optomechanical sensors
TRANSCRIPT
Optomechanical Sensors
Prof. Gaurav Bahl
University of Illinois, Urbana-ChampaignMechanical Science and Engineering
Micro-mechanical systems have harnessed many forces
2
Micro-scaleobject
Energy source
Actuation method or “force”
PiezoelectricElectrostatic
ThermalMagnetic
Light!
Photo-thermal
Radiation pressure
Electro-strictivepressure
Gradient force
Vibrational modes in optomechanical resonators
3
G. BahlSurface wave oscillations
in WGRs
M. EichenfieldMechanical excitation
of zipper cavities
T. CarmonGHz frequency breathe modes
J. ZhuFlapping modein microtoroids
G. BahlOptomechanofluidics
Radiation pressure: Comets
4
ion
tail
dust tail
Directionto sun
Comet Hale Bopp
dust tail
ion tail
1619 - Johannes KeplerObserved that comet tails (the bright ones) always opposed the sunand hypothesized ‘radiation pressure’ as the reason.
Quantization of EM energy and momentum (Photons)
5
At small scales, energy and momentum are quantizedIndeed, most other physical properties as well!
The quantum of light = A photonA photon is actually the quantum particle of all forms of electromagnetic radiation!
EnergyMomentum
E = �ω�p = ��kE = hν
E = hc
λ
h = 6.63× 10−34J · s� =
h
2π= 1.054× 10−34J · s
Argument for the existence of radiation pressure
6
Momentumimparted to the mirror
Mirror(stationary)
Momentum conservation must apply
Since the mirror velocity is changedthere must have been a force on the mirror
�p1 = �p3 − �p2
�p1 �p2 �p3
m
Let’s calculate the force
7
Change in momentumper photon
Total momentum change per second (i.e. Radiation pressure force)
Photon flux = Optical power / Energy per photon N = P/�ω
= 2�k
= 2P�k/�ω
= 2P/c
(Photons per second)
Crookes radiometer (1873)
8
ReflectiveAbsorbing
Credit: Wikipedia
Is it moving in the correct direction?
Hint: No. It’s a thermal effect here
Brief history of “radiation pressure” experiments
9
1873 - William CrookesExperimentally attempted to build a radiometer to
observe radiation pressure. Failed. Instead gave the world a desk toy.
1899/1900 - Pyotr Lebedev(Successfully) Experimentally measured the pressure of light
on a solid body.
1901 to 1903 - Ernest Nichols and Gordon Hull(Successfully) Experimentally measured the pressure of light
on a torsion balance radiometer.
Nichols & Hull Radiometer
10
Not as visually striking as the Crooke’s radiometer.
Solar sail
11
Solar sail
Starlight
Force
A proposed means of interstellar travelthat uses reflected starlight for propulsion.
IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun)
First interplanetary solar sail craft launched by Japan (JAXA) in 2010.Confirmed solar sail acceleration on July 9th 2010. On its way to Venus.Passed Venus in Dec 2010.
Images: Wikipedia
There are other optical forces too!
12
Gradient force Used for optical tweezers, optical traps,waveguide actuation. Particles get pulled into regions of highoptical intensity.
Electrostrictive force“Electric field results in constriction.”Occurs in all dielectrics.
Credit: Wikipedia
V
Force = −∇xE
Basic idea
Resonance between mirrors = Fabry-Perot resonator
13
Two waves end uppropagating oppositeto each other.
And there is constructive interference.
Under what conditions?2 x Length = integer
wavelengths
Generates standing wave
Resonances are typically periodic
14
�15 �10 �5 0 5 10 15
Reflection and absorption within material and mirrors determine the resonance width.
�15 �10 �5 0 5 10 15
Mirror reflectivityR = 0.99
Frequency Frequency
Ampl
itude
of fi
eld
Ampl
itude
of fi
eld
Mirror reflectivityR = 0.9
Material between mirrorsabsorbs and scatters some light
Some light is lostin reflection
FSR
Quality factor = Optical storage time
15
More energy stored Less energy stored
For more see Saleh + Teich. Chapter 10.
Q = 2πstored energy
energy loss per cycle
Q =νoδν
Linewidth
Optical frequencyQ ≈ νo
νFF
Low-loss mirrors Lossy mirrors
Also, more photoncollisions with walls!
Learn more
Finesse = number of round trips
16
Low-loss mirrors Lossy mirrors
δν ≈ νFF Finesse
FSR (free spectral range)
Linewidth
For more see Saleh + Teich. Chapter 10.
Valid when F � 1
Important factsFinesse is inversely proportional to cavity length → So use smaller resonators!Radiation pressure is magnified by the finesse factor.
Experimental/phenomenological
Learn more
Nomenclature: Detuning
17
Wavelength
“Detuning” is defined as the distance from the peak of the resonance. Measured in wavelength or frequency units (your choice).
A signal present here is red detuned
A signal present here is blue detuned
A signal present here is on resonance!
Res
onan
ce fr
eque
ncy
(or
wav
elen
gth)
Δλ
Frequency
Energy in the cavity depends on detuning
18
Opticalresonance
Wavelength
Couplingefficiency
Maximumintensity inside
resonator
Poorcoupling
Poorcoupling
Analyzing a sinusoidally shifting resonance
19
Schliesser, A., & Kippenberg, T. J. (2010). Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators. Advances In Atomic, Molecular, And Optical Physics, Vol 58, 58, 207–323. doi:10.1016/S1049-250X(10)05810-6
ωl
ωl is the input laser frequency
Learn more
Radiation pressure can induce mechanical oscillation
20
Pumplaser
Resonance
Wavelength
Cavity expands
Pumplaser
Resonance
Wavelength
Cavity collapses
Light in
Resonanceshifts
Less light in
x = 0
xRadiationpressure
Parametric oscillatory instability
21
This instability was originally discussed in the context of LIGO in 2001...
LIGO = Laser Interferometer Gravitational-Wave Observatory
Learn more
Optomechanical crystals exhibit this instability
22
Engineered optical resonators that exhibit simultaneous optical and acoustic modes
Optical modes
Acoustic modes
Eichenfield, M., Chan, J., Camacho, R., Vahala, K. & Painter, O. Optomechanical crystals. Nature 462, 78–82 (2009).
23
Optical field
Acoustic field
Coupling of energy in from optical field
Coupling of energy in from acoustic field
Laser source
+ Langevin noise force(not shown)
Detuning(Optical resonance)
Opticallosses
Detuning(Acoustic resonance)
Acousticlosses
Mathematically describing the opto-mechanical coupling
G is the opto-mechanical coupling coefficientrelated to ...
Cavity deformation causes optical resonance to shift ( dω/dx )Radiation pressure force is modified when optical resonance shifts relative to laserMore photons create more pressure and more deformation
Electromagnetic wave(speed of light)
24
Acoustic wave(speed of sound)
Monochromaticphotons from a laser
Q > 100,000,000Finesse = Distance traveled / Circumference
Whispering gallery resonators (WGRs)
25
What is the simplest WGR we can build in the lab?
Reflow
Reflowsomemore
Long optical fiber taper
Arc discharge methodMicrospheres can be fabricated by reflowing a
broken taper in a fiber splicing tool
25
Q ~ 4×108
~150 um
On chip ultra-high-Q toroid microcavities
26
Letters to NatureNature 421, 925-928 (27 February 2003) | doi:10.1038/nature01371
Ultra-high-Q toroid microcavity on a chipD. K. Armani, T. J. Kippenberg, S. M. Spillane & K. J. Vahala
Fabrication cross-sectional view
27
Oxide disc on silicon
XeF2 etch
CO2 laserreflow glass
moreCO2 laser
reflow
Toroid
Disc on pedestal
4 um150 um
50 um
30 um
Ellipsoid
Resonance and FSR for a WGR
28
λo/n
λo Free space wavelength
Light is confined through total internal reflection
(think of infinite reflections)Dielectric
λ2 R = M x
Resonance criterion
Zipper structures
29
Eichenfield, M., Camacho, R., Chan, J., Vahala, K. J. & Painter, O. A picogram- and nanometre-scale photonic-crystal optomechanical cavity. Nature 459, 550–555 (2009).
Acoustic mode
Optical modes
Distance between beamsis an important parameter
Optomechanical coupling coefficient
30
We can define the degree to which the optical mode shifts upon application of a
mechanical displacement.
gOM =dω
dx
Typically 1 GHz/nm - 1 THz/nm
Huge! Compared to 1 MHz - 10 MHz linewidth.
Evanescent field region outside a WGR
31
Complex k(evanescent wave)
Real k (surface wave)
Quickly decayingevanescent fieldFi
eld
stre
ngth
Radialdirection
No field here
Light “tunnels” through the “barrier”!
Large gap
Evanescentfield
(no propagation)
Coupling to a WGR using evanescent fields
32
“Waveguide”Resonator
But remember, this is a two-way street
How the resonance condition acts on coupled light
33
“Waveguide”Resonator “Waveguide”Resonator
On resonance Off resonanceLots of light is inside the resonator.
Light escaping the resonator interfereswith light inside the waveguide.
Very little light is inside resonator.Light in the waveguide
is not affected significantly.
Learn more
Photograph of tapered optical fiber waveguide
34
FiberHydrogentorch
Taper
The complete picture
35
Resonator
Evanescent couplingOptical “input”
Energy stored= F x (Input x Coupling)
Finesse (F)= # of recirculations
x
Field gets really high
3rd harmonic generation
36
Spherical microresonator3rd harmonic generation
Input IR Output green laser
Q ~ 4×108
Flicker is due to laser wavelengthbeing intentionally swept
~150 um
Infra-redlaser in
Greenlaser out
This nonlinear process occurs because the material (silica) has a nonlinear characteristic (the (3) nonlinearity).
~ 1500 nm
3W power
~ 500 nm
uW - mWpower
Finesse ~ 105-106
Origin of centrifugal radiation pressure
37
Change in momentumper photon
Total momentum change per second (i.e. force)
Centrifu
gal fo
rce
Circulating power / energy-per-photon= energy-through-cross-section-per-second / energy-per-photon= #-photons-through-cross-section-per-second
N = P/�ω
= 2�k
= 2P�k/�ω
= 2P/c
Now you can perform suitable integrals to determine force per unit length etc...
Radiation pressure can induce mechanical oscillation
38
Pumplaser
Resonance
Wavelength
Cavity expands
Pumplaser
Resonance
Wavelength
Top view of resonator
Cavity collapses
Light in
Resonanceshifts
Less light in
PRL 94, 223902 (2005) Optics Express 13, 5293 (2005) PRL 95, 033901 (2005)
Radiationpressure
Reducedradiationpressure
Waveguide
Toroid resonator
Mechanical frequency defined by geometry + materials
Radiation-pressure driven microtoroids
39
t
Poutput
t
Pinput
Input light (continuous in
time)
Photodetector
Oscilloscope
?
Effect came as an unexpected surprise
Cavity was not designed to vibrate
Morepower
Oscillation!
Mass sensing with optomechanics
40
Liu, F. & Hossein-Zadeh, M. Mass Sensing With Optomechanical Oscillation. Sensors Journal, IEEE 13, 146–147 (2013).
Optical devices provide extremely high measurement sensitivity, especially in“RF free” zones or harsh environs.
Ultimate limits still defined by Brownian thermal noise.
Ekinci, K. L. Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems. J. Appl. Phys. 95, 2682 (2004).
Optomechanical Atomic Force Microscope (AFM)
41
Srinivasan, K., Miao, H., Rakher, M. T., Davanço, M. & Aksyuk, V.
Optomechanical Transduction of an Integrated Silicon Cantilever Probe Using a Microdisk Resonator.
Nano Lett 11, 791–797 (2011).
Ultimately hit the fundamentalthermal noise limits
want low stiffness, high freq, high Q.
Coupling a vibrating beam to a WGR -- light excites the beam, and is also used for readout
Optomechanical accelerometers
42
Krause, A. G., Winger, M., Blasius, T. D., Lin, Q. & Painter, O. A high-resolution microchip optomechanical accelerometer. Nature Photonics 6, 768–772 (2012).
Thermal noise (proof mass)limits accelerometers Using a zipper resonator and proof mass
to measure acceleration.
43
Measuring displacement of a nitride beam
44
Gavartin, E., Verlot, P. & Kippenberg, T. J. A hybrid on-chip optomechanical transducer for ultrasensitive force measurements.
Nature Nanotech 7, 509–514 (2012).
74 aN Hz-1/2 at room temperature with a readout stability better than 1% at the minute scale
By applying dissipative feedback (i.e. optomechanical cooling) based on radiation pressure, force spectral density of just 15 aN Hz-1/2 within 35 s of averaging time
45
Can we build surface-acoustic-wave devices?(Then we can use the past 60 years of SAW techniques)
Acoustic waves through optical electrostriction
46
Interference of two EM waves can generate pressure that travels at the speed of sound
V
Electromagnetic waves also generate electrostrictive pressure
Electric fields exert pressure on dielectrics = Electrostriction
Speed of soundLight can generate sound
Brillouin scattering: Scattering of light from acoustic wavesThe strongest nonlinearity known to optics
47
Stationarymirror
Movingmirror
Reflected light isred-shifted
Reflection from a stationary mirror Reflection from a moving mirror
Scattered light isred-shifted
Brillouin light scattering = “Reflection” from a traveling acoustic wave
Sound scatters light
Stimulated Brillouin scattering (SBS) is a feedback process
48
Light can generate soundht
Scattered light
Brillouin scattering ‘generates’ light
Speed of sound
Speed of sound
Sound Light
feedback loop
R. Chiao, C. Townes, Phys. Rev. Lett., Vol. 12, No. 12, 1964.
ωP, kP ωS, kS
ωS, kS
ωP, kP
ΩA, kA
ΩA, kA
Occurs at high input power!
“Phase Matching” condition Energy conservation :: ħωP = ħωS + ħΩA
Momentum conservation :: kP = kS + kA
49
Lasers weretoo new
Good old days!Before Hz was widely adopted.
cps = cycles per second
Experiments in silica
50
ElectricalspectrumanalyzerDetector
Continuous lightfrom 1550 nm
laser (a few mW)
M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009)
Fixed pump laser frequency 11 GHz
SBS mode
Frequency, MHz
Elec
tric
al s
igna
l pow
er, d
Bm
Tapered opticalfiber waveguide
1 µm thick
Silica glasssphere
vsound
11 GHzacoustic wave
Generating surface acoustic waves
51
Scientific valueLarger mode (~10 ng)Higher quality factors
(longer phonon lifetime)Greater mechanical amplitude
Surface acoustic wave (SAW) sensors!
Scientific valueSmall mode (~0.5 pg)Low threshold Brillouin lasers
vsound vsound
High frequency10-12 GHz regime
Low frequency10 MHz - 2 GHz regime
G. Bahl et al, Nature Communications 2:403, doi:10.1038/ncomms1412 (2011)
Forward-scattering SBS for lower frequency acoustic waves
52
F-SBSB-SBS
G. Bahl et al, Nature Communications 2:403, doi:10.1038/ncomms1412 (2011)
Electrostriction Acousticwave
Brillouin scattering
53
Forward Brillouin scattering enables SAW generation
Pumpopticalfield
Scatteredopticalfield
Pressure vsound
vsound
|E1 + E2|2
G. Bahl et al, Nature Communications 2:403, doi:10.1038/ncomms1412 (2011)
c/n1
c/n2
54
Experimental observation
SAW-WGMon silica sphere
1550 nminfra-redpump laser
95 MHz spacing
Pump
Stokes
Optical spectrum (95 MHz mode)
Sign
al,A
U
Time, μsTime, us
Oscilloscope
Electricalspectrumanalyzer
Detector
Experimental data
5495.1 95.15
0
2
4
6
8
10
12
14
16
Frequency, MHz
Mea
sure
d el
ectr
ical
sig
nal,
pW
Experimental data
95 MHz
Sign
al, a
.u.
Femtometer-level Brownian vibration can be measured
55
Mechanical signal at extremely low input power
Increasingpumppower
Mechanical signal
=95 MHzRayleigh
SAW-WGM
Maximum amplitudecan reach nanometer-levelwith greater input power
G. Bahl et al, Nature Physics, doi:10.1038/nphys2206, Feb 2012
nsilica = 1.45
Frequency, MHz
Pow
er,dB
mChanging laser wavelength changes oscillation frequency
56G. Bahl et al, Nature Communications, 2:403, doi:10.1038/ncomms1412 (2011)
We generate one oscillation frequency at a timeOr we can scan the laser wavelength to find many frequencies
There are high transverse order acoustic modes too!
57
Merging optomechanics and microfluidics
58
“Dry”optomechanics
Microfluidics+
MEMS enabledbio-sensing
Optomechanicalbio/chemical sensors?
Burg et al, Nature 446, 2007Vollmer et al, Nature Methods 5, 2008
Opticalnanoparticle
sensing
Zhu et al, Nature Photonics 4, 2010
Lu et al, PNAS 108, 2011
Carmon et al, PRL 94 (22), 2005
Povinelli et al, Opt. Lett. 30, 2005Rokhsari et al, Opt. Express 13, 2005
...
...
Opto-Mechano-Fluidic Sensors
59
Taperedfiber
Micro-capillary
70 um
Opticaland
acousticWGR
Qoptical = 160 million Qmechanical = 4700(with liquid core)
Bottle shape enables simultaneous confinement of optical and acoustic WGMs
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
OMFR system
60
Taper
Fiber
Fiber
Hydrogentorch
OMFR
Cavity optomechanics on microfluidic resonators
61
Fluid analyte reservoir
Silicamicrofluidicresonator
CW pumpat 1.5 microns
(NIR diode laser)
Interferometricdetection
RF signal measures
mechanical mode
Outlet
(beat note)
Silica waveguideScattered light
Qmechanical = 4700with liquid coreat 100 MHz
Radiation-pressure drivenbreathing mode
Qmechanical = 2170 with liquid core
at 19 MHz
K.H. Kim, G. Bahl, et alarXiv:1205.5477
G. Bahl et alNat Comms4:19942013
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
62
Rayleigh-Lamb mode Transverse mode Longitudinal mode
Capillary whispering-gallery acoustic modesBahl, G., Fan, X. & Carmon, T. Acoustic whispering-gallery modes in optomechanical shells. New Journal of Physics 14, 115026 (2012).
Rayleigh wave Lamb wave
11.3 GHzExtremely high order
SAW-WGM
99 MHz M = 8SAW-WGM 169 MHz M = 14
SAW-WGM
277 MHz M = 24SAW-WGM 861 MHz
M = 79SAW-WGM
7.4 MHz
H1
M = 2Wineglass
mode
H2
63
Acoustic WGMs
With waterExperiments
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
Testing with sucrose solutions
64
Optomechanical interaction can be sustained even when --• Motional mass is high
(i.e. high density liquid)• Fluid-related acoustic energy losses are high
(i.e. high viscosity)
0 10 20 30 401
1.05
1.1
1.15
1.2
Sucrose concentration (% w/w)
Den
sity
(g/
ml)
Known trendExperiment
0 10 20 30 401500
1550
1600
1650
1700
Sucrose concentration (% w/w)
Aco
ustic
vel
ocity
in s
olut
ion
(m/s
)
Known trend
Non-monotonic trend may be explained by multi-parameter variation. (1) Density (2) Viscosity (3) Speed of sound.
Increasing viscosity
G. Bahl et al, Nature Communications, 4:1994, doi:10.1038/ncomms2994 (2013)
Sensing with radiation pressure modes
65
Radiation-pressure drivenbreathing mode
K.H. Kim, G. Bahl, et alarXiv:1205.5477to appear in Light: Science & Applications, Nov 2013
Optomechanical viscometer
66
Distilled water
Frequency offset, kHz
Pow
er, a
.u.
Sucrose solution 60% w/w
CF =12.4 MHzQ = 712
Frequency offset, kHzPo
wer
, a.u
.
CF = 11.6 MHzQ = 1977
Increased damping
Extract viscosity by measuring thermal mechanical fluctuations
(Brownian noise)
OMFR
Activeregion
Air
Water
Rapid screening of cells
67
Fibroblast
Taper(background)
OMFR
1 2 3
Transit of a single monkey kidney fibroblast
OMFR
Activeregion
Air
Water
stay tuned...
Optomechanical pressure sensor
68
K. Han, J. Kim, G. Bahl“Aerostatically tunable optomechanical oscillators”In review, 2013
Dual mode (RP + SBS) pressure sensing
69
Potential for f1-f2self-referencing!
Putting some challenges out thereFiber is virtually free. $0.08/meter.
70
Opticalinput
Opticalread-out
Optomechanical temperature sensor / hydrogen sensor / pressure sensor.
Fiber
Fiber-tip optomechanical sensors
Silica, LiNbO3, CaF2 are high temperature materials
Electromagneticinterference
High temperature
Photons behave linearly in most media
Sensors in harsh environments
Mechanicalinteraction
Surfacewave
Lamb wavesLove waves
Distributed fiber-SAW sensors
Surfacemechanicalinteraction Output:
Optical signals
Input:Interfering optical modes
71
Sources of noise
Equipartition theorem - Thermal mechanical fluctuations
72
At thermal equilibrium, the average kinetic energy contained in any degree of freedom is 1/2 kBT at any non-zero temperature T.
Therefore, at any non-zero temperature, a mass-spring-damper system has some “thermal occupation”, i.e. its average kinetic energy is not zero.
x(t)
x(t)
tx = 0
kB = 1.38 x 10-23 J/K
1
2kBT =
1
2k〈x2
zpf 〉
Lowering temperature lowers the thermal mechanical noise. 〈x2zpf 〉
“Zero point fluctuations”
Estimating magnitude of thermal motion
73
Example --- G. Bahl et al, Nature Physics, Vol. 8, No. 3, pp. 203-207 (2012)
G. Bahl et al, Nature Physics, doi:10.1038/nphys2206, Feb 2012
Photon shot noise
74
Incident beam
Reflection
We can use light to measure the position of an object very accurately.
DetectorDetector noise
+Signal of interest
To do a good job in measurement, we want to overcome the noise of our detector, so we increase the power at the source.
Source
Measurementgets better withincreasing input
power
Photons are discrete particles
Detector
Source
But if we pretend that detector noise is zero, we still have photon shot noise.
Detector noise+
Photon shot noise+
Signal of interest
We can also average out this randomness in arrival times by turning up the power.
Measurementgets better withincreasing input
power
Radiation pressure shot noise
75
Each photon reflection creates a tinyradiation pressure related momentum kick.
Simultaneously, we must also remember that light exerts radiation pressure.Since photon arrival times are erratic, radiation pressure shot noise is generated.
Object positionand momentum get
perturbed
The more photons we use to probe, the more significant these momentum kicks are!
Detector
SourcePhoton shot noise+
Radiation pressureshot noise
+Signal of interest
Measurementgets worse withincreasing input
power
Standard quantum limit
76
Power of source
Noise inmeasuringposition Measurement noise
RP shot n
oise
Standard quantumlimit
There is an optimum point where the total noise drops to its minimum value.This minimum value is called the standard quantum limit.
There exist techniques to beat this!
Anetsberger, G. et al. Measuring nanomechanical motion with an imprecision below the standard quantum limit. Phys. Rev. A 82, 061804 (2010).
Teufel, J. D., Donner, T., Castellanos-Beltran, M. A., Harlow, J. W. & Lehnert, K. W. Nanomechanical motion measured with animprecision below that at the standardquantum limit. Nature Nanotech 4, 820–823 (2009).
Learn more
i.e. 6x104 Hz optical frequency fluctuation for a 197 THz (telecom infrared) optical mode.
Thermorefractive noise in optical devices
77
Gorodetsky and Grudinin
The variance of temperature fluctuations u in volume V is
where T is the temperature of the heat bath, k is the Boltzmann constant, ρ is density, and C is specific heat capacity.
Thermorefractive noise in silica microsphere resonatorV = 10-9 cm3
ρ = 2.2 g/cm3
Radius = 50 um
dn/dT = 1.45 x 10-5 K-1 (coeff. of thermal refraction)
Learn more
Thermal effects in optical resonators
78
What happens to an optical resonator when the temperature is changed?
dn
dT
α
Thermal expansion coeff.
Refractive index change
fr =c/n
2πR/MResonancefrequency
Wavelength
Speed of light
Consider a WGR
Thermal effects in mechanical resonators
79
What happens to a mechanical resonator when the temperature is changed?
dE
dT
dρ
dT
α
Thermal expansion coeff.
Stiffness change (TCE)
vs ∝√
E
ρ
Geometric effect
Strained anchors/tethers
vs ∝ f
Heating and cooling processes are symmetric
80
Heating
Pumpphoton
Stokesphoton
Phonon
Cooling
Thermalphonon
Pumpphoton
anti-Stokesphoton
When the mirror moves away, momentum conservation causes the reflected light to be red-shifted
Green
Red
Mirror velocity
Energy conservation: Vibration energy increases
When the mirror moves inwards, momentum conservation causes the reflected light to be blue-shifted
Green
Blue
Mirror velocity
Energy conservation: Vibration energy decreases
x(t)
standingwave
incomingwave
Asymmetry in vibration-scattered light
81
detuning
Frequency
Anti-Stokes
Stokes
Frequency
Anti-StokesStokes
a0(t)a0(t)
a1(t)
a1(t)a1(t)
a1(t)
ΩmΩmΩmΩm
higher order terms
vibrationamplitude
Stokesanti-Stokes
The optical resonance can tilt this energy balance (optical “density of states”)
2004: Photothermal cooling of a cantilever
82
Tune optical resonances by
modifying cavity length z.
The device can be made to self-oscillate (S)or cool (C)
depending on chosen laser detuning.
+λ/25 detuned(damping)
-λ/25 detuned(anti-damping)
This experiment used the photothermal “force”
83
“The photon-induced force, which is assumed proportional to the light intensity stored in the cavity, includes of course the radiation pressure but more generally all the n independent light-induced contributions, such as the photothermal (bolometric), radiometric and photo-elastic pressure to name just a few. For instance, a bolometric force FB results from the differential thermal expansion between the silicon lever and the thin gold film.”
Au
Si
+ ΔT
Bending occurs due to differentcoefficient of thermal expansion.
Changes cavity length.
... the essence of cooling is based on the fact that the optically induced forces acting on the lever are delayed with respect to a sudden change in the lever position.
local heatingdue to
photon absorption
ΔL
Measuring effective temperature
84
Use equipartition theorem to determine temperature
Main messageThe area under the Lorentzian
curves is most important measurementfor determining temperature
Radiation pressure cooling demonstrated in 2006
85
We can also cool using Brillouin scattering
86
95 MHz spacing
Pumpresonance
Anti-Stokesresonance
OP OaS
Find candidate optical modes
Acousticalmode FEM
95 MHzSAW-WGM
G. Bahl et al, Nature Physics, Vol. 8, No. 3, p. 203, doi:10.1038/nphys2206 (2012)
Momentum
Freq
uenc
y
Increasing pump power
8 kHz
120 kHz
Increasingpumppower
Mechanical signal (linear scale) Mechanical signal (log scale)
19 K
There is potential for cooled mechanical sensors
87
Cooling on
Event of interest(e.g. rotation signal in gyro) Time
Background“noise” signal
Background“noise” signal
Signal of interest
Noise + Brownian modes
Sensor bandwidth
Frequency
PSD
Time
Some stochastic background “noise” is present because of Brownian occupation
Brownian vibrations in sensors need to be suppressed k
b
m Sensorreadout
Brownian thermalvibration
Thank you!
97
Stimulated optomechanical excitation of surface acoustic waves in a microdeviceG. Bahl, J. Zehnpfennig, M. Tomes, T. CarmonNature Communications, 2:403 (2011)
Observation of spontaneous Brillouin coolingG. Bahl, M. Tomes, F. Marquardt, T. CarmonNature Physics, Vol.8, doi:10.1038/nphys2206 (2012)
Surface-waveoptomechanics
Brillouincooling
Acoustic whispering-gallery modes in optomechanical shellsG. Bahl, X. Fan, T. CarmonNew. J. Phys. 14, 115026 (2012).
Acoustic WGMson shells
Opticaland
acousticWGR
Brillouin cavity optomechanics with microfluidic devicesG. Bahl, K.H. Kim, W. Lee, J. Liu, X. Fan, T. CarmonNature Communications, 4:1994 (2013)
Microfluidicoptomechanics
Cavity optomechanics on a microfluidic resonatorK.H. Kim, G. Bahl, W. Lee, J. Liu, M. Tomes, X. Fan, T. CarmonLight: Science & Applications, (to appear) Preview: arXiv:1205.5477
RP-driven microfluidicoptomechanics
Aerostatically tunable optomechanical oscillatorsK. Han, J. Kim, G. Bahlin review
Optomechanicalpressuresensing