. 89–92, 2011.

[15] R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser,and T. Kippenberg, “Optomechanical sideband cooling of a microme-chanical oscillator close to the quantum ground state,” Phys. Rev. A,vol. 83, no. 6, p. 063835, June 2011.

[16] M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson,F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding be-tween optical waveguides,” Opt. Lett., vol. 30, no. 22, pp. 3042–3044,Nov. 2005.

[17] M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, andH. X. Tang, “Harnessing optical forces in integrated photonic circuits,”Nature, vol. 456, no. 7221, pp. 480–484, Nov. 2008.

[18] M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “Apicogram- and nanometre-scale photonic-crystal optomechanical cav-ity,” Nature, vol. 459, no. 7246, pp. 550–555, May 2009.

[19] Q. Lin, J. Rosenberg, X. Jiang, K. Vahala, and O. Painter, “Mechani-cal Oscillation and Cooling Actuated by the Optical Gradient Force,”Phys. Rev. Lett., vol. 103, no. 10, p. 103601, Aug. 2009.

[20] I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with aCaF2 whispering gallery mode resonator,” Phys. Rev. Lett., vol. 102,no. 4, p. 043902, Jan 2009.

51

[21] M. Tomes and T. Carmon, “Photonic micro-electromechanical systemsvibrating at X-band (11-GHz) rates,” Phys. Rev. Lett., vol. 102, no. 11,p. 113601, March 2009.

[22] A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, andL. Maleki, “Surface acoustic wave opto-mechanical oscillator and fre-quency comb generator,” Opt. Lett., vol. 36, no. 17, pp. 3338–3340,Sep. 2011.

[23] G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated op-tomechanical excitation of surface acoustic waves in a microdevice,”Nat. Commun., vol. 2, p. 403, July 2011.

[24] G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation ofspontaneous Brillouin cooling,” Nat. Phys., vol. 8, no. 3, pp. 203–207,Mar. 2012.

[25] P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “GiantEnhancement of Stimulated Brillouin Scattering in the SubwavelengthLimit,” Phys. Rev. X, vol. 2, no. 1, p. 011008, Jan. 2012.

[26] S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser,and T. J. Kippenberg, “Optomechanically induced transparency.” Sci-ence, vol. 330, no. 6010, pp. 1520–1523, Dec. 2010.

[27] C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Transient optome-chanically induced transparency in a silica microsphere,” Phys. Rev.A, vol. 87, no. 5, p. 055802, May 2013.

[28] C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical darkmode,” Science, vol. 338, no. 6114, pp. 1609–1613, Dec. 2012.

[29] A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “Ahigh-resolution microchip optomechanical accelerometer,” Nature Pho-ton., vol. 6, no. 11, pp. 768–772, Oct. 2012.

[30] D. N. Hutchison and S. A. Bhave, “Z-axis optomechanicalaccelerometer,” in Proceedings of IEEE Conference on Micro ElectroMechanical Systems. IEEE, New York, Jan. 2012. pp. 615–619.

[31] F. Liu and M. Hossein-Zadeh, “Mass Sensing With OptomechanicalOscillation,” IEEE Sensors Journal, vol. 13, no. 1, pp. 146–147, 2013.

[32] F. Liu and M. Hossein-Zadeh, “On the spectrum of radiation pressuredriven optomechanical oscillator and its application in sensing,” Opt.Commun., vol. 294, pp. 338–343, May 2013.

52

[33] E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chipoptomechanical transducer for ultrasensitive force measurements,”Nat. Nanotechnol., vol. 7, no. 8, pp. 509–14, Aug. 2012.

[34] Y. Liu, H. Miao, V. Aksyuk, and K. Srinivasan, “Integrated cavityoptomechanical sensors for atomic force microscopy,” in Proceedings ofIEEE Conference on Microsystems for Measurement and Instrumenta-tion. IEEE, New York, 2012.

[35] X. Fan and I. M. White, “Optofluidic microsystems for chemical andbiological analysis,” Nature Photonics, vol. 5, no. 10, pp. 591–597,2011.

[36] I. M. White, H. Oveys, and X. Fan, “Liquid-core optical ring-resonatorsensors,” Optics Letters, vol. 31, no. 9, p. 1319, 2006.

[37] S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, andF. Vollmer, “Whispering gallery mode carousel ? a photonicmechanism for enhanced nanoparticle detection in biosensing,” OpticsExpress, vol. 17, no. 8, pp. 6230–6238, Apr. 2009.

[38] Y. Yang, J. Ward, and S. N. Chormaic, “Quasi-droplet microbubblesfor high resolution sensing applications.” Optics express, vol. 22, no. 6,pp. 6881–98, Mar. 2014.

[39] N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. A. N. T. Soares,V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhancedfluorescence emission from quantum dots on a photonic crystalsurface,” Nature Nanotechnology, vol. 2, no. 8, pp. 515–520, July2007.

[40] S. Nie, “Probing Single Molecules and Single Nanoparticles bySurface-Enhanced Raman Scattering,” Science, vol. 275, no. 5303, pp.1102–1106, Feb. 1997.

[41] F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing:label-free detection down to single molecules.” Nature methods, vol. 5,no. 7, pp. 591–6, July 2008.

[42] F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka,and S. Arnold, “Protein detection by optical shift of a resonantmicrocavity,” Applied Physics Letters, vol. 80, no. 21, p. 4057, May2002.

[43] Y. Sun and X. Fan, “Optical ring resonators for biochemical andchemical sensing,” Analytical and bioanalytical chemistry, vol. 399,no. 1, pp. 205–211, 2011.

53

[44] M. S. Luchansky and R. C. Bailey, “High-Q optical sensors forchemical and biological analysis.” Analytical chemistry, vol. 84, no. 2,pp. 793–821, Jan. 2012.

[45] J. Zhu, b. S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, andL. Yang, “On-chip single nanoparticle detection and sizing by modesplitting in an ultrahigh-Q microresonator,” Nature Photonics, vol. 4,no. 1, pp. 46–49, Dec. 2009.

[46] M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Optical microbubbleresonator,” Opt. Lett., vol. 35, no. 7, pp. 898–900, Apr. 2010.

[47] W. Lee, Y. Luo, Q. Zhu, and X. Fan, “Versatile optofluidic ringresonator lasers based on microdroplets,” Optics Express, vol. 19,no. 20, pp. 19 668–19 674, Sep. 2011.

[48] A. Watkins, J. Ward, Y. Wu, and S. Nic Chormaic, “Single-inputspherical microbubble resonator,” Opt. Lett., vol. 36, no. 11, pp.2113–2115, June 2011.

[49] S. X. Qian, J. B. Snow, H. M. Tzeng, and R. K. Chang, “Lasingdroplets: highlighting the liquid-air interface by laser emission.”Science (New York, N.Y.), vol. 231, no. 4737, pp. 486–8, Jan. 1986.

[50] A. Kiraz, A. Sennaroglu, S. Doanay, M. Dundar, A. Kurt,H. Kalaycolu, and A. Demirel, “Lasing from single, stationary, dye-doped glycerol/water microdroplets located on a superhydrophobicsurface,” Optics Communications, vol. 276, no. 1, pp. 145–148, Aug.2007.

[51] M. R. Lee and P. M. Fauchet, “Nanoscale microcavity sensor for singleparticle detection,” Optics Letters, vol. 32, no. 22, p. 3284, 2007.

[52] M. Huang, A. A. Yanik, T.-Y. Chang, and H. Altug, “Sub-wavelengthnanofluidics in photonic crystal sensors.” Optics express, vol. 17,no. 26, pp. 24 224–33, Dec. 2009.

[53] D. Yin, J. P. Barber, A. R. Hawkins, and H. Schmidt, “Highly efficientfluorescence detection in picoliter volume liquid-core waveguides,”Applied Physics Letters, vol. 87, no. 21, p. 211111, Nov. 2005.

[54] F. Eftekhari, C. Escobedo, J. Ferreira, X. Duan, E. M. Girotto,A. G. Brolo, R. Gordon, and D. Sinton, “Nanoholes as nanochannels:flow-through plasmonic sensing.” Analytical chemistry, vol. 81, no. 11,pp. 4308–11, June 2009.

[55] Y. Pang and R. Gordon, “Optical trapping of 12 nm dielectric spheresusing double-nanoholes in a gold film.” Nano letters, vol. 11, no. 9,pp. 3763–7, Sep. 2011.

54

[56] G. L. Liu, J. Kim, Y. Lu, and L. P. Lee, “Optofluidic control usingphotothermal nanoparticles.” Nature materials, vol. 5, no. 1, pp.27–32, Jan. 2006.

[57] F. M. Weinert and D. Braun, “Optically driven fluid flow alongarbitrary microscale patterns using thermoviscous expansion,” Journalof Applied Physics, vol. 104, no. 10, p. 104701, Nov. 2008.

[58] K. H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, andT. Carmon, “Cavity optomechanics on a microfluidic resonator withwater and viscous liquids,” Light: Science & Applications, vol. 2, p.e66, May 2013.

[59] W. Lee, Y. Sun, H. Li, K. Reddy, M. Sumetsky, and X. Fan, “Aquasi-droplet optofluidic ring resonator laser using a micro-bubble,”Appl. Phys. Lett., vol. 99, no. 9, p. 091102, Aug. 2011.

[60] C. Junge, S. Nickel, D. O?Shea, and A. Rauschenbeutel, “Bottlemicroresonator with actively stabilized evanescent coupling,” Opt.Lett., vol. 36, no. 17, pp. 3488–3490, Sep. 2011.

[61] G. Bahl, X. Fan, and T. Carmon, “Acoustic whispering-gallery modesin optomechanical shells,” New J. Phys., vol. 14, no. 11, p. 115026,Nov. 2012.

[62] M. Cai, O. Painter, and K. Vahala, “Observation of Critical Couplingin a Fiber Taper to a Silica-Microsphere Whispering-Gallery ModeSystem,” Phys. Rev. Lett., vol. 85, no. 1, pp. 74–77, July 2000.

[63] T. P. Burg, M. Godin, S. M. Knudsen, W. Shen, G. Carlson, J. S.Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules,single cells and single nanoparticles in fluid.” Nature, vol. 446, no.7139, pp. 1066–9, Apr. 2007.

[64] T. P. Burg and S. R. Manalis, “Suspended microchannel resonatorsfor biomolecular detection,” Appl. Phys. Lett., vol. 83, no. 13, p. 2698,Sep. 2003.

[65] G. Righini, G. Conti, S. Soria, Y. Dumeige, P. Feron, M. Ferrari, andD. Ristic, “Whispering gallery mode micro resonators: Fundamentalsand applications,” 2011.

[66] A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki,“Optical resonators with ten million finesse,” Optics Express, vol. 15,no. 11, p. 6768, 2007.

[67] D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J.Kimble, “High-Q measurements of fused-silica microspheres in thenear infrared,” Optics Letters, vol. 23, no. 4, p. 247, Feb. 1998.

55

[68] V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Qmicrosphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Optics Letters, vol. 24, no. 11, p. 723, June1999.

[69] J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matchedexcitation of whispering-gallery-mode resonances by a fiber taper,”Optics Letters, vol. 22, no. 15, p. 1129, Aug. 1997.

[70] M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators:optimal coupling to high-Q whispering-gallery modes,” Journal of theOptical Society of America B, vol. 16, no. 1, p. 147, Jan. 1999.

[71] H. Rokhsari, T. Kippenberg, T. Carmon, and K. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express, vol. 13,no. 14, pp. 5293–5301, July 2005.

[72] T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, andK. J. Vahala, “Analysis of Radiation-Pressure Induced MechanicalOscillation of an Optical Microcavity,” Phys. Rev. Lett., vol. 95, no. 3,p. 033901, July 2005.

[73] V. Braginsky, S. Strigin, and S. Vyatchanin, “Parametric oscillatoryinstability in FabryPerot interferometer,” Physics Letters A, vol. 287,no. 5-6, pp. 331–338, Sep. 2001.

[74] A. Schliesser and T. J. Kippenberg, “Chapter 5 Cavity Optome-chanics with Whispering-Gallery Mode Optical Micro-Resonators,” inAdvances In Atomic, Molecular, and Optical Physics, 2010, vol. 58,pp. 207–323.

[75] R. Chiao, C. Townes, and B. Stoicheff, “Stimulated BrillouinScattering and Coherent Generation of Intense Hypersonic Waves,”Phys. Rev. Lett., vol. 12, no. 21, pp. 592–595, May 1964.

[76] Y. R. Shen and N. Bloembergen, “Theory of Stimulated Brillouin andRaman Scattering,” Phys. Rev., vol. 137, no. 6A, pp. A1787–A1805,Mar. 1965.

[77] R. Boyd, “Stimulated Brillouin and Stimulated Rayleigh Scattering,”in Nonlinear optics. Academic Press Inc., San Diego, CA (UnitedStates), Jan. 1992.

[78] G. Bahl and T. Carmon, “Brillouin Optomechanics,” 2013, availableat arxiv.org:1309.2828.

56

[79] G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Characterizationof surface acoustic wave optomechanical oscillators,” in Proceedings ofIEEE Conference on Frequency Control and the European Frequencyand Time Forum. IEEE, New York, May 2011.

[80] H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck,Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scatteringin nanoscale silicon waveguides,” Nat. Commun., vol. 4, p. 1944, Jan.2013.

[81] P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker,H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouinscattering from multi-GHz-guided acoustic phonons in nanostructuredphotonic crystal fibres,” Nature Physics, vol. 2, no. 6, pp. 388–392,June 2006.

[82] T. Carmon, M. C. Cross, and K. J. Vahala, “Chaotic Quivering ofMicron-Scaled On-Chip Resonators Excited by Centrifugal OpticalPressure,” Phys. Rev. Lett., vol. 98, no. 16, p. 167203, Apr. 2007.

[83] D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electricalthermo-optic tuning of ultrahigh-Q microtoroid resonators,” AppliedPhysics Letters, vol. 85, no. 22, pp. 5439–5441, Nov. 2004.

[84] I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with aCaF2 whispering gallery mode resonator,” Phys. Rev. Lett., vol. 102,no. 4, p. 043902, Jan. 2009.

[85] J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of ahigh coherence, Brillouin microcavity laser on silicon,” Opt. Express,vol. 20, no. 18, p. 20170, Aug. 2012.

[86] T. Carmon, H. Rokhsari, L. Yang, T. Kippenberg, and K. Vahala,“Temporal Behavior of Radiation-Pressure-Induced Vibrations of anOptical Microcavity Phonon Mode,” Phys. Rev. Lett., vol. 94, no. 22,June 2005.

[87] M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard,P. McEuen, and M. Lipson, “Synchronization of MicromechanicalOscillators Using Light,” Phys. Rev. Lett., vol. 109, no. 23, p. 233906,Dec. 2012.

[88] J. Rosenberg, Q. Lin, and O. Painter, “Static and dynamic wavelengthrouting via the gradient optical force,” Nature Photon., vol. 3, no. 8,pp. 478–483, July 2009.

57

[89] R. Henze, T. Seifert, J. Ward, and O. Benson, “Tuning whisperinggallery modes using internal aerostatic pressure,” Opt. Lett., vol. 36,no. 23, pp. 4536–4538, 2011.

[90] S. Lacey, I. M. White, Y. Sun, S. I. Shopova, J. M. Cupps, P. Zhang,and X. Fan, “Versatile opto-fluidic ring resonator lasers with ultra-lowthreshold,” Opt. Express, vol. 15, no. 23, pp. 15 523–15 530, Nov.2007.

[91] X. Zhao, J. M. Tsai, H. Cai, X. M. Ji, J. Zhou, M. H. Bao,Y. P. Huang, D. L. Kwong, and A. Q. Liu, “A nano-opto-mechanicalpressure sensor via ring resonator,” Opt. Express, vol. 20, no. 8, pp.8535–8542, Apr. 2012.

[92] R. Madugani, Y. Yang, J. M. Ward, J. D. Riordan, S. Coppola,V. Vespini, S. Grilli, A. Finizio, P. Ferraro, and S. Nic Chormaic,“Terahertz tuning of whispering gallery modes in a PDMS stand-alone,stretchable microsphere,” Opt. Lett., vol. 37, no. 22, pp. 4762–4764,Nov. 2012.

[93] M. N. M. Nasir, M. Ding, G. S. Murugan, and M. N. Zervas,“Microtaper fiber excitation effects in bottle microresonators,” Proc.SPIE LASE, vol. 8600, p. 860020, Mar. 2013.

[94] T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behaviorand thermal self-stability of microcavities,” Opt. Express, vol. 12,no. 20, p. 4742, 2004.

[95] S. Timoshenko, D. H. Young, and W. Weaver, “Beams of Elastic Bod-ies,” in Vibration Problems in Engineering. John Wiley & Sons, 1974,pp. 455, 477.

[96] Comsol Group, “COMSOL Multiphysics,” http://www.comsol.com/.

[97] P. Chidamparam and A. W. Leissa, “Vibrations of Planar CurvedBeams, Rings, and Arches,” Appl. Mech. Rev., vol. 46, no. 9, p. 467,1993.

[98] D. N. Nikogosyan, Properties of Optical and Laser-Related Materials:A Handbook. John Wiley & Sons, May 1997.

[99] R. Melamud, B. Kim, S. A. Chandorkar, M. A. Hopcroft, M. Agarwal,C. M. Jha, and T. W. Kenny, “Temperature-compensated high-stability silicon resonators,” Appl. Phys. Lett., vol. 90, no. 24, p.244107, 2007.

58

[100] A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, andL. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A, vol. 76, no. 2, p. 023816,Aug. 2007.

[101] T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone,and K. J. Vahala, “Static Envelope Patterns in Composite ResonancesGenerated by Level Crossing in Optical Toroidal Microcavities,” Phys.Rev. Lett., vol. 100, no. 10, p. 103905, Mar. 2008.

[102] S. Olcum, N. Cermak, S. C. Wasserman, K. S. Christine, H. Atsumi,K. R. Payer, W. Shen, J. Lee, A. M. Belcher, S. N. Bhatia, and S. R.Manalis, “Weighing nanoparticles in solution at the attogram scale,”Proceedings of the National Academy of Sciences, pp. 1 318 602 111–,Jan. 2014.

[103] S. Son, A. Tzur, Y. Weng, P. Jorgensen, J. Kim, M. W. Kirschner,and S. R. Manalis, “Direct observation of mammalian cell growth andsize regulation.” Nature methods, vol. 9, no. 9, pp. 910–2, Sep. 2012.

[104] F. Feijo Delgado, N. Cermak, V. C. Hecht, S. Son, Y. Li, S. M.Knudsen, S. Olcum, J. M. Higgins, J. Chen, W. H. Grover, and S. R.Manalis, “Intracellular water exchange for measuring the dry mass,water mass and changes in chemical composition of living cells.” PloSone, vol. 8, no. 7, p. e67590, Jan. 2013.

[105] C. J. Montrose, “Brillouin Scattering and Relaxation in Liquids,” TheJournal of the Acoustical Society of America, vol. 43, no. 1, p. 117,July 1968.

[106] D. A. Pinnow, “Brillouin Scattering: Viscoelastic Measurements inLiquids,” The Journal of the Acoustical Society of America, vol. 43,no. 1, p. 131, July 1968.

[107] S. A. Lee, S. M. Lindsay, J. W. Powell, T. Weidlich, N. J. Tao, andG. D. Lewen, “A Brillouin scattering study of the hydration of Li- andNa-DNA films.” Biopolymers, vol. 26, no. 10, pp. 1637–65, Oct. 1987.

[108] W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou,“Observation and tuning of hypersonic bandgaps in colloidal crystals.”Nature materials, vol. 5, no. 10, pp. 830–6, Oct. 2006.

[109] G. Scarcelli and S. H. Yun, “Confocal Brillouin microscopy forthree-dimensional mechanical imaging.” Nature photonics, vol. 2,no. 1, pp. 39–43, Dec. 2007.

59

[110] G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation ofspontaneous Brillouin cooling,” Nat. Phys., vol. 8, no. 3, pp. 203–207,Jan. 2012.

[111] M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. Vahala,“Characterization of a radiation-pressure-driven micromechanicaloscillator,” Physical Review A, vol. 74, no. 2, p. 023813, Aug. 2006.

[112] B. A. Martin, S. W. Wenzel, and R. M. White, “Viscosity anddensity sensing with ultrasonic plate waves,” Sensors and ActuatorsA: Physical, vol. 22, no. 1-3, pp. 704–708, June 1989.

[113] K. A. Ronaldson, A. D. Fitt, A. R. H. Goodwin, and W. A.Wakeham, “Transversely Oscillating MEMS Viscometer: The Spider,”International Journal of Thermophysics, vol. 27, no. 6, pp. 1677–1695,Oct. 2006.

[114] P. Smith, R. Young, and C. Chatwin, “A MEMS viscometer forunadulterated human blood,” Measurement, vol. 43, no. 1, pp.144–151, Jan. 2010.

[115] I. Puchades and L. F. Fuller, “A Thermally Actuated Microelec-tromechanical (MEMS) Device For Measuring Viscosity,” Journal ofMicroelectromechanical Systems, vol. 20, no. 3, pp. 601–608, June2011.

[116] S. Tadigadapa and K. Mateti, “Piezoelectric MEMS sensors: state-of-the-art and perspectives,” Measurement Science and Technology,vol. 20, no. 9, p. 092001, Sep. 2009.

[117] E. D. Black, “An introduction to PoundDreverHall laser frequencystabilization,” American Journal of Physics, vol. 69, no. 1, p. 79, Jan.2001.

[118] L. A. DeLorenzo and K. C. Schwab, “Superfluid Optomechanics:Coupling of a Superfluid to a Superconducting Condensate,” Aug.2013, available at arXiv.org:1308.2164.

[119] J. Vig, “Dual-mode oscillators for clocks and sensors,” in Proceedingsof IEEE Ultrasonics Symposium. IEEE, New York, 1999, pp. 859–868.

[120] J. C. Salvia, R. Melamud, S. A. Chandorkar, S. F. Lord, and T. W.Kenny, “Real-Time Temperature Compensation of MEMS OscillatorsUsing an Integrated Micro-Oven and a Phase-Locked Loop,” J.Microelectromech. S., vol. 19, no. 1, pp. 192–201, Feb. 2010.

[121] T. Mason and D. Weitz, “Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids,” PhysicalReview Letters, vol. 74, no. 7, pp. 1250–1253, Feb. 1995.

60

[122] T. A. Waigh, “Microrheology of complex fluids,” Reports on Progressin Physics, vol. 68, no. 3, pp. 685–742, Mar. 2005.

[123] M. Pelton, D. Chakraborty, E. Malachosky, P. Guyot-Sionnest,and J. Sader, “Viscoelastic Flows in Simple Liquids Generated byVibrating Nanostructures,” Physical Review Letters, vol. 111, no. 24,p. 244502, Dec. 2013.

[124] X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overviewof novel integrated optical ring resonator bio/chemical sensors,” pp.64 520M–64 520M, Feb. 2007.

61