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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
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